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.
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
Checked against published worked examples from: Naval Education and Training Professional Development and Technology Center (US Navy).
Details, formula, and sources
Formula or tablestage_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.
Source and editionFirst-principles gear math; AGMA 2000 (gear classification) for tolerance by name.
Free accessFree at agma.org for the AGMA standards table of contents.
What governsEstimate. AHJ and licensed mechanical contractor govern. ACCA Manual J / D / S supersede rules of thumb.
API field namesstages, 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 a tooth count below 18 undercuts a standard 20-degree full-depth spur tooth (2/sin^2 20 deg = 17.1; about 14 is the practical minimum)first-principles gear geometry