The Genius Of Slide Rule Precision

Most people have heard of or seen slide rules, with older generations likely having used these devices in school and at their jobs. As purely analog computers these ingenious devices use precomputed scales on slides, which when positioned to a specific input can give the output to a wide range of calculations, ranging from simple divisions and multiplications to operations that we generally use a scientific calculator for these days. Even so, these simple devices are both very versatile and can be extremely precise, as [Bob, the Science Guy] demonstrates in a recent video.

Slide rules at their core are very simple: you got different scales (marked by a label) which can slide relative to each other. Simple slide rules will only have the A through D scales, with an input provided by moving one scale relative to the relevant other scale (e.g. C and D for multiplication/division) after which the result can be read out. Of course, it seems reasonable that the larger your slide rule is, the more precision you can get out of it. Except that if you have e.g. the W1 and W2 scales on a shorter (e.g. 10″) slide rule, you can use those to get the precision of a much larger (20″) slide rule, as [Bob] demonstrates.

Even though slide rules have a steeper learning curve than punching numbers into a scientific calculator, it is hard to argue the benefits of understanding such relationships between the different scales, and why they exist in the first place.

49 thoughts on “The Genius Of Slide Rule Precision

  1. I got my EE degree with only a Post Versalog, and didn’t have access to a four function calculator until a year after I graduated and was working in industry. One of my professors had a Wang “portable” computer that took up half the space in the trunk of his car. It all seems really primitive in retrospect.

  2. The one time I used a slide rule it was no more accurate than using rounded numbers due to errors in printed numbers and parallax effect

    These things are at best quick math for spot checks proper tools were used for precision

      1. This is correct. My dad used his Post Versalog slide rule when he was working at NASA on the Apollo program. Every engineer had one and used it extensively.

      2. My Dad worked at NASA and when his old house was abandoned after my mother went to a nursng home, I went in there and got some of his things so they wouldn’t be stolen by crackheads. This included his 30-30 rifle, a surveyors’ compass, and two aluminum slide rules.

    1. It’s a poor workman who forgets his lunch. Stupid grapes, probably sour anyway. “I tried once and underperformed so the tool is bad.” Words to something or other by. But we can all agree that improperly printed slide rules are at least a national problem and parallax poses a threat on the scale of Satanic abuse in our day care centers. Parallax lurks around every corner.

      In my day we simply fed the homework to the dog. Team sliderule!

  3. Not a big fan of slide rules, always messing up on the decimal point. Got a simple add-subtract-multiply-divide calculator ($100+ at the time) to help with this. For intro lessons, some classrooms had a giant slide over the chalkboard. Graduated about the time scientific calculators came out, and never touched the slide rule again.

    1. That is one of the advantages of being proficient with a slide rule. Doing quick mental estimates and keeping track of orders of magnitude mentally is a great skill and prevents many errors. One might find they easily spot errors in the numbers in news reports and the flood of AI generated Youtube videos, etc. And they are fast, with no keypad.

    2. Dimensional analysis. If you don’t have a scientific calculator or an IBM 360, a slide rule is better and faster than doing it by hand. I was in the last freshman Chemistry class that had tomuse slide rules. A fellow student came to class in January with an HP-35. I had a Bowmar 4-banger, so I contijued to bring my slide rule for trig functions,roots and logs. Don’t sell the slide rule short, in skilled hands it can do an awful lot, but the scientific calculator is even faster and more accurate.

  4. 20inch is NOT long!

    I have slide rules with a 500inch (21ft, 12,7m) scale. I have too many of them; must sell some.

    They were in production continuously for 94 years, until the HP35 stole their market.

  5. When I started my O-Levels we were recommended by the science teachers to buy a slide rule and a subscription to New Scientist magazine.
    I still use one on a weekly basis. The other was retired a year later when my Grandad gifted me his Sinclair Scientific calculator after he had upgraded it for something less reverse polishly.
    While it lasted I enjoyed using the slide rule. Better imo than the well thumbed log table booklets.

    1. Interesting. Aged about 7 I persuaded my parents to buy a Sinclair Scientific, because they’d come massively down in price, but neither I nor my parents understood RPN. After a while I gave up trying to understand how I was supposed to enter calculations and swapped it out for a Commodore 4-function calculator (with ‘%’ !!!).

      It was only later during work experience in my fourth year of secondary school where I learned how to use a slide rule, because my line manager had a circular slide rule. Admittedly as I already understood logs etc it was pretty easy. I then bought a Thornton slide rule from a local Preedy’s stationary shop as they were being sold off cheaply (no-one needed a slide rule in 1983!). I still have that too, & it’s pretty complex, so I wonder if it’s got the Wx scales talked about here, or the equivalent?

  6. A slide rule got me through tech school in the seventies. Two place accuracy was acceptable for some courses, scientific notation took care of decimal places, often large ones.
    Log tables were used for more precision. Beyond that it was hand calculations.
    We had adding machine size calculators at work. When they became obsolete I diceted one out of curiosity. The most fascinating component was the buffer memory implement with a coil of piano wire.

  7. The one absolutely overriding benefit of learning to use a slide rule is the discipline that how learning to use it imposes on one’s thinking and ability to calculate accurately and quickly–most specifically: keeping track of the decimal point.
    Most students today cannot handle this simple task even with a calculator (scientific? four-function? Doesn’t matter.) This fact has forced me to impose a ‘no calculators or other electronic devices allowed for taking quizzes’ policy for all tests / quizzes I give. This policy also increase my work-load tremendously, as I must ensure that all problems require that students’ mental mathematical gymnastics are reduced to, at worst, dividing or multiplying by ten, or two. Even then, the amount of errors and wrong answers are–to put it mildly–stupefying.
    (one doesn’t need any leaps of imagination to guess at the uproar and indignation that the appearance of this requirement, in the course’s syllabus, generates)

    I will never forget one of the most prescient and accurate lectures I ever heard on engineering–in general–as a profession, and as an undertaking: “…never forget that in–in general–engineering, as in life: ‘close’ is good enough. The really good…the exceptional…engineer knows when this approach is NOT good enough“.

    ‘Smart’phones; ‘smart’ TVs; ‘smart’ electronic calculators…all have one thing in common: they are all oxymorons.

  8. Used a pocket-sized circular slide rule in freshman chemistry. The C and D scales were accurate enough for three places. The inner scales weren’t much use; too small. For logarithms I used log tables instead. Learning where to place the decimal was a useful mental exercise.

    This particular slide rule was all-purpose. The back had a periodic table, and there was an insert that could be removed, with conversion factors of all sorts. The chem prof said I could use the slide rule but not the insert… Everything was engraved so that it wouldn’t wear.

    Calculators had barely come in. A guy in my dorm got a Sears calculator for high school graduation. Add, subtract, multiply, divide, and glorious! square roots! $200 (1973). By the time I reached junior year a similar calculator was about $20. A godsend during PChem.

    1. We must be the same age. I started physics with a Pickett and the CRC Handbook and the CRC Math Tables. When I was a junior I bought an HP45 by working afternoons in the Univ. print shop. It was fantastic and I have been firmly RPN ever since. Today I still have the Pickett and a Faber-Castell (which is fairly expensive today due to collectors) in my desk.

  9. Still have my Lafayette 99-7031 from 1969 (high school physics). My dad, who was an electrical engineer, bought it for me. Usually use HP 35s now. Used to have the slide rule on my desk at work and younger engineers would sometimes look at it and ask, “What’s that?”

  10. I’ve still got a British Thornton AD 150 on my desk. I was the last year to be taught how to use one when at school. I’ve no practical justification for occasionally using it, I just enjoy it.

  11. First off I admit I’m old. used a circular slide rule from grade 8-12. The first calculator’s came out when I was in grade 10. Very expensive, students where not allowed to use them . the thought being it would be unfair to the students that could not afford them .
    I got very fast at using the device. We were grading tests of another class , basically lust taking the test score and coming up with a percentage. The teacher supervising the class had just bought a shiny , very expensive calculator. He spotted me using the slide rule and said “that must be pretty slow, and challenged me to a race . We started with 6 test papers each . He was just starting his second when I finished. For anyone that has used one, just had to move my curser to the total of the test and the percentage was on the next scale .

  12. I had a professor who had a cylindrical (helical) slide rule in his office. It could muster four figures of precision… and he didn’t need it. He could compute anything (including natural logs and square roots) in his head faster than anybody could do on a slide rule, let alone punching it into a calculator. Impressive fellow.

  13. It must be slide rule week. I re-discovered this old Pickett 12-inch slide rule in my desk drawer a couple of days ago, and spend a fun half hour remembering how to use it. It really is a neat concept.

    Then today, going through a drawer at work, I found an ancient Ohmite slide rule with parallel resistance (special marks for the E24 series!) and Ohm’s law scales. Also AB and CD, FWIW. Marked “Made in USA, 1970”, I saved it from a co-worker’s desk after he passed away.

    1. That reminds me of a tip I read on USENET; to mark/highlight regular resistance values on a sliderule (1.0, 1.2, 4.7, 5.6, etc.) So if you are trying to find parallel resistance values you can see which values are closest to your objective.

  14. Heh. It looks like this article could have been designed to extract age demographics from HaD readership.

    Dang, this is an old bunch. I am not a graybeard myself. I look terrible with a beard.

  15. Some of the comments make the logical fallacy – “argument from antiquity”.

    just because slide rules are “good ‘ol” tech from days gone by doesn’t mean they are superior, or even necessarily suitable for use today.

    Yes, they are simple, no batteries, accurate, etc. But today when scientific calculators are affordable and ubiquitous, the argument that a slide rule was good enough for [insert spacecraft, aircraft, bridge, skyscraper or other notable design here] doesn’t mean they still need to be used today.

    Keep them around, keep the knowledge going, we need to preserve tech history. But no one needs to think they are relevant for day to day work or lament the fact that these young upstarts don’t know how to use them.

  16. There is an advantage that a sliderule has that a keyboard doesn’t. If you line up a ratio, then you have all the elements of the same ratio laid out before you. Choose those numerators or denominators that work for you.

    1. Very easily overlooked until you’ve used one, for sure! I might commit to using my slide rule for a few weeks just for the mental exercise. Messing with it for a few minutes reinforced some numerical relationships I had sort of buried in my head.

    2. Ratio’s aren’t bad, but the calculator gets there almost as fast with more precision. The thing I thought was cool was the special functions, starting with trigonometry. Because figuring a quick low precision answer to a large number of simple geometric problems is exactly what you want when you intend to immediately use that answer to tell you where to cut your lumber when building something. Especially if you plan on adjusting your values to what looks right or is convenient, as opposed to a one-and-done calculation. It does take a little focus to set up the function in your head if you haven’t done it in awhile though.

      1. Suppose you have a resistance and you select a voltage, then you have a range of current values anywhere you slide the cursor. You don’t need to keep entering numbers. As for precision, in designing circuits with real valued voltages, currents and resistors, you shouldn’t expect any accuracy better than 3 significant figures, if that, in any real circuit. It’s like that in any common engineering problem.

        1. I know that, although I also know that it’s easier to figure errors if they’re all from tolerances and not calculations. But it’s only a ratio; it doesn’t have to take long any way you do it.

          And if you have an entire circuit full of unknowns to calculate, the modern calculator makes it easiest because you can just assign each a letter and type in a few current or voltage law equations, even using complex numbers for impedance, and then the calculator will solve either in numbers or each as a function of the remaining unknowns. And if you need more than that, you can use a simulator.

  17. I wish i had kept my Fabar Castel rule. It served me well in the late 60’s during my engineering apprenticeship qualifications. With a good eye we could achieve an answer to 3 decimal places.

  18. Using a sliderule is way different from a calculator because the brain is a lot more engaged.
    The precision (or accuracy) of a sliderule is certainly sufficient to build all the electronic circuits I’m familiar with. 5% resistors, +100,,-20% capacitors, etc.
    Really fast doing a microwave path loss.

  19. Engineering data is often not known to more than 3 digits of accuracy. A slide rule suffices.

    I used a slide rule for the first year or 2 of engineering school. When the HP35 came out at $400 the wealthy guys bought them. Not too long after, TI came out with their scientific calculator at half the price, and I got on board.

    The discipline of using scientific notation and keeping track of the decimal place is useful, as others have stated.

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