Gear Ratio Calculator
Find gear ratio, output speed, and output torque from tooth counts.
Reduction — slower output, more torque
Gear ratio = driven (output) teeth ÷ driver (input) teeth. A 20-tooth driver turning a 60-tooth driven gear gives 60 ÷ 20 = 3.00 : 1. At 1500 RPM and 50 N·m in, the output turns at 500 RPM with 150 N·m — the ratio trades speed for torque, slowing the shaft threefold while tripling its turning force.
What a gear ratio tells you
A gear ratio compares how fast the input turns to how fast the output turns. It is fixed entirely by the tooth counts: divide the driven (output) gear’s teeth by the driver (input) gear’s teeth. A ratio written 3.00 : 1 means the input spins three times for every one turn of the output. Because power is roughly conserved in an ideal, lossless mesh, whatever speed the output loses it gains back as torque.
Output speed = input speed ÷ ratio · Output torque = input torque × ratio (ideal, lossless)
Worked example
A 20-tooth pinion drives a 60-tooth gear, with the motor spinning at 1500 RPM and delivering 50 N·m. What comes out the other side?
- 1 Count the teeth. Driver (input) = 20 teeth; driven (output) = 60 teeth.
- 2 Divide driven by driver. ratio = 60 ÷ 20 = 3.00, written 3.00 : 1.
- 3 Scale the speed down. Output speed = input ÷ ratio = 1500 ÷ 3.00 = 500 RPM.
- 4 Scale the torque up. Output torque = input × ratio = 50 × 3.00 = 150 N·m.
Reading the ratio
How the numeric ratio maps to the behaviour of the output shaft.
| Ratio | Name | Effect on the output |
|---|---|---|
| Greater than 1 | Reduction | Slower than the input, with more torque |
| Exactly 1 | Direct drive | Same speed and torque as the input |
| Less than 1 | Overdrive | Faster than the input, with less torque |
Speed and torque trade off
Gears cannot create energy, so they swap speed for torque and back. A reduction (ratio > 1) slows the shaft but multiplies its turning force — useful for climbing hills or lifting loads. An overdrive (ratio < 1) does the reverse, spinning faster at the cost of torque. These figures are ideal: a real mesh loses a few percent to friction, so measured output torque runs slightly below input × ratio. For a compound gear train, multiply the individual stage ratios together to get the overall ratio.