Gear Ratio Formula
Calculate gear ratio from driving and driven gear tooth counts.
Returns RPM reduction, torque multiplication, and compound gear train ratios for machines.
Need to calculate, not just reference? Use the interactive version.
Open Gear Ratio / RPM at Speed Calculator →
The Formula
Gear Ratio = N_driven / N_driver = ω_driver / ω_driven
The gear ratio determines how speed and torque are exchanged between gears. A ratio greater than 1 means the output turns slower but with more torque.
Variables
| Symbol | Meaning |
|---|---|
| N_driver | Number of teeth on the driving gear (input) |
| N_driven | Number of teeth on the driven gear (output) |
| ω_driver | Rotational speed of the driving gear (RPM) |
| ω_driven | Rotational speed of the driven gear (RPM) |
Example 1
A 20-tooth gear drives a 60-tooth gear. The motor spins at 3000 RPM.
Gear ratio = 60 / 20 = 3:1
Output speed = 3000 / 3 = 1000 RPM
Output turns 3x slower with 3x more torque
Example 2
A bicycle: front sprocket has 44 teeth, rear has 11 teeth
Gear ratio = 44 / 11 = 4:1
Each pedal revolution turns the wheel 4 times (high gear = more speed)
When to Use It
Use the gear ratio formula when:
- Designing gear trains for motors and machinery
- Calculating output speed and torque in transmissions
- Choosing bicycle gears for different terrain
- Understanding how clocks, robots, and vehicles work
Key Notes
- Torque and speed trade off inversely: output torque = input torque × gear ratio; a 3:1 ratio triples torque but reduces speed by 3× — power is approximately conserved (minus friction losses)
- For a gear train with multiple stages, the overall ratio is the product: total ratio = R₁ × R₂ × R₃ — a 3:1 stage followed by a 4:1 stage gives a 12:1 overall reduction
- A ratio less than 1 (e.g., 0.5:1) is an "overdrive" — output rotates faster than input; used in bicycle high gears and automotive overdrive to increase top speed at the cost of torque
- Gear ratio from tooth count requires that both gears have the same tooth pitch (module) — mixing gears of different modules will cause binding, noise, and premature wear