Torque with Horsepower and Speed Calculator

This calculator links torque, mechanical shaft power, and rotational speed. Choose the variable to calculate, then enter the other two. It can determine transmitted torque from horsepower and rpm, power from torque and rpm, or rpm from power and torque.

The formulas

Rotational mechanical power is P = Tω, where T is torque and ω is angular velocity. For speed N in revolutions per minute, ω = 2πN/60. Therefore T = P/ω, P = Tω, and N = 60P/(2πT). The calculator converts inputs to watts, newton-metres, and radians per second before solving.

Solve in any direction

• Torque (T) — enter mechanical shaft power and rotational speed.
• Shaft power (HP or P) — enter torque and rotational speed.
• Rotational speed (N) — enter mechanical shaft power and torque.

Worked example

A shaft transmitting 100 hp at 1,750 rpm has an angular velocity of 183.26 rad/s and transmits 300.12 lbf·ft of torque, equivalent to 406.91 N·m. Solving backward with that torque and speed returns 100 hp.

Use mechanical shaft power

HP or P must be the mechanical power at the shaft section where torque is required. Electrical motor input includes motor losses and will overstate shaft power unless efficiency is applied. Likewise, pump hydraulic power is lower than shaft power because the pump has hydraulic and mechanical losses. Use brake horsepower or measured shaft power when available.

Keep torque, power, and speed at the same point

A gearbox changes torque and speed while approximately conserving power minus losses. Do not combine motor-side rpm with pump-side torque, or power measured before a lossy transmission with values after it. Convert all three variables to the same shaft location and operating condition.

Assumptions and limits

• Power, torque, and speed are steady or consistently averaged values from the same operating point.
• The calculation represents transmitted mechanical power and does not add drivetrain efficiency or service factors.
• It does not calculate starting, accelerating, stall, jam, impact, or torsional-vibration peak torque.
• Mechanical horsepower is used in US mode, not metric horsepower (PS).
• The result is operating torque, not a shaft, coupling, gearbox, or motor torque rating.