Gear ratio RPM calculator

What gear-ratio RPM means for a two-gear mesh

Each full revolution of the driving gear advances exactly as many teeth as that gear has, so the driven gear must rotate by driving_teeth over driven_teeth of a revolution. Angular speeds therefore scale with the reciprocal of tooth counts: output_rpm equals input_rpm times driving_teeth divided by driven_teeth. That identity is the same as dividing the input speed by the gear ratio GR, defined here as driven_teeth over driving_teeth, which is the ratio named in the search this page answers. Compound trains, belt ratios, and planetary carriers are out of scope: multiply stage ratios offline or call this endpoint once per mesh.

Input contract, response shape, and error behaviour

Both tooth counts must be whole numbers greater than zero; a zero tooth count, a negative count, a non-integer such as twelve point five, or a non-numeric string is rejected rather than silently truncated. POST a JSON body with three required fields. input_rpm (aliases rpm_in, driver_rpm, n_in, and input_speed) is the driving-shaft speed in revolutions per minute; it must be a finite number, and missing, empty, NaN, or infinite values fail with invalid_input naming the field. driving_teeth (aliases driver_teeth, pinion_teeth, n1, and driving) is the positive integer tooth count on the input gear. driven_teeth (aliases gear_teeth, n2, and driven) is the positive integer tooth count on the output gear. Absolute magnitudes stay within the published limit of one trillion so the quotient remains finite in IEEE double precision on the Worker and in the browser. On success the response echoes the rounded input_rpm, driving_teeth, and driven_teeth, sets gear_ratio to driven_teeth over driving_teeth, sets output_rpm to input_rpm times driving_teeth over driven_teeth, and includes the closed formula string. Failed validation returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item. Prefer JSON numbers when you control the client; numeric strings that match a strict finite decimal pattern are accepted so paste-from-spreadsheet paths keep working without opening the door to arbitrary text.

Where a gear-ratio RPM calculator earns its keep

Keep tooth counts and speeds inside the published range so the scaled output rpm cannot overflow into a non-finite value that the solver must reject. Prefer this capability when you already know motor rpm and the two integer tooth counts of a single mesh and you need the output rpm as the primary answer. If you only need the dimensionless ratio without a speed, a dedicated gear-ratio landing may be a better search match; if you are sizing a four-by-four crawl stack, use a crawl-ratio calculator instead. Pair classroom examples deliberately: twenty driving teeth and forty driven teeth at one thousand rpm yields a two-to-one reduction and five hundred rpm out; eighteen driving and fifty-four driven at thirty-six hundred rpm yields a three-to-one reduction and twelve hundred rpm out; equal counts leave rpm unchanged; and a zero or fractional tooth count demonstrates the hard invalid_input path. This landing targets people searching for a gear ratio rpm calculator, output shaft speed from tooth counts, or driving and driven gear rpm conversion online. It is not a full multi-stage compound gearbox solver, not a bicycle chainring and sprocket development tool, not a crawl-ratio product of first gear, transfer case, and axle, and not a module or diametral-pitch geometry helper. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately pass illegal tooth counts. Round-trip checks are easy: recompute input_rpm times driving_teeth divided by driven_teeth by hand and confirm it equals the published output_rpm within the same twelve-decimal rounding.