Work and power calculator

The formula

$$W = F\,d\cos\theta$$ $$P = \frac{W}{t}$$

$F$ is the force, $d$ the distance the object moves, $\theta$ the angle between the force and the direction of motion, $W$ the work in joules, $t$ the time taken and $P$ the average power in watts.

Where it comes from

Work is how physics counts energy handed over by a force. Push a box along the floor, and the energy you put in grows with how hard you push and how far it goes, so work is force times distance.

Only the part of the force that points along the motion counts. If you pull a sled with a rope at angle $\theta$ above the ground, the rope’s pull splits into a forward part, $F\cos\theta$, and an upward part, $F\sin\theta$. The upward part doesn’t move the sled forward, so:

$$W = (F\cos\theta)\,d$$

At $\theta = 0$ all of the force counts. At $90°$, none does. Carrying a bag across a level room does no work on it in the physics sense, because your upward force is at right angles to the motion.

One joule is one newton pushing through one meter. Power is how fast the work happens: one watt is one joule per second. James Watt defined one horsepower as 550 foot-pounds per second, which is 745.7 W.

Worked example

You push a stalled car with 200 N over 15 m, and it takes 30 s:

$$W = 200 \times 15 \times \cos 0^\circ = 3000\ \text{J}$$ $$P = \frac{3000}{30} = 100\ \text{W}$$

That’s about 0.13 hp, which is a sustainable effort for most people.

Watch out for

• Work can be negative. Brakes push backward while the car moves forward ($\theta = 180°$), so they do negative work and take energy out.
• Average versus peak. $W/t$ is the average. A weightlifter’s peak power during a lift can be several times the average.
• Effort isn’t work. Holding a heavy box still tires your muscles but does no work on the box, because it doesn’t move.

Sources

• OpenStax, University Physics Volume 1, section 7.1 "Work"
• OpenStax, University Physics Volume 1, section 7.4 "Power"

Last checked November 11, 2026