Shaft Power Calculator

The Fundamental Power Equation

Mechanical power transmitted through a rotating shaft is the product of torque and angular velocity:

P = T * omega

• P: Power (Watts) - rate of energy transfer
• T: Torque (N*m) - rotational force times lever arm
• omega: Angular velocity (rad/s) = RPM * pi / 30

This fundamental relationship governs all rotating machinery: motors, generators, pumps, compressors, gearboxes, and more.

Unit Conversions - Power

• 1 Horsepower (HP) = 745.7 Watts = 0.7457 kW
• 1 Kilowatt (kW) = 1000 Watts = 1.341 HP
• 1 Metric Horsepower (PS) = 735.5 Watts
• Common conversion: HP to kW multiply by 0.7457

Unit Conversions - Torque

• 1 N*m = 0.7376 lb*ft = 8.851 lb*in
• 1 lb*ft = 1.3558 N*m = 12 lb*in
• 1 kg*m = 9.80665 N*m (force, not mass)
• Common conversion: N*m to lb*ft multiply by 0.7376

Practical Formulas

For quick calculations without converting to SI units:

• Metric: P (kW) = T (N*m) * RPM / 9549
• Imperial: HP = T (lb*ft) * RPM / 5252
• Also: HP = T (lb*in) * RPM / 63025

The magic numbers 9549, 5252, and 63025 come from combining unit conversions with the factor 2*pi/60.

Mechanical Advantage in Drive Trains

When power passes through gears, belts, or chains:

• Speed Reduction: Lower speed = Higher torque (minus losses)
• Speed Increase: Higher speed = Lower torque (minus losses)
• Gear Ratio: Output Torque = Input Torque * Ratio * Efficiency
• Power: Remains constant (minus efficiency losses)

A 10:1 speed reducer increases torque by 10x (minus ~2-5% losses per stage).

Efficiency Losses

Real-world power transmission always involves losses:

• V-Belt Drive: 93-98% efficiency (2-7% loss)
• Timing Belt: 95-99% efficiency
• Roller Chain: 95-98% efficiency
• Helical Gears: 96-99% efficiency per mesh
• Worm Gear: 50-90% efficiency (depends on ratio)
• Bearings: 98-99.5% efficiency each

Multiple stages compound: 95% * 95% * 95% = 85.7% overall efficiency.

Motor Selection Considerations

• Service Factor: Motors typically rated with 1.0-1.25 service factor
• Starting Torque: May need 150-300% of running torque
• Duty Cycle: Continuous, intermittent, or variable
• Oversize: Common practice to select next larger standard size