Ratio
Ratio Z₂/Z₁.
Mechanics · Transmission and rotation
Gear ratio, output speed and torque
Enter the driver and driven gears, then input speed and torque.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Output speed
Driven gear speed.
Output torque
Torque after efficiency.
Relation and numerical substitution
i = Z₂ / Z₁ ; n₂ = n₁ / i ; T₂ = T₁ · i · η—
Two external gears. Positive integer tooth counts. Backlash and dynamics ignored.
01Formulas and symbols
Formulas used
i
Z₂ / Z₁Ration₂
n₁ / iOutput speedT₂
T₁ · i · ηOutput torque02Assumptions and limits
Scope of validity
- Two external gears.
- Positive integer tooth counts.
- Backlash and dynamics ignored.
03Validation example
Reference numerical case
- 20/60 teeth, 1,500 rpm, 10 N·m, η = 95%.
- i = 3, n₂ = 500 rpm, T₂ = 28.5 N·m.
04References
Technical references
- External gear kinematic relations.
- Power conservation with efficiency.
Power transmission
Relations between torque, power, speed and ratio
A ratio trades speed for torque without creating power. Efficiency reduces the torque actually available.
Torque from P and n
With P in kW and n in rpm, the result is in N·m.
T = 9,549.3 · P / nRatio
Gears: Z₂/Z₁. Pulleys: D₂/D₁ without slip.
n₂ = n₁ / iOutput torque
Apply the ratio and then the efficiency.
T₂ = T₁ · i · η