What Is the Work and Power Calculator Formula?
Work is the energy transferred when a force moves an object through a distance, measured in joules (J) in the SI system. One joule is the work done by a force of one newton acting over one metre. Power is the rate of doing work, measured in watts (W), where one watt equals one joule per second.
The work formula is W = F × d × cos θ, where W is work in joules, F is the force in newtons, d is the displacement in metres, and θ is the angle between the force and the direction of motion. Power is P = W ÷ t, where t is the time in seconds.
The International System of Units (SI) defines the joule as 1 kg·m²/s² and the watt as 1 J/s. One mechanical horsepower equals about 745.7 watts, and one dietary kilocalorie (kcal) equals 4,184 joules.
How to Use This Work and Power Calculator
Enter the values below and the calculator updates instantly. Each field accepts a choice of units, so you can mix metric and imperial inputs:
- Force: the constant force applied, in newtons, pound-force or kilogram-force. To lift a mass, use its weight (for example 20 kgf for a 20 kg object).
- Distance moved: how far the object travels in metres, feet, miles or other units. This is the displacement along the path.
- Angle: 0° if you push or pull exactly along the motion, 90° if the force is perpendicular (no work), and up to 180° if the force opposes the motion (negative work).
- Time (optional): leave it blank for work only, or enter it to get power in watts and horsepower.
Results are shown in joules, kilojoules, foot-pounds and kilocalories. Pound-force and foot inputs are converted using the international definitions (1 lbf = 4.448 N, 1 ft = 0.3048 m), so the calculator works for US, UK and metric users alike.
How Does the Angle Change the Work Done?
Only the component of force along the direction of motion does work. The table below shows the share of a 100 N force, applied over 10 m, that becomes work at common angles.
| Angle (θ) | cos θ | Work (100 N × 10 m) | Example |
|---|---|---|---|
| 0° | 1.000 | 1,000 J | Pushing a box straight ahead |
| 30° | 0.866 | 866 J | Pulling a sled by a rope |
| 60° | 0.500 | 500 J | Steep rope angle |
| 90° | 0.000 | 0 J | Carrying a bag horizontally |
| 180° | −1.000 | −1,000 J | Friction or braking force |
According to the NASA Glenn Research Center, a force perpendicular to the motion does no work, which is why a satellite in a circular orbit gains no energy from gravity. Under the work-energy theorem, the net work on an object equals its change in kinetic energy.
Frequently Asked Questions
What is the formula for work and power?
Work is W = F × d × cos θ, in joules, where F is force in newtons, d is distance in metres and θ is the angle between force and motion. Power is P = W ÷ t, in watts, where t is the time in seconds.
What is the difference between work and power?
Work is the total energy transferred, in joules, while power is how fast that energy is transferred, in watts. Lifting a 10 kg box 1 m takes about 98 J of work whether it takes 1 second or 10 seconds, but the faster lift needs ten times the power.
Can work be negative or zero?
Yes. Work is zero when the force is perpendicular to the motion (90°) or nothing moves, and negative when the force opposes the motion, as with friction or braking. Negative work removes energy from the object.
How do I convert work and power to horsepower or calories?
Divide power in watts by 745.7 to get mechanical horsepower, and divide work in joules by 4,184 to get kilocalories. This calculator shows both conversions automatically, along with kilojoules and foot-pounds.