Work Calculator - Physics Work Done (W = Fd cos θ)
Calculate physics work done from force, distance, and the angle between force and displacement.
Default 0° means the force acts fully in the direction of motion
Work Done
100 J
How to Calculate Work Done (Physics)
In physics, work is done when a force moves an object through a distance. It equals the force applied multiplied by the distance moved, multiplied by the cosine of the angle between the force direction and the direction of movement. When the force acts exactly along the direction of motion (angle = 0°), cosine is 1 and the formula simplifies to just force × distance.
Example
Pushing a box with 20 N of force across 5 meters in the same direction as the push gives Work = 20 × 5 × cos(0°) = 100 joules. If instead the force were applied at a 60° angle to the direction of motion, Work = 20 × 5 × cos(60°) = 50 joules — only half as much useful work, since part of the force doesn't contribute to the motion.
Common Use Cases
- Physics homework calculating work done by a force over a distance.
- Understanding how an angled force (like pulling a sled with a rope) reduces effective work.
- Estimating energy transferred when lifting, pushing, or pulling an object.
FAQs
What units does the result come out in?
If force is in newtons (N) and distance is in meters (m), the result is in joules (J) — the standard SI unit of work and energy. Keep your input units consistent for the result to make physical sense.
Why does a 90° angle give zero work?
At 90°, the force is applied entirely perpendicular to the direction of motion, so cos(90°) = 0 — none of the force contributes to moving the object along its path, so no work is done in the physics sense, even if the object is moving.
Can work be negative?
Yes — when the angle is greater than 90°, cosine becomes negative, meaning the force opposes the direction of motion (like friction slowing something down). Negative work represents energy being removed rather than added.