Work and Power Calculator
Work is force times the distance moved in the direction of the force. Enter the force, the distance and the angle between them, plus the time taken to get power in watts and horsepower. Choose which of work or power is the headline answer.
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Formula
- Work:
W = F × d × cos θ - Average power:
P = W ÷ t
θ runs from 0° (force along the motion) to 180° (force against it). Inputs are converted exactly: 1 lbf = 4.4482216 N, 1 ft = 0.3048 m, 1 mile = 1609.344 m. Outputs add 1 ft·lbf = 1.3558179 J and 1 mechanical horsepower = 550 ft·lbf/s = 745.69987 W.
Worked example
A 50 N force moves a crate 10 m, with the rope at 60° to the floor, in 5 s.
- Work = 50 × 10 × cos 60° = 50 × 10 × 0.5 = 250 J
- Power = 250 ÷ 5 = 50 W, which is 50 ÷ 745.7 = 0.0671 hp
In line with the motion (0°) the same push does 500 J; at 90° it does no work.
Frequently asked questions
What is the work formula?
W = F × d × cos θ, where θ is the angle between the force and the direction of motion. A 50 N push along 10 m in a straight line does 50 × 10 × cos 0° = 500 J.
Why does the angle matter?
Only the part of the force along the motion does work. Pulling a sled with a rope at 60° gives 50 × 10 × 0.5 = 250 J; at 90° (such as carrying a bag level) the work is 0 J.
Can work be negative?
Yes. If the force points against the motion (angle above 90°), it removes energy. Friction acting opposite to a 10 m slide with 50 N does 50 × 10 × cos 180° = −500 J.
How do I calculate power from work?
Power is work divided by time, P = W ÷ t. Doing 250 J in 5 s takes 50 W. One mechanical horsepower is 550 ft·lbf per second, exactly 745.7 W, so 50 W is about 0.067 hp.
How do I convert between joules and foot-pounds?
One foot-pound-force is exactly 1.3558179 J. Lifting a 20 lbf weight 15 ft straight up is 300 ft·lbf, or 300 × 1.3558179 = 406.7 J; at 30° to the motion it is 259.8 ft·lbf.