// physics › Work & Power
Calculate the work done by a force over a distance, allowing for the angle between the force and the movement.
W = F d cosθ
In physics, you do work when you push or pull something and it actually moves. Push a box across the floor — that is work. The bigger the push and the farther it moves, the more work you do. If nothing moves, you did zero work, no matter how hard you strained.
Because the direction you push matters. Only the part of your push that goes the same way the object moves actually helps. If you pull a sled with a rope at an angle, some of your pull lifts the rope upward and is wasted; only the part pulling forward does the work. The 'cos' in the formula measures how much of your push points the right way.
At 0 degrees you push straight along the movement — all your force counts. At 60 degrees, only half of it counts. At 90 degrees (pushing sideways to the movement) none of it counts, so you do zero work. That is why carrying a heavy bag flat across a room does no work against gravity — you lift it straight up, but you walk sideways.
Yes. Push a box with 10 N of force, straight along the floor (angle = 0), and it moves 5 m. The formula is Work = force × distance × cos(angle). At 0 degrees, cos is 1, so it is just 10 × 5 × 1 = 50. You did 50 joules of work. (A newton, N, is a unit of push; a joule, J, is the unit of work and energy.)
Yes, and it is a neat idea. If a force pushes against the movement — like friction dragging on a sliding box, or brakes slowing a car — it does negative work, meaning it takes energy away instead of adding it. That is how brakes stop you.
No. Degrees and radians are just two ways of writing the same angle, like writing a date as '1 Jan' or '01/01'. Use the toggle to switch. The same angle gives the same answer either way — 60 degrees and pi/3 radians are the same turn, so they give identical work.