Shaft Power Calculator
Calculates the mechanical power transmitted through a rotating shaft given its torque and rotational speed. Use this when sizing motors, gearboxes, or drive shafts in mechanical systems.
About this calculator
Shaft power is the mechanical power delivered by a rotating shaft to a load. It depends on two quantities: the torque (T) applied at the shaft and the angular velocity (ω) at which it rotates. Rotational speed in RPM must first be converted to radians per second using ω = RPM × 2π / 60. The power is then found by multiplying torque by angular velocity: P = T × (RPM × 2π / 60), where P is in watts, T is in newton-metres, and RPM is revolutions per minute. This formula comes directly from the definition of power as the rate of doing work: for rotation, work per revolution equals torque times the angle swept (2π radians), divided by the time per revolution. Engineers use this relationship constantly when matching motors to mechanical loads or calculating drivetrain efficiency.
How to use
Suppose a motor shaft produces a torque of 50 N⋅m and spins at 1,200 rpm. Step 1 – Convert rpm to rad/s: ω = 1,200 × 2π / 60 = 125.66 rad/s. Step 2 – Multiply by torque: P = 50 × 125.66 = 6,283 W ≈ 6.28 kW. Enter 50 in the Torque field and 1,200 in the Angular Velocity field. The calculator returns approximately 6,283 watts, which you can convert to horsepower by dividing by 745.7 (≈ 8.43 hp).
Frequently asked questions
What is shaft power and how is it different from electrical power?
Shaft power is the purely mechanical power transmitted through a rotating shaft, measured in watts or kilowatts. Electrical power input to a motor is always higher than shaft power output because of motor inefficiencies such as heat loss and friction. To find shaft power from electrical power you must multiply by the motor's efficiency factor. This calculator deals only with the mechanical side of the equation.
How do I convert shaft power in watts to horsepower?
One mechanical horsepower equals 745.7 watts. To convert, simply divide your shaft power result in watts by 745.7. For example, 6,283 W ÷ 745.7 ≈ 8.43 hp. Many pump and motor datasheets still list ratings in horsepower, so this conversion is frequently needed in practice.
Why does increasing RPM increase shaft power if torque stays the same?
Power is the rate of doing work, and a shaft rotating faster completes more work cycles per second. Since each revolution transfers energy equal to torque × 2π, more revolutions per second means more energy transferred per second, i.e., higher power. This is why high-performance engines are designed to operate at high RPM: even moderate torque can yield large power outputs at elevated speeds. Conversely, heavy-duty machinery often runs at low RPM but produces enormous torque to achieve the necessary power.