Work & Power Calculator
Calculate work from force and distance, power from work and time or from force and speed, and the efficiency of a machine. Solve for any value, in watts, kilowatts or horsepower.
How to Use
- Choose an equation and the value to find: work, force, distance or angle; power, energy or time; power, force or speed; or efficiency.
- Enter the known values with their units. Force can be in newtons, pound-force or kilogram-force, so 50 kgf is the weight of a 50 kg load.
- For work, give the angle between the force and the direction of motion: 0° when pushing straight along it, 90° when the force does no work.
- Read the answer and its conversions: power in horsepower, energy in kilowatt-hours and kilocalories. Add a time in Work mode to get the power too.
- Check the diagram and the Show Work section for each step.
Worked Example
Lifting a 50 kg sack onto a 2 m platform in 3 s. The force needed is its weight, F = mg = 50 × 9.80665 = 490.3 N, along the motion (θ = 0°). W = Fd = 490.3 × 2 = 980.7 J, and P = W ÷ t = 980.7 ÷ 3 = 326.9 W, or 0.44 hp.
Pulling a sled 50 m with 200 N along a rope at 30°. Only the horizontal part of the pull, 200 × cos 30° = 173.2 N, moves the sled forward, so W = 200 × 50 × cos 30° = 8,660 J. Pulling level would do 10,000 J over the same distance.
The common mistake: using the mass as the force. W = 50 × 2 = 100 is not the work done lifting 50 kg by 2 m; 50 is a mass in kilograms, not a force. Multiply by g first: 50 kg weighs 490.3 N, so the work is 980.7 J, nearly ten times as much. (Entering 50 kgf here does that conversion.)
Show Work
Formulas
Horses, Watts and Joules
James Watt needed a way to sell his improved steam engines to mine and mill owners who used horses, so in the 1780s he defined the horsepower as 33,000 foot-pounds of work per minute, which is 550 foot-pounds per second or 745.7 W. Horsepower is still the usual rating for car engines in the US and UK.
The word work in its physics sense comes from Gaspard-Gustave Coriolis, who in 1829 defined it as force times the distance moved. The unit of power was named after Watt when the British Association for the Advancement of Science adopted the watt in 1882, at the suggestion of William Siemens; the joule, the unit of work, honours James Prescott Joule, who measured how much heat a given amount of work produces.
One watt is one joule per second, so energy bills in kilowatt-hours are really bills for work: 1 kWh is 1,000 W kept up for an hour, 3.6 million joules.
About This Calculator
This calculator covers the three equations of mechanical work and power, W = Fd cos θ, P = W/t and P = Fv, plus efficiency, and solves each one for any of its values, including the angle at which a force acts. In Work mode an optional time also gives the power.
Forces can be entered in newtons, kilonewtons, pound-force or kilogram-force; energies in joules, kilojoules, watt-hours, kilowatt-hours, kilocalories, foot-pounds or BTU; and powers in watts, kilowatts, horsepower or metric horsepower. Everything runs in your browser; nothing is sent anywhere.
Related tools: Kinetic & Potential Energy Calculator, Force Calculator, and Momentum & Collisions Calculator.
Frequently Asked Questions
What is the difference between work and power?
Work is energy transferred by a force, in joules; power is how fast it is transferred, in watts (joules per second). Lifting 50 kg by 2 m is 980.7 J of work whether it takes 3 s or 30 s, but that is 327 W in 3 s and only 32.7 W in 30 s.
Why does the angle of the force matter?
Only the part of the force along the motion does work: W = Fd cos θ. Pulling a sled 50 m with 200 N along a rope at 30° does 8,660 J, not 10,000 J. Carrying a bag along a level path, with the force straight up at 90°, does no work on it at all.
How many watts is one horsepower?
James Watt’s mechanical horsepower is 550 foot-pounds per second, 745.7 W. The metric horsepower (PS) is 735.5 W. A car needing 600 N of thrust at 25 m/s (90 km/h) uses P = Fv = 15 kW, or 20.1 hp.
How do I work out my power when climbing stairs?
Your weight times the height climbed, divided by the time. A 70 kg person climbing 3 m in 4 s does 70 × 9.80665 × 3 = 2,059 J of work, a power of 515 W or 0.69 hp. In this calculator, enter the force as 70 kgf.
What does efficiency mean?
The share of the input that comes out as useful work: η = output ÷ input. A motor drawing 750 W that delivers 600 W of mechanical power is 80% efficient; the other 150 W becomes heat. To deliver 600 W at 80%, it must draw 600 ÷ 0.8 = 750 W.
How do I use the Work & Power Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Electricity use
A 100 W bulb left on for an hour uses 360 kJ, or 0.1 kWh; a 2 kW heater for 30 minutes uses 1 kWh.
Vehicles
Overcoming 600 N of drag at 25 m/s takes 15 kW (20.1 hp), which is 16.7 kWh for every 100 km.
Cranes and hoists
Raising a 1 t load by 10 m is 98.1 kJ of work; doing it in 20 s needs 4.9 kW, about 6.6 hp, before motor losses.
Fitness
A 70 kg person running up 3 m of stairs in 4 s produces 515 W, about 0.69 hp.
Motors and pumps
A pump delivering 600 W from 750 W of electricity is 80% efficient and sheds 150 W as heat.
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