πͺ Work Calculator
Calculate W = FΒ·dΒ·cos(ΞΈ), work done by a force.
Result
How to Use This Calculator
This calculator finds the work done by a constant force. Enter the force magnitude, the distance moved, and the angle between the force and the displacement.
Enter the force in newtons.
Enter the distance in meters that the point of application moves.
Enter the angle in degrees between the force direction and the direction of motion. Use 0 when pushing straight along the motion.
Click Calculate. The work appears in joules: positive, negative, or zero.
The Work Formula
Work is energy transferred by a force acting through a distance, but only the component of force along the motion counts. That is the job of cos(theta): it projects the force onto the displacement direction. Push straight along (theta = 0Β°) and every newton works. Push at a right angle and none of it does. Push backward and the work goes negative, draining energy instead of adding it.
This definition powers the work-energy theorem: the net work done on an object equals its change in kinetic energy. It is the bridge between forces and energy, letting you skip the detailed motion and jump straight from pushes to speeds. Roller coaster designers use it constantly: gravity does positive work downhill and negative work uphill, trading height for speed and back.
Worked Example
Where This Comes Up
Every engine and motor is rated by how fast it does work, which is power, but the work itself is what moves the world: lifting elevators, pumping water, accelerating cars. Physiotherapists estimate joint work during rehab exercises, and ergonomists redesign tasks to cut the work (and the injuries) that jobs demand.
Angle errors are the standard trap. Students plug in F x d and forget the cosine, which is fine only for straight pushes. The other is confusing work with effort: holding a plank is exhausting and zero work, while a crane lifting the same load slowly does real work. Physics counts displacement, not sweat.
Frequently Asked Questions
Why does carrying a bag horizontally count as zero work in physics?
Work needs force along the displacement. Your upward force is vertical while you walk horizontally, so theta = 90 degrees and cos(90Β°) = 0. Your muscles burn energy, but physics work is zero.
Can work be negative?
Yes. When the force opposes the motion, like friction or a brake, theta exceeds 90 degrees and the cosine goes negative. Negative work removes energy from the object.
What are the units of work?
Joules (J). One joule is one newton of force applied over one meter. Energy and work share the unit because work is energy transferred.
What is the difference between work and power?
Work is the total energy transferred; power is how fast it happens. Doing 1,000 J of work in 10 s is 100 W, but the same work in 1 s is 1,000 W.
Does holding a heavy weight count as work?
No. Without displacement there is no work, regardless of effort. Your arms get tired from continuous muscle contraction, but d = 0 makes W = 0.