How Slide Rules Work
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Slide Rules
Computing History
Mathematics
The post explains how slide rules work, sharing a resource on the history of computing, with no discussion or controversy arising in the comments.
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Nov 19, 2025 at 4:07 PM EST
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I played with creating a logarithmic slider thing [1] in Javascript that I hoped I could package up as a kind of "widget" people could use on their web pages. But I don't really know Javascript that well—or rather how to make an API out of a Javascript thing.
Anyway, to test it I tried to make an Ohm's Law calculator [2].
I would love to see a site like the one in this post have some kind of interactive slide rule on the web page itself.
[1] https://github.com/EngineersNeedArt/SlideRule
[2] https://www.engineersneedart.com/ohmslaw/index.html (the yellow slider is not directly user-moveable in this example)
I never spent the time to get quick with it, but I could absolutely see it being quicker than a calculator. You’d just have to be aware of the limits to its precision if you were in a field that required it.
One problem with a slide rule is that it only performs operations on normalized mantissas. You have to keep a parallel exponent calculation in your head, and that slows you down. Also, maintaining best precision slows you down.
I did keep a slide rule as a backup for exams in college when calculators were still LED but never really used one after a couple of years in high school.
They do what people want, the keyboard feel is infinitely smoother than tapping on a phone, etc.
Yeah, the 12C was the standard in business school. But I needed a new calculator and the 41 with its various modules worked fine and was more general purpose.
For multiplication, the DLDP in the result is:
- the sum of the DLDPs of the multiplicands MINUS 1 if the multiplication is done with the slide sticking out to the right of the ruler's body (for example 2.0 x 3.0 = 6.0).
- the sum of the DLDPs of the multiplicands if the multiplication is done with the slide sticking out to the left of the ruler's body (for example 5.0 x 4.0 = 20.0).
There's a similar rule for division, but that's left as an exercise for the student.
We were taught to estimate and use the rule to refine. I date back to the early electronic calculator era and we still had textbooks referencing slide rules etc.
"I want a dropping resistor for a plain old 1980s LED in a car" (back in ye old red LED 20 mA days) "Well experience indicates that will be far more than 500 ohms and somewhat less than 1K and IRL you're probably going to install a 680 and call it good" If you want an actual calculation for engineering purposes you calculate the ideal value under worst case conditions as about 585-ish ohms or whatever using the slide rule, purchasing LOLs at the idea of buying 0.1% precision resistors for mere LEDs, installs cheap 680 ohms and ships it. Maybe 680s if you want it bright to see in daylight or 820 if you want better odds to survive an alternator field winding dump or open battery (about the same thing). You can at least use the slide rule to verify everyone rounded in the "safer" direction to handle the worst case scenario.
We have speed electronic calculators now instead of slide rules, but they give a wronger answer and people aren't even aware of it or know why.
Two Meter Slide Rule
When the "cloud" is raining and your laptop and phone batteries are drained and you suddenly need to navigate your 4823 times table - its got you covered.
You will also need to work out how to write with a pen or pencil on paper or try and fix up your atrophied ability to remember arbitrary "facts" short term.
I have a Casio fx-991ES calculator, and twenty years later I have yet to need to replace the button cell in it thanks to the tiny solar cell.
Solar EMPs won't be powerful enough to impact electronics. A nuclear EMP can impact electronics, but only over a small geographic area; close enough that if you are in the electronics-frying radius of a nuclear weapon explosion, you either have much larger problems to worry about, or nothing at all to worry about ever again.
Here's info from Los Alamos Lab on it: https://www.lanl.gov/media/publications/national-security-sc...
But perhaps you were referring to one of the many other parts of the E6B which I am not familiar with.
Grad students or undergrad STEM students would have something like a 900 series, I have several, very nice. This is a desk rule it will not fit in a pocket. Something like a 600 series is a short pocket model, anodized aluminum, very nice and desirable.
The microline series was definitely made to a price point and unless you find one in unusually good condition or its your first collector rule I would not bother picking it up. They stick very strongly and the cursor cracks after half a century and they are slippery in the hand and warp more than most rule and I don't think they're easy to read. They were cheap to make and cheap to buy.
Slide rules in the 2020s are an efficient market; something that barely works "the walmart solar calculator of its generation" like a microline series sells for around $20 today, a VERY desirable N600 series sells for like a hundred bucks and I think its a bargain at that price.
If you mean most popular as in most desired today not most sold back in the day, that's probably the 600 series or specialty rules like I have a N-16-ES with the electronics engineering scales. The latter sells for about as much as a working HP48 calculator, which is interesting. If you mean popular as in attractive that is surely the Faber-Castell short 83N series, I think that's a 62/83N. I would like one of those LOL. Unleash 1960s German graphics artists on industrial design and tell them to make the coolest looking slide rule possible under 60s industrial design rules, you get the 83N series, very very cool way to spend $300 or so, its the kind of thing you put in a lighted display case to admire.
* https://www.youtube.com/watch?v=oYQdKbQ-sgM
"Professor Herning" (?) also has a good series of videos on the use of various scales as well:
* https://www.youtube.com/@ProfessorHerning/videos
His playlist starting at the beginning (C and D scales) with a Manheim layout:
* https://www.youtube.com/playlist?list=PL_qcL_RF-ZyvWJJkJOk_O...
* https://sliderulemuseum.com/Manuals/M37_Post_Manheim_Instruc...
Some manuals / books on slide rules:
* 1909: https://archive.org/details/mannheimsliderul00coxwrich
* 1922: https://archive.org/details/cu31924002978561/mode/2up
I still have the slide rules, so this post was a great rabbit hole to go down. In software there's no need for them but I still find them fascinating as a window into how engineers used to get their work done.
... but in the Real World they work pretty well for the sort of calculations you might need to do in the field (literally, in a field, sometimes) and don't require batteries, are reasonably waterproof, and reasonably robust if dropped.
They're pretty useful for teaching amateur people how to implement algorithms. Multiple ways to solve problems, some easier than others, some more efficient than others, with immediate rewards of faster higher accuracy.
Never thought of that, and I used to work in an ATEX environment where calculators powered by watch batteries had to be carefully logged and carried across to a "safe" area inside a special (horribly expensive) Peli case.
For used, see perhaps "Where to Buy Slide Rules?":
Most of my like-new rules came from antique malls, though I've also purchased one from Etsy. Estate sales are occasionally fruitful. As long as they were stored properly (e.g., in a desk drawer, like it seems they mostly were after the electronic calculator took over), they don't degrade. Occasionally you see minor yellowing that is cured by some time in the sun. Carrying cases (often leather) are typically more affected by time. I soak new (to me) leather cases in neatsfoot oil and give them at least a week before putting the rule back.
You could make your own with prints from the Slide Rule Museum [0]. 3D printing would make quick work of it, but I'm sure wood or metal units could be accomplished. The cursor benefits from spring loading,
They also have some pretty nice simulators [1], if that's your thing.
[0] https://sliderulemuseum.com/SR_Scales.shtml [1] https://www.sliderulemuseum.com/VirtualSR.shtml
I bought a newly manufactured one from ThinkGeek several years ago, some geek-catering company will pop up and supply pent up demand eventually. Curiosity Box fills that niche right now.
It reminds me a little of AI now. The question of whether students should use AI will probably soon go away and everybody will use AI. Not sure what the results will be.
* https://cseweb.ucsd.edu/~pasquale/Classes/SlideRule/
* Mathematical Foundations of the Slide Rule (PDF): https://cseweb.ucsd.edu/~pasquale/Papers/IM11.pdf
* Why Does A Slide Rule Work? (PDF): https://cseweb.ucsd.edu/~pasquale/SlideRuleTalkLasVegas14.pd...
The gist of it is:
1. First, define a way to represent any univariate monotonic function f(x) on a graduated scale. (Specifically: select a discrete set of x values, and for each of these x values, place a mark with label x at a distance proportional to (f(x) - f(x_L)) from the left endpoint, where x_L is the leftmost x value.)
2. Then, if we have two such scales f(x) and g(x) that can slide relative to each other, we can compute functions of the form h(x, y, z) = f_inverse(f(x) + g(y) - g(z)).
It ends up being surprisingly versatile -- the above resources show how you can compute:
1. Multiplication: x * y using f(x) = log(x) and g(y) = log(y), with z fixed at 1
2. Hypotenuse: sqrt(x^2 + y^2) using f(x) = x^2 and g(y) = y^2, with z fixed at 0
3. Parallel resistors: 1/(1/x + 1/y) using f(x) = 1/x and g(y) = 1/y, with z fixed at +infinity
4. Exponentiation: x^(y/z) using f(x) = log(log(x)) and g(y) = log(y)
This article: “lol, is that the depth of your commitment”
My version has a couple interesting properties compared to ordinary linear slide rules:
1. It has three octaves, so it can scale from 1 to 1k or from 1k to 1m, or from 1m to 1b. This is great for calculating point values
2. It's rotary
3. It can be easily 3d-printed!
Source code and .STL files here: https://www.printables.com/model/1026662-jimbos-rotary-slide...
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