Gear ratio calculator

Optionally add input shaft speed in any consistent unit (commonly RPM) to receive matching output speed from n_out equals n_in times N1 over N2. Zero or non-positive tooth counts are rejected with a clear invalid_input error so the API never silently divides by zero or invents a mesh.

How to call the API and what comes back

Both tooth counts must be strictly positive; values at or below zero—including exact zero teeth—are rejected. Send a JSON body with two required finite numbers: driver_teeth (aliases N1, teeth_driver, driver, and pinion_teeth) and driven_teeth (aliases N2, teeth_driven, driven, and gear_teeth). Absolute values must stay within the published limit of one trillion so quotients remain finite in IEEE double precision on the Worker and in the browser. Optionally include input_speed (aliases driver_speed, rpm_in, omega_in, and n1) as a finite signed number in the same unit you expect for output_speed, typically revolutions per minute. On success the response echoes rounded driver_teeth and driven_teeth, mirrors them as N1 and N2, sets gear_ratio and ratio to the same rounded GR equals N2 over N1, velocity_ratio to N1 over N2, ratio_string to an N2:N1 style label, transmission to one of reduction, overdrive, or 1:1, formula to the string GR equals N2 over N1, message to a short English summary, and steps to an ordered array of substitution lines. When input_speed is provided the response also includes input_speed, output_speed, and speed_formula for n_out equals n_in times N1 over N2. Failed validation—missing fields, non-finite numbers, values outside absolute limits, non-finite ratio or speed, or zero teeth—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

Keep tooth counts and speeds inside the published absolute range so N2 over N1 and the scaled output speed cannot overflow into non-finite values that the solver must reject. Prefer this capability when you already have N1 and N2 for a single mesh; if your source is a multi-stage box, multiply stage ratios offline or chain calls. Prefer sending JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern, which keeps paste-from-spreadsheet paths working without accepting arbitrary text. Pair classroom examples deliberately: twenty driver teeth and forty driven teeth yields GR equals two and a reduction; forty driver and twenty driven yields GR equals one half and overdrive; equal counts yield one-to-one; and driver_teeth equals zero demonstrates the hard invalid_input path for zero teeth. When you only need the dimensionless ratio, omit input_speed; when you already know motor RPM from a nameplate, send it so homework and firmware tests can assert both GR and n_out in one call. This landing targets people searching for a gear ratio calculator, driver and driven teeth ratio, gearbox reduction calculator, or output speed from tooth counts online; it is not a full multi-stage compound train solver, not a module or diametral-pitch geometry tool, and not a power-loss or efficiency estimator. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately pass zero teeth. Round-trip checks are easy: recompute N2 divided by N1 by hand and confirm it equals the published gear_ratio within the same twelve-decimal rounding, and confirm that n_out equals n_in times N1 over N2 when speed is supplied.