Work and Power Calculator
The work a force does over a distance, W = Fd cos θ, and the average power, P = W ÷ t, or the energy or time from a power.
Result
Work: 5,000 ft·lbf
A steady force over a straight path; power is the average over the time.
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How to use the Work and Power Calculator
- Choose what to find, the work done by a force, the power from work and time, the energy from a power, or the time.
- For work, enter the force, the distance moved and the angle between them, and optionally how long it took.
- Read the work in foot-pounds or joules and the average power in horsepower or watts.
The formulas
work W = F × d × cos θaverage power P = W ÷ tenergy W = P × ttime t = W ÷ PA joule is a newton metre and a watt is a joule per second. A foot-pound is about 1.356 J, and the mechanical horsepower is 550 ft·lbf per second.
Limits
The force is taken as steady in size and direction over a straight path. A force that varies, such as a stretching spring, or a curved path, needs the work added up piece by piece. Power here is the average over the whole time, not the peak, and says nothing about how efficiently a motor or a person produces it.
With your numbers
- W = F × d × cos θ = 100 lbf × 50 ft × cos 0 ° = 5,000 ft·lbf
- P = W ÷ t = 5,000 ft·lbf ÷ 10 s = 0.909091 hp
Quick reference
A steady force over a straight path; power is the average over the time.
| Example | Result |
|---|---|
| 100 lbf pushed 50 ft in 10 s | Work: 5,000 ft·lbf |
| Lawn mower, 75 N at 35° over 25 m | Work: 1,536 J |
| Pulling 10 N at 120° over 5 m | Work: -25 J |
| Pull-up, 423.36 J in 0.8 s | Average power: 529.2 W |
| 1,500 J in 3 s | Average power: 500 W |
| 1.5 kW for 2 hours | Work: 10,800,000 J |
| 10,000 J at 500 W | Time: 20 s |
Common questions about the Work and Power Calculator
- How do I calculate work done?
- W = Fd cos θ: force times distance times the cosine of the angle between the force and the motion. Pushing a crate with 100 lbf along the floor for 50 ft does 5,000 ft·lbf of work, about 6,779 J. OpenStax University Physics example 7.1 pushes a lawn mower with 75.0 N at 35° below the horizontal for 25.0 m: 75 × 25 × cos 35° ≈ 1,536 J.
- Why does the angle matter?
- Only the part of the force along the motion does work. Pushing down on a mower handle wastes some of the effort pressing it into the ground. At 90° a force does no work at all, and beyond 90° it works against the motion and the work is negative, as friction and brakes do.
- What is the difference between work and power?
- Work is the energy transferred; power is how fast it is transferred, P = W ÷ t. Climbing a flight of stairs takes the same work walking or running, but running takes more power. OpenStax example 7.11 has a pull-up doing 423 J in 0.8 s, about 529 W.
- How many watts is a horsepower?
- The mechanical horsepower is 550 foot-pounds per second, about 745.7 W. OpenStax rounds it to 746 W. The horsepower calculator works from an engine’s torque and speed; this page works from a force, a distance and a time.
- How much energy does a power use over a time?
- Multiply them: W = P × t. A 1.5 kW heater running for 2 hours uses 1,500 W × 7,200 s = 10.8 million joules, which is 3 kWh. The time to deliver a given amount of work at a steady power is W ÷ P.