Gear Ratio Calculator

How the gear ratio works

The gear ratio is the ratio of teeth on the driven gear to teeth on the driving gear:

Ratio = N_driven ÷ N_driver

Output speed divides by the ratio and ideal output torque multiplies by it (minus losses):

RPM_out = RPM_in ÷ Ratio     T_out ≈ T_in × Ratio × η

The efficiency factor η captures mesh losses — a single spur mesh runs roughly 98–99%, each additional stage subtracts again, and worm gears can drop to 50–90%. Power is conserved apart from those losses: you can never get more power out than in, only trade speed for torque along the way.

Worked example

A 12-tooth pinion drives a 36-tooth gear at 1800 RPM. Ratio = 36 ÷ 12 = 3:1. Output speed = 1800 ÷ 3 = 600 RPM. A 10 N·m input torque yields roughly 29.4 N·m at the output with 98% mesh efficiency (10 × 3 × 0.98). This 3:1 reduction is why e-bike mid-drives climb steep grades: the motor spins fast with small torque, the gears convert that into wheel torque.

Compound and idler gears

An idler gear between driver and driven changes rotation direction but not the overall ratio. Compound trains multiply: total ratio is the product of each stage's ratio (two 3:1 stages = 9:1). For belt and chain drives the same math applies with sprocket or pulley tooth counts.

Frequently asked questions

1. What is the gear ratio formula?

Ratio = teeth on driven gear ÷ teeth on driving gear. A 36-tooth gear driven by a 12-tooth pinion gives 36/12 = 3:1 — the output spins at one third the speed with three times the ideal torque.

2. How do I calculate output RPM?

Divide the input RPM by the gear ratio. At 1800 RPM into a 3:1 reduction, the output turns at 600 RPM.

3. Does an idler gear change the ratio?

No. An idler only reverses output direction; the speed ratio still depends only on the first driver and last driven gear.

4. Why is real output torque lower than the ideal multiplier?

Mesh friction, bearing drag and lubricant churning consume a few percent per stage. A single spur mesh is about 98–99% efficient; multiply the ideal torque by the stage efficiencies to get the realistic value.