Work Calculator
W = Fd cos θ, including the case that comes out zero.
W = Fd cos θ, including the case that comes out zero. Work is force times distance times the cosine of the angle between them.
Optional — gives the power.
Work done (joules)
1,000
200 W · 0.2682 hp
W = Fd cos θ. Only the component of the force along the direction of motion counts, which is why the angle matters: at 0° just 100 N of the 100 N applied is doing anything useful.
How the Work Calculator works
Work is force times distance times the cosine of the angle between them. The cosine is what surprises: carrying a heavy box across level ground does no work on the box at all, because the force is vertical and the motion horizontal.
Also known as: work done calculator · work formula physics · force times distance calculator · how to calculate work
The cosine nobody expects
W = Fd cos θ. Only the component of force along the direction of motion counts, and at 90° that component is zero.
So carrying a heavy box across level ground does no work on the box. The force holding it is vertical; the motion is horizontal; nothing is transferred.
But it feels like work
It certainly does, and your muscles are genuinely burning energy — just not on the box. Holding a load requires continuous cycles of muscle fibres contracting and releasing, which costs energy without moving anything.
A table holding the same box does zero work and consumes nothing, which is the cleanest way to see that the physics definition is about energy transferred to the object rather than effort expended by the carrier.
This is also why work can be negative: friction and braking apply force against the motion, so energy flows out of the object rather than into it.
Where to go next
The Work question rarely arrives on its own. These are the ones that usually come with it:
- Power Calculator — Watts, kilowatts and horsepower, with a running cost.
- Kinetic Energy Calculator — ½mv², and why doubling speed quadruples the damage.
- Force Calculator — F = ma, in newtons, kilograms-force and pounds-force.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What is the work formula?
W = Fd cos θ. A 100 N force over 10 metres in the same direction does 1,000 joules of work.
Why is carrying a box zero work?
Because the force holding it up is vertical while the motion is horizontal, and cos 90° is zero. Your muscles are working hard, but against themselves — no energy is transferred to the box.
What is the difference between work and power?
Work is an amount of energy transferred; power is how fast it is transferred. The same work done in half the time needs twice the power.
Can work be negative?
Yes — when the force opposes the motion, as with friction or braking. The energy flows out of the object rather than into it.
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Related calculators
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Watts, kilowatts and horsepower, with a running cost.
OpenKinetic Energy Calculator
½mv², and why doubling speed quadruples the damage.
OpenForce Calculator
F = ma, in newtons, kilograms-force and pounds-force.
OpenSpeed Distance Time Calculator
Any one of the three from the other two, in four units.
Open