Work Calculator
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Work is force times the distance moved in the direction of the force: \(W = Fd\cos\theta\). Pulling a sled with 50 N at 60° above the ground for 10 m does \(50 \times 10 \times \cos 60^{\circ} = 250\) J of work.
0° if the force points along the motion.
| Joules | 250 J |
| Kilojoules | 0.25 kJ |
| Foot-pounds | 184.391 ft·lbf |
| Calories | 59.7514 cal |
| Power (work ÷ time) | 50 W = 0.0670511 hp |
Show steps
- Convert: F = 50 N, d = 10 m.
- \(W = Fd\cos\theta = 50 \times 10 \times \cos(60^{\circ}) = 250\ \text{J}\)
- Power: \(P = \frac{W}{t} = \frac{250}{5} = 50\ \text{W}\)
How to use the work calculator
- Enter the force, the distance and the angle between them.
- Optionally enter the time to get the power.
- Press Calculate.
Formula
\(W = Fd\cos\theta\), in joules (1 J = 1 N·m). Power is the rate of doing work: \(P = \frac{W}{t}\), in watts (1 W = 1 J/s).
- θ = 0°: all the force does work, W = Fd.
- θ = 90°: no work (carrying a bag horizontally at steady speed).
- θ = 180°: negative work (friction slowing an object).
Worked example
Lifting a 10 kg box (weight 98 N) up 1.5 m: W = 98 × 1.5 = 147 J. Doing it in 2 s takes P = 73.5 W.
Work and energy
The work–energy theorem says the net work on an object equals its change in kinetic energy. Work done against gravity is stored as potential energy, mgh.
Work and power practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
How do you calculate work?
Multiply the force by the distance and by the cosine of the angle between them: W = Fd cos θ.
Can work be negative?
Yes, when the force points against the motion, like friction or braking.
What is the difference between work and power?
Work is energy transferred (joules). Power is how fast it is transferred (watts = joules per second).
Why is no work done carrying a bag across a room?
The upward force on the bag is perpendicular to the horizontal motion, so cos 90° = 0.
How many joules are in a calorie?
One calorie is 4.184 J; one food Calorie (kcal) is 4,184 J.
Sources
- OpenStax University Physics Volume 1
- OpenStax College Physics 2e
- NIST Special Publication 811: Guide for the Use of the SI
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