Gear Ratio Calculator
Calculate the gear ratio between two meshing gears from their tooth counts.
How to use this tool
- Count (or look up) the teeth on both gears.
- Enter the driven gear (output) teeth and the drive gear (input) teeth.
- The calculator shows the gear ratio and torque multiplication factor.
Determine gear ratio and torque multiplication from the number of gear teeth.
Formula
Gear Ratio = Driven gear teeth ÷ Drive gear teeth
Torque multiplication = Gear Ratio (same value; output torque is input torque × ratio, ignoring friction losses).
How it works
This calculator finds the mechanical advantage between two meshing gears by dividing the tooth count of the driven (output) gear by the tooth count of the drive (input) gear. A ratio greater than 1 means the output shaft turns slower but with greater torque; a ratio less than 1 is an overdrive. The torque multiplication figure assumes 100% mechanical efficiency — real gear meshes lose roughly 1–3% per mesh to friction.
Worked example
Worked example
- Drive gear has 14 teeth; driven gear has 42 teeth.
- Gear Ratio = 42 ÷ 14 = 3.0.
- Torque multiplication = 3.0× — the output shaft produces three times the input torque.
- The output shaft also spins at one-third the input shaft speed.
Gear ratio = 3.0 : 1, Torque multiplication = 3.0×
Key terms
- Drive gear
- The input gear connected to the power source (e.g., engine); it initiates rotation.
- Driven gear
- The output gear that receives motion from the drive gear; its size relative to the drive gear determines speed and torque changes.
- Gear ratio
- The ratio of output gear teeth to input gear teeth, indicating how many times the drive gear must turn for the driven gear to complete one revolution.
- Torque multiplication
- The factor by which output torque exceeds input torque, equal to the gear ratio when mechanical efficiency is 100%.
- Overdrive
- A gear ratio less than 1:1 where the output shaft spins faster than the input shaft, reducing torque but increasing speed.
Frequently asked questions
- How do you calculate gear ratio?
- Gear ratio = driven gear teeth ÷ drive gear teeth. A ratio of 3:1 means the output shaft turns once for every three turns of the input shaft, multiplying torque by 3×.
- Does a higher gear ratio mean more speed or more torque?
- A numerically higher gear ratio (e.g. 4:1 vs 2:1) gives more torque multiplication but lower output speed. Lower ratios give higher speed with less torque amplification.