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Calculator Answers

Gear Ratio Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A gear ratio calculator is a mechanical engineering tool used to compute the rotational relationship between two or more intermeshing gears. By dividing the number of teeth on the driven gear by the number of teeth on the driver gear, the calculator determines the mechanical advantage and rotational speed ratio. It can also estimate the output speed in rotations per minute (RPM) and the output torque based on input specifications. Automotive mechanics and robotics engineers use this tool to design drive systems, optimize gearboxes, and configure vehicle differentials.

Enter the driver and driven gear teeth counts, the input RPM, and an optional input torque. The calculator returns the gear ratio, output RPM, and an ideal output torque estimate.

See also: Torque Converter, Power Converter, and Ratio Calculator.

Quick Answer

Determine the gear ratio between two gears based on their teeth count, and calculate output RPM and torque.

Gear connected to the input shaft. · e.g. 12

Gear connected to the output shaft. · e.g. 36

e.g. 3,000

Any consistent torque unit (N·m, lb-ft, etc.). · e.g. 100

About this estimate

Gear ratio = driven teeth ÷ driver teeth. A ratio greater than 1 is a reduction (slower output, more torque). A ratio less than 1 is an overdrive (faster output, less torque). The output torque calculation assumes 100% efficiency; real gear trains lose 1 to 10% to friction and oil shear per stage.

Educational estimate. Not engineering or drivetrain advice. Production designs account for shock loading, lubrication, backlash, and material limits.

Gear ratio

Reduction gear ratio

3 : 1

Driver 12T → driven 36T

Driver teeth12
Driven teeth36
Gear ratio (driven / driver)3
Input RPM3,000 RPM
Output RPM1,000 RPM
Input torque100
Output torque (ideal)300

Output RPM = input RPM ÷ gear ratio. Output torque ≈ input torque × gear ratio, ignoring drivetrain losses. Real efficiency is 90 to 99% per stage depending on gear type, lubrication, and load.

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Examples

12T → 36T · 3000 RPM · 100 N·m

Ratio 3:1 · 1000 RPM · 300 N·m

20T → 40T · 1800 RPM · 50 lb-ft

Ratio 2:1 · 900 RPM · 100 lb-ft

30T → 12T · 1500 RPM (overdrive)

Ratio 0.4:1 · 3750 RPM

How it works

Gear ratio relates two rotating shafts connected through meshing teeth. A larger driven gear turns more slowly and with more torque; a smaller driven gear turns faster and with less torque. The math is the same for chains, belts, and any mechanism with a clean rolling-without-slipping ratio.

Gear ratio · driven_teeth / driver_teeth

Output RPM · input_RPM / gear_ratio

Output torque (ideal) · input_torque × gear_ratio

Real drivetrains have losses; output torque is slightly lower than the ideal calculation predicts.

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Frequently asked questions

Gear ratio is the ratio of the driven gear's tooth count to the driver gear's tooth count. A 12-tooth pinion driving a 36-tooth wheel has a 3:1 reduction ratio (sometimes written 3.000:1). The driven shaft turns once for every three turns of the driver shaft.

A reduction ratio (>1) slows the output shaft and multiplies torque by the same ratio. A 3:1 reduction divides RPM by 3 and (ideally) multiplies torque by 3. An overdrive ratio (<1) speeds up the output and divides torque. The product of RPM and torque (proportional to power) is conserved minus drivetrain losses.

No. The calculation assumes 100% efficiency. Real gear stages lose 1 to 10% to friction, oil shear, and bearing drag, depending on gear type (spur, helical, worm), lubrication, alignment, and load. Use the result as an upper-bound estimate.

Gear ratio usually refers to a single gear pair. Final drive ratio is the total reduction from the engine output to the wheels, which combines transmission, transfer case, and differential ratios. To find the overall ratio of a multi-stage system, multiply the individual stage ratios.

Yes, in the same way. Replace teeth with sprocket teeth (for chains), belt-pulley diameters, or any consistent measure of effective rolling radius. A 14-tooth front sprocket driving a 42-tooth rear has a 3.0:1 reduction (42 / 14).