How to Calculate Gear Ratio: Teeth, Stages and Electronic Gearing
Apr 11, 2026
A gear ratio sets how much a stage reduces speed and multiplies torque between a motor and its load. This guide covers the ratio from tooth counts, trains with multiple gears, and the electronic gear ratio on a servo drive: the numbers you need to size a gearbox, a belt or sprocket stage, or a servo axis.
Machine design, not vehicles. This guide covers gearboxes, pulley and sprocket stages, and servo drives. It does not cover axle ratios, final drives or tire-size gearing for cars.
TL;DR
- From teeth: ratio = driven teeth ÷ driving teeth. A 12-tooth pinion driving a 48-tooth gear is 4:1.
- Multiple stages: multiply the stage ratios. Two 5:1 stages make 25:1. Idler gears do not change the ratio.
- Speed and torque: output speed = input speed ÷ ratio. Output torque = input torque × ratio × efficiency.
- Electronic gear ratio: a servo-drive parameter that scales command units to encoder counts. No teeth involved.
What is a gear ratio?
A gear ratio compares how fast the input shaft turns with how fast the output shaft turns. It is written as input : output, or as a single number.
A gear ratio of 5:1 (or "5") means: - The input turns 5 times for every turn of the output - Output speed = input speed ÷ 5 - Output torque = input torque × 5, minus efficiency losses
A ratio above 1 is a reduction: the output is slower and delivers more torque. A ratio below 1 steps speed up and torque down.
How to calculate gear ratio from the number of teeth
Meshing teeth pass each other at the same rate on both gears, so the tooth counts give the ratio directly:
Ratio = teeth on driven (output) gear / teeth on driving (input) gear
Example: a 12-tooth pinion driving a 48-tooth gear gives 48 ÷ 12 = 4:1. A motor at 3000 rpm turns the output at 750 rpm.
The same formula works for timing pulleys and chain sprockets: count the teeth on each. Flat and V-belt pulleys have no teeth, so use pitch diameters:
Ratio = driven pulley pitch diameter / driving pulley pitch diameter
Pulley Types & Calculations lists pitch diameters for common timing pulleys.
Gear ratio with multiple gears
Idler gears do not change the ratio
In a simple gear train each shaft carries one gear, and the tooth counts of the gears in between cancel out. A 12-tooth driver, a 30-tooth idler and a 48-tooth output gear:
Ratio = (30 / 12) × (48 / 30) = 48 / 12 = 4:1
The idler sets the direction of rotation and the center distance, not the ratio. Each idler reverses the direction once.
Compound gear trains multiply
In a compound train two gears share an intermediate shaft, so their tooth counts no longer cancel. The total ratio is the product of the stage ratios:
Total ratio = Stage 1 ratio × Stage 2 ratio × Stage 3 ratio
Example: a 12-tooth pinion drives a 36-tooth gear (3:1). A 15-tooth pinion on the same shaft drives a 60-tooth gear (4:1). The total is 3 × 4 = 12:1, so a 3000 rpm motor turns the output at 250 rpm.
Stages keep gear sizes practical. A single 12:1 stage with a 12-tooth pinion needs a 144-tooth gear.
The Gear Finder searches your available tooth counts for 1- and 2-stage combinations that hit a target ratio.
Speed vs. torque trade-off
Gears trade speed for torque (or vice versa):
| Higher ratio (e.g. 20:1) | Lower ratio (e.g. 2:1) |
|---|---|
| Much slower output | Slightly slower output |
| Much more torque | Slightly more torque |
| Better for heavy loads | Better for fast motion |
| More precision | Less mechanical advantage |
Efficiency
No gear stage is 100% efficient. Typical efficiency values:
| Gear Type | Efficiency |
|---|---|
| Spur gears | 95-98% |
| Helical gears | 95-98% |
| Planetary gears | 90-95% |
| Belt drive | 95-98% |
| Worm gear | 40-90% (depends on ratio) |
With multiple stages, efficiencies multiply: three stages at 95% each = 0.95³ = 85.7% total efficiency.
Electronic gear ratio (servo drives)
A servo drive has no gear teeth, but it does have an electronic gear ratio, also called electronic gearing or E-gear. It scales the position units the controller commands into encoder counts at the motor. Set it wrong and the axis runs the right profile over the wrong distance.
For an axis with a gearbox and a ball screw:
counts per mm = encoder counts per motor rev × gear ratio / screw lead (mm)
electronic gear ratio = counts per mm / command units per mm
Example: a 20-bit encoder (1,048,576 counts per rev), a 10:1 gearbox, a 5 mm lead screw, and a controller that commands in µm (1000 units per mm):
counts per mm = 1,048,576 × 10 / 5 = 2,097,152
electronic gear ratio = 2,097,152 / 1000 = 262144 / 125
Most drives take the ratio as a numerator and a denominator, so enter 262144 and 125. The fraction is exact. Rounding it to 2097 counts per µm leaves the axis about 0.07 mm short over every metre of travel.
Vendors name and orient the parameter differently. Some define it as counts per command unit, others as the inverse, so check which way round your drive expects it. On CiA 402 drives the same scaling lives in objects 0x608F (position encoder resolution), 0x6091 (gear ratio: motor revolutions per shaft revolution) and 0x6092 (feed constant: feed per shaft revolution).
Finding the right ratio
Use the Gear Finder to find tooth counts for a target ratio across 1 or 2 stages. Then check the whole axis (motor, gear stages and output) in the Drivetrain Builder.