Power Transmission Formula
Calculate mechanical power transmitted through shafts, belts, and gears.
Covers torque and RPM relationships.
The Formula
P = T × ω
P = (2π × T × n) / 60
P (hp) = (T × n) / 5252 (T in ft·lb, n in RPM)
P = (2π × T × n) / 60
P (hp) = (T × n) / 5252 (T in ft·lb, n in RPM)
Power transmission formulas relate the torque on a rotating shaft to the power it delivers. Higher torque or higher speed means more power transmitted.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| P | Power transmitted | Watts (W) or horsepower (hp) |
| T | Torque | N·m or ft·lb |
| ω | Angular velocity | rad/s |
| n | Rotational speed | RPM (revolutions per minute) |
Example 1
A motor shaft delivers 50 N·m at 1500 RPM. Find the power in watts.
P = (2π × 50 × 1500) / 60
= (2 × 3.14159 × 50 × 1500) / 60
= 7,854 W ≈ 7.85 kW
Example 2
An engine produces 200 ft·lb of torque at 3000 RPM. Find the horsepower.
P = (T × n) / 5252 = (200 × 3000) / 5252
= 114.2 hp
When to Use It
Use the power transmission formula when:
- Selecting motors and engines for mechanical systems
- Designing shaft sizes for required power loads
- Calculating belt and chain drive specifications
- Converting between torque, RPM, and power ratings