Gear Ratio and RPM Cascade

Per-stage and overall ratio, output RPM, and output torque across up to four gear stages with a per-stage efficiency.

Run the calculator

Example

You enter

Stages N (in) 12, N out 36; N (in) 15, N out 45
Input RPM (optional) 1800
Input torque (lb-in; optional) 100
Per-stage efficiency (0-1) 0.97

You get

Overall ratio 9:1
Output RPM 200
Output torque (lb-in) 846.81

Details, formula, and sources

stage_ratio = N_out / N_in; overall_ratio = product of stage ratios; RPM_out = RPM_in / overall_ratio; T_out = T_in * overall_ratio * efficiency^stages.

First-principles gear math; AGMA 2000 (gear classification) for tolerance by name.

Free at agma.org for the AGMA standards table of contents.

Estimate. AHJ and licensed mechanical contractor govern. ACCA Manual J / D / S supersede rules of thumb.

Field names used by the API: stages, input_rpm, input_torque, efficiency, overall_ratio, output_rpm, output_torque

Per-stage efficiency 0.97 default for spur gears; the user can overridetypical spur-gear practice
Undercut threshold tooth count below 8 risks undercut on a standard 20-degree spur toothfirst-principles gear geometry