How this calculator works
Power is torque multiplied by angular speed. A shaft spinning faster therefore delivers more power for the same torque. The calculator converts the entered speed to radians per second, multiplies by torque in newton-metres to get watts, and converts the result to the output unit you choose. When you solve for torque or speed, the same equation is rearranged. Mechanical horsepower is 550 foot-pounds-force per second, which is 745.6998715822702 W.
Formula
power (W) = torque (N-m) x angular speed (rad/s). angular speed = 2 x pi x rpm / 60. rpm = power / torque x 60 / (2 x pi). horsepower = watts / 745.6998715822702.
Worked example
100 N-m at 3,000 rpm gives an angular speed of 314.159 rad/s and a power of 31,415.9 W, or 31.4159 kW and 42.1295 hp. Solving the other way, 10 kW at 3,000 rpm needs 31.8310 N-m of torque.
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Frequently asked questions
Why can power rise with engine speed when torque is flat?
Power is torque times angular speed, so the same torque delivered twice as fast delivers twice the power. A torque curve that stays flat therefore produces a power curve that keeps climbing with speed.
What is the 5,252 constant?
With torque in pound-feet and speed in rpm, mechanical horsepower is torque x rpm / 5,252. The constant is 33,000 ft-lbf/min divided by 2 pi, and it comes from the definition of one horsepower.
Which horsepower is used here?
The mechanical or imperial horsepower of exactly 745.6998715822702 W. Metric horsepower (PS) is 735.49875 W and electric horsepower is 746 W, so a value in one convention is not a value in another.