The gear finder (for a given ratio) uses a data base to dramatically speed things up. I tried a brute force method first and after 12 or so hours I stopped it. While a brute force method will find the results the time taken makes it un usable. For a quadruple reduction (8 gears) there are about 360,040,606,269,696 permutations with a choice of 66 gears from 12 to 100 teeth that I can make with my dividing head.

ShopCalc does not come with the data base because the gears you can cut depends on the dividing head/rotary table setup you have. It is imperative that you first select the your dividing head/rotary table and any custom hole plates you may have. Building the data base will take 5 to 10 minutes and will happen automatically when you make your first calculation. Should your dividing head/rotary table change at any time (including custom hole plates) then your data base needs to be rebuilt. To do this go to the folder where ShopCalc lives and either delete or rename "DoNotEditOrDelete.dat". Renaming is good if you want to be able to swap back and forth. The next time you do a calculation a new data base will be built.

Specifying the ratio say 1.25 - 1, that means 1.25 turns on the input gear to get 1 turn on the output gear (just to avoid any confusion) and give a speed reduction. While 0.8 - 1 means 0.8 turns on the input gear gives 1 turn of the output gear, a speed increase. (0.8 - 1 is the inverse of 1.25 - 1)

Select the smallest and largest gears, 20 and 50 work well and will find most ratios.

Results is the most you want to be presented to you, 10 to 15 is lots

The error percent that is acceptable (to a minimum of 0.001 percent). Then select + - error or + error or - error.

Press the "Calculate" button and get your solutions.

A word about accuracy. Computers do not handle decimal numbers at all computers use fractional numbers and then display as a decimal number. There are very few decimal numbers that work out correctly as fractional numbers, computers just get as close as they can. The data base will only store 6 decimal digits so all the calculations are only to 6 decimal digits accuracy. For practical purposes this lots of accuracy.

The displayed results are in the form of fractions with the drivers on the top and the driven gears on the bottom.

A search for a ratio of 1.99 to 1 with a maximum error of 0.01%, returns

With an actual ratio of 1.9900002538006649577321892845359 but is shown as 1.99 because of rounding. The "Error" is shown as 0.0% but the error is 2.538006325885013763927150072e-9% ,there is a very slight error and for most purposes irrelevant. All values shown are rounded to the 6th decimal digit so if the error shows as 0.0% then it could still not be an exact ratio.

If you have forgotten your fractions there is just one thing you need to remember. The driver gears can be swapped around as can the driven gears, the order makes no difference to the gear ratio. Swapping the gears around can be useful for mechanically making things fit. Just do not swap driver gears with driven gears.

The results. This calculator will show you results using the least amount of gears. In testing the absolute worst case I could come up with was a 6 gear (3 drivers and 3 driven gears). The calculator will try up to an 8 gear gear train before giving up.