Retrotechtacular: The CURTA Mechanical Calculator

The CURTA mechanical calculator literally saved its inventor’s life. [Curt Herzstark] had been working on the calculator in the 1930s until the Nazis forced him to focus on building other tools for the German army. He was taken by the Nazis in 1943 and ended up in Buchenwald concentration camp. There, he told the officers about his plans for the CURTA. They were impressed and interested enough to let him continue work on it so they could present it as a gift to the Führer.

This four-banger pepper mill can also perform square root calculation with some finessing. To add two numbers together, each must be entered on the digit setting sliders and sent to the result counter around the top by moving the crank clockwise for one full rotation. Subtraction is as easy as pulling out the crank until the red indicator appears. The CURTA performs subtraction using nine’s complement arithmetic. Multiplication and division are possible through successive additions and subtractions and use of the powers of ten carriage, which is the top knurled portion.

Operation of the CURTA is based on [Gottfried Leibniz]’s stepped cylinder design. A cylinder with cogs of increasing lengths drives a toothed gear up and down a shaft. [Herzstark]’s design interleaves a normal set of cogs for addition with a nine’s complement set. When the crank is pulled out to reveal the red subtraction indicator, the drum is switching between the two sets.

Several helper mechanisms are in place to enhance the interface. The user is prevented from ever turning the crank counter-clockwise. The crank mechanism provides tactile feedback at the end of each full rotation. There is also a lock that disallows switching between addition and subtraction while turning the crank—switching is only possible with the crank in the home position. There is a turns counter on the top which can be set to increment or decrement.

You may recall seeing Hackaday alum [Jeremy Cook]’s 2012 post about the CURTA which we linked to. A great deal of information about the CURTA and a couple of different simulators are available at Make the jump to see an in-depth demonstration of the inner workings of a CURTA Type I using the YACS CURTA simulator.

Retrotechtacular is a weekly column featuring hacks, technology, and kitsch from ages of yore. Help keep it fresh by sending in your ideas for future installments.

[Thanks to Andrew for the tip!]

39 thoughts on “Retrotechtacular: The CURTA Mechanical Calculator

  1. hmm… just saved two partially-working Walther Multa 32 from trash a few days ago (Walther office machines, related to the gun manufacturer). Multa 32 mulitply by repeated additions and make a lot of “number crunching” noise during the process :D . Anyone got tech data on those? has some info. I got best results from google patents search e.g. but a “service manual” of some kind would be great to get ’em back to work.

      1. Indeed, it was advanced technology for it’s time, and no doubt it would have helped the Nazi war effort had it been manafactured for their scientists.
        I used the word trinket because it was to be presented as a gift to Hitler.

      2. *We* sent men to the moon. The nazis used the very same scientists to attack Britain.

        I read a story about the gestapo coming to confiscate nobel prize medals from Jewish scientists (all jew-owned gold was to be turned over). A colleague of prizewinner was disgusted by the idea, so he tossed the medal into a jar of a chemical that dissolved the gold, resulting in boring yellowish sludge. He then put the unlabeled jar on a shelf with a bunch of other unlabeled jars, where it stayed safely hidden in plain sight. When the war was over, he mixed in another chemical that caused the gold to precipitate out so it could be re-cast into a “new” medal.

        What it comes down to is that nazi ideology poisoned everything they tried to accomplish. It caused them to drive out many of their finest minds, it caused them to waste resources on mass-murder even as they began to lose the war (since conquest without racial domination was no conquest at all), and it rendered them incapable of rationally evaluating the capabilities of the soviet union.

        The lesson: you can be a genocidal racist or a conquering emperor, but it’s a bad idea to be both. :)

        1. Just for historical accuracy: nazis were just looking for any gold. At that time, gold standard was still in force and they had decreed any gold under German borders was to be turned in to help the -future- war effort. James Franck was Jew, indeed, and I guess he left his medal with Bohr during the time he spent at Copenhagen, before leaving for the USA to work in the Manhattan Project. Not quite sure why he didn’t take it with him, though.

          The other medal was from Max von Laue. Not Jew himself, but radically opposed to Nazi ideas, particularly about the Jews, so he was not really happy with getting his medal confiscated and used for the greater glory of the Führer. He sent it to Bohr hoping for the best (illegally -remember, gold was not to be kept).

          Then Germany invaded Denmark and this was a serious problem, of course: both for Bohr, which had been trusted with the medals; and potentially lethal for von Laue, because the name of the awardee is in big letters in the medal itself! So yeah, disposing of the gold was of essence.

      1. I bet someone could 3D print one using the model in the video. Just kidding, but I bet the parts could be machined via CNC not to expensively and then sold as a kit. I would definitely buy a kit.

  2. If we’re talking about the history of the Curta – A big part of this history is Road Rally and Stage Rallies in the US. Co-Drivers used these mechanical wonders to compute speed and distance on the move. This took the sport to a whole new level of technical accuracy. Even after the digital calculators came out in the 70’s, the rugged, no batteries needed Curta was still often used.

    Checkout a manual to use your Curta for TSD Rally:

    I obtained one in good working condition a few years ago, and I cherish it.
    – Kris

  3. Wow… That was just… That was engineering porn. Plain and simple. :] But dammit, now I won’t be satisfied until I’ve produced a functional replica with my mill and lathe… (Since, looking at eBay, the prices for an original range from ‘comparable to one of my machine tools’, to ‘comparable to all of my tools combined’.)

    If I ever start on such a fool’s errand– starting with making the CAD files –you can bet your ass HAD will hear about it. ;D

  4. The neat thing is with today’s technology many of the multi-part assemblies in a Curta could be multi-axis CNC machined as a single piece, eliminating several fasteners and (if enough were made) drastically reducing the cost of updated replicas.

    Another cost saving could come from injection molding of some parts using plastics that are every bit as strong as the metals used in the original.

    1. I was thinking the same thing– using modern CNC manufacturing to reduce the part count, especially on some of the shafts –but judging from the assembly process, having all those individual parts was as much about ease of assembly as it was ease of manufacture. The major exception possibly being the drum itself… But I’m not sure whether it’d be simpler to CNC the drum, or just do the original ‘leaves’ but have them laser or waterjet cut. I’m pretty sure the latter would be a lot more economical though.

      (I wish the aspect ratio wasn’t screwed up. It annoyed me enough to use one of those shady YouTube ripping sites to download the video so I could watch it in MPC with the correct aspect…)

  5. I loved the explanation and graphics in the video almost as much as the Curta itself. I wonder what program was used to animate the model? I have done 3D CAD work with TurboCAD and SketchUp, but neither of the versions I have do simulations easily. I love using CAD to model an object but would really be able to see how the parts interact.

    I’ve tried the “Physics” plug-in for SketchUp, but never quite got the hang of it.

    HAD needs to do a follow up with the Curta2.

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