About the Work and Power Calculator (Physics)
This work calculator finds the mechanical work done when a force moves an object through a distance, using W = F·d·cos θ. Enter the force (in newtons, kilonewtons, pounds-force or dynes), the distance moved (metric or imperial) and the angle between the force and the direction of motion. Add the time taken and the calculator also gives the average power in watts and horsepower.
It is built for physics students solving work-energy problems, teachers checking worksheets, and anyone estimating the effort of pulling a sled, pushing a cart, winching a load or climbing stairs. Results are shown in joules and converted to kilojoules, food kilocalories and foot-pounds so they are easy to compare.
The calculator assumes a constant force and straight-line motion. Only the component of the force along the motion does work: at 90° the work is zero, and beyond 90° it becomes negative, as with friction or braking that removes energy.
With the default inputs, the work done is 1,000 J. Change any value above to recalculate instantly.
How to use the work and power calculator (physics)
- 1Enter the force and choose its unit.
- 2Enter the distance moved and its unit.
- 3Set the angle between the force and the direction of motion (0° if they line up).
- 4Add the time taken to also get power.
- 5Read the work in joules and the conversions, and check the chart for other angles.
Formula and method
Work is the energy transferred when a force moves an object. Only the part of the force that points along the displacement counts, which is F cos θ, so W = F·d·cos θ. With force in newtons and distance in metres, work is in joules (1 J = 1 N·m). The calculator converts pounds-force, kilonewtons, dynes, feet, inches and other units to SI first.
Average power is the rate of doing work, P = W ÷ t, measured in watts (joules per second). One mechanical horsepower is 745.7 W. Energy conversions use 1 kcal = 4,184 J and 1 ft·lbf = 1.35582 J.
- W
- Work done (J)
- F
- Magnitude of the applied force (N)
- d
- Distance moved (m)
- θ
- Angle between force and direction of motion
- P
- Average power (W)
- t
- Time taken (s)
Worked examples
Pushing a cart 10 m with 100 N
With the force along the motion, W = 100 × 10 × cos 0° = 1,000 J. Done in 5 seconds, the average power is 1,000 ÷ 5 = 200 W, about 0.27 hp.
Pulling a sled with a rope at 30°
Only 50 × cos 30° = 43.3 N acts along the ground, so W = 43.3 × 20 = 866 J. Over 15 seconds that is 57.7 W.
Imperial units: 50 lbf over 10 ft
50 lbf is 222.4 N and 10 ft is 3.048 m, so W = 677.9 J — exactly 500 ft·lbf. In 2 seconds the power is 339 W.
Frequently asked questions
What is the formula for work in physics?+
Work is W = F × d × cos θ, where F is the force, d the distance moved and θ the angle between them. When the force points along the motion, cos 0° = 1 and W = F × d.
What is the unit of work?+
The SI unit of work is the joule (J), equal to one newton of force acting over one metre. Other units include the kilojoule, foot-pound (1 ft·lbf ≈ 1.356 J) and calorie.
Can work be negative or zero?+
Yes. Work is zero when the force is perpendicular to the motion (θ = 90°) or nothing moves, and negative when the force opposes the motion (θ > 90°), such as friction slowing a sliding box.
What is the difference between work and power?+
Work is the total energy transferred, while power is how fast it is transferred. Lifting the same box slowly or quickly does the same work, but doing it faster requires more power.
How many watts is one horsepower?+
One mechanical (imperial) horsepower is about 745.7 watts. Metric horsepower (PS) is slightly smaller at about 735.5 W.