Work and Power Calculator

By Calxy · Calculation methodology

Work out the work done by a force over a distance at any angle, the power delivered over a time, or rearrange to find the force, work or time.

Printed from Calxy · https://www.calxy.net/other/work-power-calculator

Work2,000.0000 J
N

0 – 1000000000000000

m

1e-12 – 1000000000000000

°

0° when pushing straight along the direction of motion; 90° does no work.

s

1e-12 – 1000000000000000

Work

2,000.0000 J

  • Work2.0000 kJ
  • Power400.0000 W
  • Kilowatts0.4000 kW
  • Mechanical horsepower0.5364 hp

Assumes a constant force over a straight-line displacement. Work is negative when the force opposes the motion (θ > 90°).

How this was calculated

W = F × d × cos θ = 200 N × 10 m × cos 0° = 2,000 J.

P = W ÷ t = 2,000 J ÷ 5 s = 400 W.

Formulas

Work done by a constant force is W = F × d × cos θ, where θ is the angle between the force and the direction of motion. Pushing straight along the motion (θ = 0°) gives W = Fd; a force at 90° does no work; a force opposing motion (θ = 180°) does negative work.

Average power is work divided by time: P = W ÷ t. One watt is one joule per second, and one mechanical horsepower is 550 ft·lbf/s, which is 745.69987 W.

Worked example

Pulling a sled 10 m with a 200 N force along a rope at 60° to the ground: W = 200 × 10 × cos 60° = 1,000 J.

If that takes 5 s, the power is 1,000 ÷ 5 = 200 W, about 0.27 hp.

Assumptions

The force is treated as constant over a straight-line displacement. For a varying force, split the path into pieces or use the area under a force–distance graph. The power found is the average over the time you enter.

References

Frequently asked questions

What is the difference between work and power?

Work is energy transferred, measured in joules. Power is how fast that energy is transferred, in watts. Lifting a box slowly or quickly takes the same work but different power.

Why can work be negative?

When the force points against the motion, like friction or braking, it removes energy from the object and the work is negative.

How many watts is one horsepower?

One mechanical (imperial) horsepower is 745.69987 W. Metric horsepower (PS) is slightly smaller at 735.49875 W.

Last updated . Results are estimates for informational purposes only.