Work and Power Calculator

Calculate the work done by a force at any angle with W = Fd cos θ, and the power from work and time, in joules, watts or horsepower.

Work done

W = F d cos θ
Solve for
W
Work done
1,558.85J
1 sig figs: 2000
≡
Same value in
1.559 kJ
0.001559 MJ · 372.6 cal · 0.3726 kcal
  1. Rearrange: W = F d cos θ
  2. Substitute: F = 150 N, d = 12 m, θ = 30 ° (converted to SI units first).
  3. Result: W = 1,558.85 J, rounded to 1 significant figures because the least precise input has 1.

Power

P = W ÷ t
Solve for
P
Power
600W
1 sig figs: 600
≡
Same value in
0.6 kW
0.0006 MW · 600,000 mW · 0.8046 hp
  1. Rearrange: P = W ÷ t
  2. Substitute: W = 36 kJ, t = 60 s (converted to SI units first).
  3. Result: P = 600 W, rounded to 1 significant figures because the least precise input has 1.

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Worked example

You pull a sled 12 m with a 150 N force along a rope angled 30° above the ground. W = 150 × 12 × cos 30° = 1560 J. Only the horizontal part of the pull (130 N) does work; the vertical part just lightens the sled. If it takes 20 s, your power is 1560 ÷ 20 = 78 W.

Frequently asked questions

What is the formula for work?
W = F d cos θ, where F is the force, d the distance moved and θ the angle between the force and the direction of motion. If the force is along the motion, θ = 0 and W = Fd. Unit: joule (N·m).
When is no work done?
When the object does not move (d = 0), or the force is perpendicular to the motion (cos 90° = 0). Carrying a bag horizontally at constant speed does no work on the bag against gravity.
What is the formula for power?
P = W ÷ t, the rate of doing work, in watts (J/s). Equivalent forms: P = Fv for a constant force at speed v, and P = E ÷ t for energy transfer.
How many watts is one horsepower?
One mechanical horsepower is 745.7 W. A 150 hp car engine delivers about 112 kW at peak.
What is a kilowatt-hour?
Energy, not power: 1 kW for 1 hour = 3.6 × 10⁶ J. It is the unit on electricity bills.