Mathematics & Number

The Slide Rule: A Calculator Made of Sliding Sticks

⏱ 45 minutes 🎓 Primary & Secondary 📚 mathematics, history, science, ethics, language

Core question How did a simple wooden stick with numbers printed on it become the calculating tool of engineers and scientists for 350 years — and what is the deep mathematical idea that made it work?

A Faber-Castell 67/54 Darmstadt slide rule from 1960s Germany. For 350 years, instruments like this were the standard calculating tool of engineers and scientists worldwide. Photo: Slashme / Wikimedia Commons / CC0

Introduction

A slide rule is a calculating tool made of sliding pieces of wood, plastic, or bamboo. It has no electricity, no batteries, no buttons, no screen. Instead, it has lines and numbers printed on its surface, arranged in a very particular way. By sliding the parts past each other and reading where the numbers line up, a skilled user can multiply, divide, calculate squares and square roots, find logarithms, and work out trigonometric functions. The slide rule was invented in England in the 1620s by William Oughtred, an Anglican clergyman and mathematician, just a few years after John Napier of Scotland discovered logarithms (1614). The basic idea is beautiful and a little startling. When you add two logarithms, you multiply the original numbers. So if you make a ruler whose spacing follows a logarithmic scale, sliding two of them past each other adds the logarithms — and therefore multiplies the numbers. The slide rule turns multiplication into sliding. For 350 years, the slide rule was the standard calculating tool of engineers and scientists. The Brooklyn Bridge was designed with slide rules. The Empire State Building was designed with slide rules. The B-29 bomber, the Spitfire, and the Boeing 747 were all designed with slide rules. The Apollo astronauts who walked on the Moon in 1969 took slide rules with them — Buzz Aldrin had a Pickett N600-ES on Apollo 11. Then, in 1972, the Hewlett-Packard HP-35 scientific calculator went on sale. It cost about 400 US dollars but it did everything a slide rule could do, and faster, and to more decimal places. Within five years, the slide rule was almost entirely gone from engineering offices and university classrooms. One generation of engineers used slide rules every day. The next generation could barely operate one. This lesson asks how a simple wooden stick changed engineering and science for 350 years, what mathematical idea made it work, and what its sudden disappearance teaches us about how technologies live and die.

The object

Origin: Invented in England in the 1620s by William Oughtred, an Anglican clergyman and mathematician. Built on the discovery of logarithms by John Napier of Scotland (1614) and the logarithmic scale by Edmund Gunter of England (1620). The earliest slide rules combined two of Gunter's logarithmic scales so they could slide against each other.
Period: In use for about 350 years, from the 1620s until the early 1970s. The modern form (the Mannheim layout) was standardised in the 1850s. The slide rule was the dominant calculating tool of engineers and scientists worldwide from the 1850s until 1972, when the Hewlett-Packard HP-35 scientific calculator made it obsolete almost overnight.
Made of: Early slide rules were made of boxwood. Later versions were made of mahogany or other hardwoods with celluloid scales glued on top. By the mid-20th century, plastic (often a stiff acrylic) was the standard material. Aluminium was used by the American Pickett company. Bamboo was used by the Japanese Hemmi company. Scales were typically engraved into the surface and then filled with ink. The cursor (the sliding glass or plastic window with the hairline) was made of glass with a metal frame, later all plastic.
Size: A standard pocket slide rule is about 12 to 15 centimetres long. A standard desk slide rule is about 25 to 30 centimetres long. Large demonstration slide rules for teaching could be up to 2 metres long. Specialist versions included tiny pocket-watch sized circular slide rules and very long cylindrical slide rules (50 centimetres or more) for higher precision.
Number of objects: Hundreds of millions were produced over the 350 years of the slide rule era. Probably most of them have been thrown away. The MIT Museum in Cambridge, Massachusetts, has hundreds in its Keuffel and Esser collection. The Oughtred Society (founded 1991) is a worldwide community of slide rule collectors. Working slide rules are still sold by some specialist makers — the Concise Company of Tokyo continues to produce circular slide rules. The Breitling Navitimer pilot's wristwatch (since 1952) has an integrated circular slide rule.
Where it is now: Mostly in museums and private collections. The MIT Museum (Cambridge, Massachusetts), the Science Museum (London), the Deutsches Museum (Munich), and the Smithsonian's National Air and Space Museum all hold significant collections. Buzz Aldrin's slide rule from Apollo 11 was sold at auction in 2007. The slide rule taken on Apollo 13 is at the National Air and Space Museum.

Before you teach this — reflect

Questions for you

The slide rule is a wonderful entry point into logarithms — but logarithms are also a challenging mathematical concept. How will you teach the slide rule's principle without losing students who haven't met logarithms yet?
The slide rule died almost overnight when electronic calculators arrived. This is a real story of technological change with winners and losers (the makers of K&E, Pickett, Faber-Castell, and Hemmi all collapsed). How will you handle the human cost honestly?
Many of the engineers who designed the Moon missions used slide rules. Today this seems extraordinary. How will you convey both the wonder and the ordinariness of this — for those engineers, it was just their tool?

Common student difficulties — tick any you have noticed

My students may not know that the slide rule was invented in England in the 1620s by William Oughtred, an Anglican clergyman and mathematician.
My students may not know that the slide rule works because of logarithms — adding two logarithmic distances multiplies the underlying numbers.
My students may not know that the Apollo astronauts took slide rules to the Moon — Buzz Aldrin's Pickett N600-ES went on Apollo 11.
My students may not know that the slide rule was killed almost overnight in 1972 when the Hewlett-Packard HP-35 scientific calculator arrived.
My students may not know that there is a Japanese tradition of slide-rule making — Hemmi made beautiful bamboo slide rules, prized today by collectors.
My students may not know that the Breitling Navitimer pilot's wristwatch (introduced in 1952) has a working circular slide rule built into its bezel, and still does today.

Discovery sequence

Imagine you are an engineer in 1960. You are designing a bridge. To check that one of the steel beams will not bend too much under the weight it has to carry, you need to multiply 347 by 0.0826, then divide by 12.5, then take the square root. You do not have a calculator. Calculators do not exist yet. You do not have a computer (well, there are computers, but they fill rooms and cost millions and you are not going to walk down the corridor to wait for time on one for a quick calculation). You have a pencil and paper. You could do the calculation by hand — long multiplication, long division, then look up the square root in a table. That would take five minutes, with several chances to make a mistake. Or you reach into your shirt pocket and pull out a slide rule. You slide a few pieces past each other. You move the cursor. You read where the lines align. The answer appears. It takes about ten seconds. You write it down and move on. This was the daily life of every engineer, scientist, navigator, surveyor, and many other professionals for 350 years. The slide rule was their pocket calculator. Why did people invent the slide rule, and why did it stay in use for so long?

Points to consider (for the teacher)

Because doing arithmetic by hand is slow and error-prone, and there was no faster way for most of human history. Hand multiplication of two three-digit numbers takes about thirty seconds for an experienced person, with a real chance of mistakes. The slide rule does it in five seconds, with the mistakes you make being limited in size (you might read the answer slightly wrong by a percent or two, but you will not be off by a factor of ten). For most engineering and scientific work, two or three digits of accuracy is enough. The slide rule was fast enough, accurate enough, cheap enough, portable enough, and reliable enough. It also did not need electricity or batteries. It worked the same in a laboratory, on a building site, in an aircraft cockpit, in a ship's navigation room, or in a tent in the desert. Strong answers will see that a tool survives because it fits its work well. The slide rule fitted the work of engineering for 350 years. When something better came along (the electronic calculator), the slide rule went away — quickly. End by noting that almost everything humans built between the 1850s and the 1970s — every bridge, every skyscraper, every aircraft, every ship, every car factory, every dam, every road — was designed with the help of slide rules. The objects last. The tool that built them is now a museum piece.

The slide rule works because of an idea called logarithms. Logarithms were discovered by John Napier, a Scottish mathematician, in 1614. The idea is simple but startling. The logarithm of a number tells you how many times you have to multiply ten by itself to get that number. The logarithm of 100 is 2, because 10 x 10 = 100. The logarithm of 1,000 is 3, because 10 x 10 x 10 = 1,000. The logarithm of 1 is 0. The logarithm of 10 is 1. The logarithms of in-between numbers are in-between values — the logarithm of 2 is about 0.301, the logarithm of 5 is about 0.699. Here is the beautiful part. If you want to multiply two numbers, you can add their logarithms instead. Then you find the number whose logarithm is the sum. For example, to multiply 2 by 5, you add their logarithms (0.301 + 0.699 = 1.000), and find the number whose logarithm is 1 (which is 10). So 2 x 5 = 10. The same trick works for any two numbers. Adding logarithms multiplies the underlying numbers. In 1620, the English mathematician Edmund Gunter invented a 'Gunter's scale' — a ruler with the numbers spaced according to their logarithms. The 1 is at one end. The 10 is at the other. In between, 2 is about 30 per cent of the way along, 5 is about 70 per cent of the way along. The spacing follows the logarithms. Two years later, in 1622, William Oughtred took two of Gunter's scales and slid them past each other. By doing this, he could add the logarithmic distances mechanically — which meant he was multiplying the underlying numbers. This was the first slide rule. Why did logarithms make a calculator possible?

Points to consider (for the teacher)

Because they convert hard multiplication into easy addition. Adding numbers is slow but straightforward. Multiplying numbers is much harder — it takes proper paper-and-pencil long multiplication. But if you can convert each number into its logarithm, add the logarithms, and convert back — you have done the multiplication. The slide rule does the converting and adding automatically, by the spacing of the numbers on the ruler. The user does not need to know about logarithms at all. They just slide the pieces and read the answer. Strong answers will see that this is a deep mathematical idea wearing a simple physical form. Napier's logarithms (1614) were a major discovery in their own right. Within ten years, that discovery had been turned into a calculating tool used by every navigator, astronomer, and engineer for three centuries. End by noting that this is how mathematics often reaches the wider world — not as theorems on a page, but as objects that work. The slide rule was logarithm-engineering for the working professional.

For the first 230 years of the slide rule, designs varied a lot. There were many different layouts, many different scales, many different makers. The standard slide rule we recognise today emerged in the 1850s, when a French artillery officer named Amedee Mannheim simplified the design. Mannheim's slide rule had four basic scales — labelled A, B, C, and D — arranged with the slide between the A and D scales. The C and D scales were single-decade logarithmic scales (running from 1 to 10), used for the main multiplication and division work. The A and B scales were double-decade (running from 1 to 100), used for squares and square roots. Mannheim's design also added a cursor — a sliding window with a thin hairline that let you align numbers on different scales accurately. This became the basic 'Mannheim rule', and it spread fast. Later slide rules added more scales — an L scale for logarithms, S and T scales for trigonometry (sines and tangents), LL scales for very large numbers, and many more specialised ones. A typical engineering slide rule of the 1960s had ten or twelve scales packed onto its surface. The makers also became famous. In the United States, Keuffel and Esser (K&E), based in Hoboken, New Jersey, was the dominant maker for nearly a century. Pickett, based in California, made distinctive aluminium slide rules — light, durable, and yellow with black scales. In Germany, two famous companies competed — Faber-Castell (still famous today for pencils) and Aristo. In Japan, Hemmi made beautiful slide rules with bamboo bodies — the bamboo was naturally self-lubricating and held its shape in any climate. The Post company sold Hemmi slide rules under their own name in the United States. The Pickett N600-ES, an aluminium slide rule with five-inch pocket size, was the model Buzz Aldrin took to the Moon on Apollo 11. The Pickett N600-ES from Apollo 13 is now at the Smithsonian's National Air and Space Museum. The thought that humans walked on the Moon partly with the help of slide rules sometimes amazes modern readers. Why were there so many different makers, models, and scales?

Points to consider (for the teacher)

Because different users needed different things. A surveyor wanted scales for trigonometry. An electrician wanted scales for ohms and volts. A chemist wanted scales for pH. A navigator wanted scales for compass directions. A pilot wanted scales for airspeed and fuel. Makers competed by adding specialised scales for specific professions. Faber-Castell sold engineering slide rules with one set of scales, electrical slide rules with another, and so on. Strong answers will see that the slide rule, far from being a simple device, was a sophisticated piece of professional equipment, often customised for the specific work it had to do. End by noting that this is true of most professional tools. The carpenter has different chisels for different jobs. The surgeon has different scalpels. The slide rule was the same. There was no single 'best' slide rule. There was the best one for your work.

Then, in 1972, the slide rule died. In January of that year, the Hewlett-Packard company, an American electronics firm based in California, put on sale a new pocket calculator. It was called the HP-35. (The name came from the fact that it had 35 buttons.) It was about the size of a thick paperback book. It cost 395 US dollars — a serious amount of money at the time, equivalent to several thousand dollars today. But the HP-35 was a scientific calculator. It could do everything a slide rule could do. It could multiply, divide, find squares and square roots, calculate logarithms and trigonometric functions. It worked to ten decimal places — far more accurate than any slide rule could ever be. It made no mistakes — once you typed in the numbers correctly, the answer was right. It worked in the dark. It worked on a plane. It fitted in a coat pocket. And it was just as fast as a slide rule, often faster. The effect was immediate and brutal. Engineers who had used slide rules for decades bought HP-35s and never picked up a slide rule again. By 1975, the price had dropped to about 100 US dollars. By 1977, basic scientific calculators sold for under 20 dollars. The major slide rule companies — K&E, Pickett, Aristo — collapsed within a few years. K&E stopped making slide rules in 1976, after 109 years. Pickett closed in the late 1970s. Faber-Castell stopped making slide rules in 1975, though they continued to sell stock through the late 1990s and finally cleared the last from their warehouse in 2018. The slide rule had been killed by something completely different — a piece of electronics with no moving parts that worked on the same logarithms, but found them by digital calculation rather than by physical sliding. One generation of engineers had used slide rules every day for their whole working lives. The next generation had never touched one. The skill, the tradition, the muscle memory — gone within about five years. What does the slide rule's death teach us about technological change?

Points to consider (for the teacher)

Several things at once. First, that technology can change extremely fast. The 350-year reign of the slide rule ended in about five years. Second, that the change has winners and losers. The makers of slide rules went out of business. The skilled slide-rule users had to retrain. Some of the workers in slide-rule factories lost their jobs. The buyers of electronic calculators won — they got a better tool, cheaper. Third, that some kinds of knowledge can be lost quickly. A skilled slide-rule user in 1970 could do calculations in seconds. The skill took years to learn. Today, almost no one has that skill. The slide rules survive but the muscle memory does not. Fourth, that the new tool is not always better in every way. The slide rule made the user think about the order of magnitude (you had to know where to put the decimal point — the slide rule did not tell you). The calculator does not require this — and some old engineers complained that the new generation lost a feel for whether their answers made sense. Strong answers will see that technological change is rarely simple progress. It is gains and losses together. The slide rule died and gave us cheaper, faster, more accurate calculation. It also took with it a certain way of thinking. End by noting that we are watching the same pattern play out today, with computers replacing many other tools. The lessons of the slide rule are not finished.

What this object teaches

A slide rule is a calculating tool made of sliding pieces of wood, plastic, bamboo, or aluminium, with logarithmic scales printed on their surfaces. By sliding the parts past each other and reading where lines align, the user can multiply, divide, find squares and square roots, calculate logarithms, and work out trigonometric functions. The slide rule was invented in England in the 1620s by William Oughtred, an Anglican clergyman and mathematician, using two of Edmund Gunter's logarithmic scales (1620) sliding against each other. The underlying mathematical idea is John Napier's logarithms (1614) — when you add two logarithms, you multiply the original numbers. The slide rule does this addition mechanically, by sliding logarithmic scales past each other. The Mannheim layout, developed by a French artillery officer in the 1850s, became the standard design. Famous makers included Keuffel and Esser (USA), Pickett (USA, aluminium), Faber-Castell (Germany), Aristo (Germany), and Hemmi (Japan, bamboo). For 350 years, the slide rule was the standard calculating tool of engineers, scientists, navigators, and surveyors worldwide. The Brooklyn Bridge, the Empire State Building, the Spitfire fighter, the Boeing 747, and the Apollo missions to the Moon were all designed with the help of slide rules. Buzz Aldrin took a Pickett N600-ES to the Moon on Apollo 11; the one from Apollo 13 is at the Smithsonian's National Air and Space Museum. Then, in 1972, the Hewlett-Packard HP-35 scientific calculator went on sale. Within five years, the slide rule was almost entirely gone. K&E stopped making slide rules in 1976. Pickett collapsed in the late 1970s. Faber-Castell stopped production in 1975. The Concise Company of Tokyo still makes circular slide rules today. The Breitling Navitimer pilot's wristwatch, introduced in 1952, has a working circular slide rule built into its bezel and still does today. The MIT Museum, the Science Museum in London, the Deutsches Museum in Munich, and the Smithsonian all hold significant collections. The slide rule is a beautiful example of mathematics made into a physical object, and its sudden replacement by the electronic calculator is one of the clearest cases of technological change in modern times.

Date	Event	What changed
1614	John Napier of Scotland publishes the idea of logarithms	Foundation of all later slide rule mathematics
1620	Edmund Gunter of England invents the logarithmic scale	A ruler whose number spacing follows logarithms
1622	William Oughtred slides two Gunter's scales past each other	The first slide rule — mechanical multiplication
1850s	Amedee Mannheim of France standardises the slide rule design	The Mannheim layout becomes the worldwide standard
Late 1800s	Keuffel & Esser, Pickett, Faber-Castell, Aristo, Hemmi all founded or expand	Major slide rule industry develops across countries
1952	Breitling Navitimer pilot's watch introduced with circular slide rule	The slide rule on the wrist for aviation
1969	Buzz Aldrin takes a Pickett N600-ES to the Moon on Apollo 11	The slide rule reaches the Moon
January 1972	Hewlett-Packard releases the HP-35 scientific calculator	The slide rule's competitor arrives
1972-1977	Slide rule industry collapses; K&E, Pickett, Faber-Castell stop production	The 350-year reign ends in five years

Key words

Slide rule

A mechanical calculating tool with sliding parts carrying logarithmic scales. By sliding the parts past each other and reading where the numbers line up, the user can multiply, divide, find squares and square roots, calculate logarithms, and work out trigonometric functions. In the United States, often called a 'slipstick'.

Example: A typical engineering slide rule of the 1960s — like the Faber-Castell 67/54 Darmstadt from Germany — has ten or twelve different scales packed onto a piece of stiff plastic about 25 centimetres long. It can do the bulk of an engineer's daily calculations in seconds.

Logarithm

A number that tells you how many times you have to multiply a base (usually 10) by itself to get a given number. The logarithm of 100 is 2 (because 10 x 10 = 100). The logarithm of 1,000 is 3. The logarithm of 1 is 0. Logarithms were discovered by John Napier of Scotland in 1614.

Example: The deep magic of logarithms is that adding them multiplies the original numbers. To multiply 2 by 5, you can add log(2) + log(5) = 0.301 + 0.699 = 1.000, then find the number whose log is 1 — which is 10. So 2 x 5 = 10. This is the principle on which every slide rule works.

C and D scales

The two main logarithmic scales on a slide rule, each running from 1 to 10. The C scale is on the slide; the D scale is on the stator (fixed part). By sliding the C scale against the D scale and reading where numbers align, the user performs multiplication and division.

Example: To multiply 2 by 3 on a slide rule: slide the 1 of the C scale to the 2 of the D scale; the C scale's 3 now lines up with the D scale's 6. So 2 x 3 = 6. The same procedure works for any two numbers.

Cursor

A sliding window — usually clear glass or plastic with a thin hairline — that runs across the entire width of the slide rule. The cursor lets the user align numbers on different scales accurately. The cursor was added to the standard slide rule design by Amedee Mannheim in the 1850s.

Example: The cursor's hairline is usually a very fine line scratched or painted on the underside of the clear material. To use the slide rule, the user lines up the hairline with the relevant numbers on the different scales, then reads off the answers.

Mannheim layout

The standard slide rule design developed by Amedee Mannheim, a French artillery officer, in the 1850s. The Mannheim slide rule has A, B, C, and D scales arranged with the slide between A and D, and includes a cursor. This became the worldwide standard.

Example: Almost every slide rule made from about 1860 to 1975 used the Mannheim layout. Manufacturers added extra scales (S and T for trigonometry, L for logarithms, LL for very large numbers) but the basic Mannheim structure was kept. The Faber-Castell 67/54 Darmstadt, the Pickett N600-ES, the K&E Log-Log Decitrig — all are Mannheim-based.

Pickett N600-ES

A five-inch pocket aluminium slide rule made by the American Pickett company. It became the slide rule of choice for the Apollo astronauts. Buzz Aldrin carried one to the Moon on Apollo 11 in 1969. The slide rule from Apollo 13 is at the Smithsonian's National Air and Space Museum.

Example: The Pickett N600-ES was bright yellow with black scales. Pickett claimed the yellow was 'easier on the eyes' than white. Buzz Aldrin's Apollo 11 slide rule sold at auction in 2007 for over 70,000 US dollars. The Apollo astronauts used slide rules as backup, in case the spacecraft's computer failed.

Use this in other subjects

Mathematics: In small groups, students try a simple multiplication on a paper 'slide rule' — two strips of paper with a logarithmic scale printed on each. Slide the strips past each other to multiply. Discuss: this is the mathematics of logarithms, made physical. The slide rule is logarithms you can touch.
History: Build a timeline of calculating tools — counting boards (3000 BCE), the abacus (2500 BCE onwards), logarithms discovered (1614), the slide rule invented (1622), the mechanical calculator (1640s onwards), the electronic calculator (1972), the spreadsheet (1979), the smartphone (2007). Discuss: humans have been making calculation easier for 5,000 years.
Science: Discuss how slide rules were used in real engineering and science — the design of bridges, aircraft, ships, dams, factories. Every engineer of the 1950s and 1960s carried a slide rule in their shirt pocket. The Apollo astronauts took them to the Moon. Without slide rules, modern engineering as we know it could not have developed.
Ethics: The slide rule industry collapsed in five years (1972-1977) after the electronic calculator arrived. Thousands of workers lost their jobs. Skilled craftspeople watched their work become worthless. Discuss: when a new technology destroys an old industry, what responsibilities do we have? The same question is asked today about artificial intelligence.
Art: Show students images of fine slide rules from different makers — the cream-coloured Faber-Castell from Germany, the yellow Pickett from America, the bamboo Hemmi from Japan. Each has its own design culture. Discuss: even a working tool can be a piece of beautiful design. The slide rule was both.
Language: Trace the language of slide rules. 'Slipstick' was the American nickname. 'Mannheim rule' came from a French inventor. 'Cursor' comes from the Latin 'curere' (to run) — the cursor runs across the slide rule. The Japanese word for slide rule is 'keisanjaku', literally 'calculation ruler'. Different languages, different names, same idea.

Common misconceptions

Wrong

A slide rule is just a fancy ruler.

Right

A slide rule is a calculating tool — a mechanical version of a logarithmic calculator. A standard ruler measures lengths. A slide rule does multiplication, division, squares, square roots, logarithms, and trigonometry. The two look similar but do completely different things.

Why

This confusion is common because both have straight edges with numbers. The slide rule has logarithmic scales, multiple sliding parts, and a cursor — none of which a ruler has.

Wrong

The slide rule was made obsolete by computers.

Right

The slide rule was made obsolete by the pocket electronic calculator — specifically the Hewlett-Packard HP-35, released in January 1972. Computers existed long before this but were the size of rooms and used in completely different ways. It was the pocket calculator, not the computer, that killed the slide rule in 1972-1977.

Why

The two technologies are often confused. Computers and pocket calculators are different machines used for different things, though they share underlying electronics.

Wrong

The Apollo astronauts used slide rules because they did not have computers.

Right

The Apollo missions had sophisticated onboard computers — the Apollo Guidance Computer was one of the most advanced of its time. The slide rules were backup. If the computer failed (as it nearly did on Apollo 11 during landing), the astronauts could perform critical calculations by hand using their slide rules. Buzz Aldrin's Pickett N600-ES went to the Moon as part of a comprehensive emergency-procedures plan.

Why

The image of astronauts using slide rules can suggest they were short of better tools. The truth is more interesting: they had the best computers of their day, plus slide rules as a deliberate backup.

Wrong

Logarithms are too hard for primary school children.

Right

The basic idea of a logarithm — counting how many tens you multiply together to get a number — can be taught to children of any age. Children easily grasp that log(100) = 2 and log(1,000) = 3. The slide rule was historically used by children as young as 12 in many countries. Mastery takes time, but the idea is approachable.

Why

Logarithms have a fearsome reputation in higher mathematics. The core idea is actually simple, and the slide rule makes it visible. Many adults find logarithms easier when they see them on a slide rule than when they meet them in algebra.

Teaching this with care

Treat the slide rule with the seriousness it deserves. It is not a toy or a museum curiosity — it was the working calculator of professionals worldwide for 350 years. Use proper terms — slide rule, slipstick, cursor, stator, slide, C scale, D scale, Mannheim layout. Pronounce 'Oughtred' as 'AW-tred' (the 'gh' is silent, like in 'thought'). Pronounce 'Mannheim' as 'MAN-hime' (the German way). Pronounce 'Keuffel and Esser' as 'KOY-fel and ESS-er'. Pronounce 'Hemmi' as 'HEM-mee'. Pronounce 'Faber-Castell' as 'FAH-ber kas-TEL' (the German way). Pronounce 'Napier' as 'NAY-pee-er'. Be respectful of multiple national traditions in slide-rule making. The American Pickett, the German Faber-Castell, the Japanese Hemmi, the British Thornton, the French Graphoplex were all major makers. None was 'the original' or 'the best'. Each had its strengths and its fans. Be careful about the 'old tool versus new tool' framing. The slide rule did not become 'wrong' or 'bad' in 1972 — it was simply replaced by something faster. Most users were happy with the change. Some lost their jobs, and we should not pretend otherwise. Be honest about the human cost of technological change. The slide rule companies employed thousands of workers — engineers, machinists, scale-engravers, packers, salespeople. Within five years of the HP-35, most of these jobs were gone. K&E had been making slide rules since 1867 — over a century of continuous production ended in 1976. Mention this honestly. Be careful with the Apollo material. The Apollo astronauts were extraordinary people who did extraordinary things, but the use of slide rules in Apollo should not be presented as 'because they did not have computers' — they had the best computers of their day. The slide rules were backup. Be respectful of the underlying mathematics. Logarithms are a major mathematical idea, not a trick or a curiosity. They are still used today throughout science and engineering — in pH measurement, decibels, earthquake magnitude, music theory, and many other places. The slide rule is gone but the mathematics is not. Avoid presenting the slide rule as a 'failure' that was replaced. It was a complete success for 350 years. Almost everything humans built in the modern industrial era was calculated with it. Most successes do not last forever. End the lesson on the present. The Concise Company of Tokyo still makes circular slide rules today. The Breitling Navitimer wristwatch still has one. The Oughtred Society still has members. The story is not closed.

Check what students have understood

Answer each question in one or two sentences. Use what you have learned about the slide rule.

What is a slide rule, and what does it do?

A slide rule is a mechanical calculating tool made of sliding pieces of wood, plastic, bamboo, or aluminium, with logarithmic scales printed on their surfaces. By sliding the parts past each other and reading where the numbers line up, the user can multiply, divide, find squares and square roots, and calculate logarithms and trigonometric functions.

Marking note: Award full marks for any answer that mentions both the physical form (sliding parts with scales) and at least one of the operations it performs.
What is the basic mathematical idea behind the slide rule?

The slide rule uses logarithms. When you add two logarithms, you multiply the original numbers. A slide rule has scales whose numbers are spaced according to their logarithms, so sliding two scales past each other adds the logarithmic distances — which means multiplying the underlying numbers.

Marking note: Strong answers will mention both logarithms and the addition-equals-multiplication principle. Either alone earns most marks.
Who invented the slide rule, and when?

The slide rule was invented in England in 1622 by William Oughtred, an Anglican clergyman and mathematician. He built on Edmund Gunter's logarithmic scale (1620), which in turn built on John Napier's discovery of logarithms in Scotland in 1614.

Marking note: Award full marks for any answer that mentions Oughtred and the 1620s. Mentioning Gunter or Napier earns extra credit.
How did the slide rule reach the Moon?

Buzz Aldrin carried a Pickett N600-ES five-inch pocket slide rule on Apollo 11 in 1969. It was a backup, in case the spacecraft's computer failed. The Apollo 13 slide rule is now at the Smithsonian's National Air and Space Museum.

Marking note: Award full marks for any answer that mentions both an Apollo mission and the role of the slide rule (backup, calculating tool).
What happened to the slide rule in the 1970s, and why?

The slide rule was made obsolete almost overnight by the Hewlett-Packard HP-35 scientific calculator, released in January 1972. The HP-35 could do everything a slide rule could do, but faster and to more decimal places. Within five years (1972-1977), the slide rule industry had collapsed — K&E, Pickett, Faber-Castell, Aristo, and others all stopped making slide rules.

Marking note: Strong answers will mention both the HP-35 and the rapid collapse of the industry. Either alone earns most marks.

Discuss together

These questions have no single right answer. Talk in pairs or small groups, then share your ideas with the class.

For 350 years, the slide rule was the calculating tool of engineers and scientists worldwide. Then it died in five years. What does this teach us about technological change?

This is a question about how technologies live and die. Strong answers will see that change can be very fast even after very long stability. The slide rule had a 350-year run. Most people in 1971 would have assumed it would continue indefinitely. They were wrong. The HP-35 in January 1972 changed everything within five years. The lesson is that technological change is not always gradual. Sometimes a new tool comes along that is decisively better, and the old tool dies quickly. The horse-drawn carriage died fast after the automobile arrived. The typewriter died fast after the personal computer arrived. The film camera died fast after the digital camera arrived. Strong answers will see that the speed of change varies — some technologies stay around for centuries; others vanish in a few years. The slide rule had both — three and a half centuries of dominance, then a five-year extinction. End by noting that we are watching the same kind of change today, with computers and artificial intelligence replacing many other tools. The lessons of the slide rule are not just historical. They are about what happens when something better comes along.
Some old engineers complained that students who used calculators lost the ability to estimate — to feel whether an answer made sense. Do we lose something when we replace older tools with newer ones?

This is a real question. Strong answers will see that the answer is usually 'yes, something is lost, and yes, something is gained'. The slide rule required the user to keep track of the decimal point separately. The slide rule tells you the digits (2-7-4) but not the magnitude (is it 274? 2.74? 27,400?). To use a slide rule well, you had to estimate the answer first, then use the slide rule to refine the digits. This habit of estimation is genuinely useful in engineering — it catches mistakes. A calculator does not require this habit, and some users do lose it. Strong answers will see that this is true in many fields. People who use spell-checkers may lose some spelling skill. People who use map apps may lose some sense of direction. People who use search engines may lose some skill at finding things in libraries. None of this means the new tools are wrong. It does mean that what we practise is what we keep, and what we stop practising slowly fades. End by saying that this is one reason some teachers still teach long multiplication, even though calculators exist. It is not because the calculator is bad. It is because doing it by hand teaches something the calculator does not. The same is true of the slide rule. The mathematics it taught was a real skill, and it has been partly lost. Whether that matters is a question worth discussing.
The Apollo astronauts had powerful computers, but they took slide rules to the Moon as backup. When is it wise to keep an old technology alongside a new one?

This is a question about resilience. Strong answers will see that the Apollo team had a deep principle — never depend on a single point of failure for anything critical. The computers were brilliant, but they could fail. (The Apollo 11 computer nearly did fail during landing, throwing 'program alarms' that the controllers had to interpret in real time.) If the computer had failed completely, the slide rule was the backup. The astronauts could perform critical navigation and engineering calculations by hand. This is a deep insight about how to design any high-stakes system. Modern aircraft still have backups within backups — three or four independent systems for critical functions. Ships still carry sextants alongside satellite navigation. Hospitals still keep paper records as well as digital. Power stations still have manual override systems. Strong answers will see that the slide rule on Apollo is a small example of a much bigger principle — when failure is unacceptable, build redundancy. Do not put all your eggs in one basket, even if the basket is the most advanced computer of its time. End by noting that this is a question for the future too. As we depend more and more on digital systems, what backups are wise? When the GPS fails, can the modern navigator still find their way? When the search engine fails, can we still find information? When the artificial intelligence fails, can we still think? Worth discussing.

Teaching sequence

THE HOOK (5 min)

Hold up a wooden ruler. Ask: 'Could a ruler do multiplication?' Take answers. Most students will say no. Then say: 'For 350 years, a special kind of sliding ruler was the calculator of every engineer, scientist, and navigator in the world. It went to the Moon on Apollo 11. Then it died almost overnight in 1972. Today we are going to find out how.'
HOW THE SLIDE RULE WORKS (10 min)

On the board, draw a simple two-strip 'slide rule' — two strips with logarithmic scales. Show how sliding them past each other can multiply small numbers. Pause and ask: 'How does this work?' Then introduce logarithms — the discovery that adding logarithms multiplies numbers. The slide rule is logarithms made into a tool. Strong students will see the trick.
THE SLIDE RULE IN HISTORY (15 min)

Tell the story. William Oughtred (1622), the Mannheim layout (1850s), the major makers (K&E in America, Faber-Castell and Aristo in Germany, Hemmi in Japan, Pickett in California). The slide rule designed the Brooklyn Bridge, the Empire State Building, the Spitfire, the Boeing 747. Buzz Aldrin took one to the Moon. Then in January 1972 the HP-35 arrived, and within five years the slide rule was dead.
WHAT THE SLIDE RULE TEACHES (10 min)

Discuss the deeper lessons. Technologies can have long reigns and sudden deaths. New tools are not always better in every way — the slide rule taught estimation, which the calculator does not require. Some skills, once lost, are hard to recover. The Apollo astronauts kept slide rules as backups even though they had the best computers of their time. Resilience matters.
CLOSING (5 min)

Ask: 'When you hear a calculator beep, what do you not think about?' Take answers. End by saying: 'The mathematics inside that calculator is logarithms, the same mathematics that William Oughtred turned into a sliding wooden stick 400 years ago. The form has changed completely — wood to plastic to silicon. The mathematics is the same. Every time you use a calculator, you are using Napier's logarithms and Oughtred's slide rule, hidden inside something faster and smaller. The slide rule died in 1972. The mathematics it embodied is alive in every calculator, every spreadsheet, every smartphone in the world.'

Classroom materials

Paper Slide Rule

Instructions: Give each student two strips of paper with a logarithmic scale printed on them, running from 1 to 10. Show how to use them to multiply. To multiply 2 by 3: slide the 1 of the top strip to the 2 of the bottom strip; the 3 of the top strip now lines up with the 6 of the bottom strip. So 2 x 3 = 6. Have students try other multiplications.

Example: In Mr Patel's class, every student made a paper slide rule and worked through several multiplications. The teacher said: 'You have just done what every engineer of the 1960s did dozens of times every day. The slide rule made hard arithmetic easy by turning it into sliding. The mathematics was hidden in the spacing of the numbers. You did not need to understand logarithms to use it. You just slid the pieces and read the answer.'

Logarithm Detective

Instructions: On the board, write a logarithmic scale from 1 to 10. Mark where 2, 5, and 10 fall. (10 at the end; 2 at about 30 per cent of the way along; 5 at about 70 per cent of the way along.) Discuss: why is the spacing not even? Because the spacing follows the logarithms — and logarithms grow slowly. Strong students will see that this is the same logic behind every slide rule.

Example: In Ms Tanaka's class, students were astonished to see that the spacing on a slide rule is not uniform. The teacher said: 'You have just discovered something important about logarithms. They grow slowly. Going from 1 to 2 is the same logarithmic distance as going from 5 to 10. The slide rule is built on this fact. The whole instrument is logarithms made physical.'

Apollo at the Slide Rule

Instructions: Tell the students about Buzz Aldrin taking a Pickett N600-ES to the Moon on Apollo 11. Show a picture if possible. Discuss: why would the most advanced spaceflight programme in history take a wooden stick to the Moon? Because the computer might fail, and the slide rule was the backup that always worked. Strong answers will see that this is about resilience — never trust a single tool with your life if you can carry two.

Example: In Mr Lee's class, students were amazed that the Apollo astronauts had slide rules. The teacher said: 'You have just learned something about how serious engineers think. Apollo had the best computers of its time. The computers were also brand new and could fail. So the astronauts also had slide rules they could fall back on. This is how you build systems that do not kill people when something goes wrong. Never depend on a single tool for anything critical. Even on the most advanced spaceflight in history, the backup was a piece of plastic that had been invented 350 years earlier.'

Where to go next

Try a lesson on the abacus for another pre-electronic calculating tool, with a rich global tradition.
Try a lesson on the Bakhshali manuscript for the early history of zero and the Indian mathematical tradition.
Try a lesson on the quipu for a non-Western recording-and-counting system, used by the Inca.
Connect this lesson to mathematics class with a longer project on logarithms — pH measurement, decibels, earthquake magnitude, the Richter scale, all use logarithms.
Connect this lesson to history class with a longer project on the technologies of the Apollo programme. The slide rule is one small example of a much bigger story.
Connect this lesson to engineering or science class with a project on how the modern world was built. Until 1972, every engineer's pocket had a slide rule. The world the slide rule built is still around us.

Key takeaways

A slide rule is a mechanical calculating tool with sliding parts carrying logarithmic scales. By sliding the parts past each other, the user can multiply, divide, find squares and square roots, and calculate logarithms and trigonometric functions.
The slide rule was invented in 1622 by William Oughtred in England, building on John Napier's discovery of logarithms (1614) and Edmund Gunter's logarithmic scale (1620). The Mannheim layout (1850s) became the worldwide standard.
The deep idea behind the slide rule is that adding two logarithms multiplies the original numbers. The slide rule does this addition mechanically by sliding logarithmic scales.
For 350 years, the slide rule was the standard calculating tool of engineers, scientists, navigators, and surveyors worldwide. The Brooklyn Bridge, the Empire State Building, the Spitfire, and the Boeing 747 were all designed with slide rules. Buzz Aldrin took one to the Moon on Apollo 11.
The slide rule was killed in five years by the Hewlett-Packard HP-35 scientific calculator (January 1972). K&E, Pickett, Faber-Castell, Aristo, and other makers collapsed. The 350-year reign ended in 1972-1977.
The slide rule teaches that technologies can have long reigns and sudden deaths, that new tools are not always better in every way (the slide rule taught estimation, which the calculator does not require), and that resilience often means keeping an old tool alongside a new one — as the Apollo astronauts did.

Sources

Slide rule — Wikipedia (2026) [encyclopedia]
A History of the Logarithmic Slide Rule — Florian Cajori (1909) [book]
The Slide Rule: A Short History — Cliff Stoll (2006) [academic]
Oughtred Society Journal — Oughtred Society (2024) [institution]
Apollo Lunar Surface Journal — NASA (2024) [institution]

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