Education
Gear Ratio Calculator
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.
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.
Reduction gear ratio
3 : 1
Driver 12T → driven 36T
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.
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.
Related calculators
- Torque converter for converting between N·m, lb-ft, and other torque units.
- Power converter for power-related unit conversions.
- Frequency converter for RPM-to-Hz conversions on rotational speed.
- Scientific calculator for the underlying arithmetic.
- All education calculators.
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).
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