Work Calculator
Solve W = F·d·cos θ for work, force or distance at any angle, and convert work into power over a time — with the rearranged formula shown each way.
W = F·d·cos θ (power: P = W ÷ t)
Work
Formula used for this direction
W = F·d·cos θ
Your values
F = 200 N, d = 15 m, θ = 0
Work Is Energy Transferred
In physics, work has a precise meaning that diverges from the everyday one: it is energy moved from one place or form to another by a force acting through a distance. Both parts are required. No force, no work. No movement, no work — however tiring the effort feels.
The cos θ term handles direction. Only the component of force lying along the direction of motion transfers energy. Push a trolley straight ahead and every newton counts; push it at an angle and only part of your effort does anything useful.
Worked example — pushing a crate 15 metres
A steady 200 N, straight along the direction of travel:
W = 200 × 15 × cos 0° = 3,000 J (3 kJ)
Push at 60° instead — leaning down on it as you shove — and only 1,500 J gets transferred. Half your effort is pressing the crate into the floor, which increases friction and actively works against you.
Carry it 15 m instead, force straight up and motion straight ahead: 0 J. Exactly zero, no matter how heavy the crate.
Drag against it at 180°, as friction does: -3,000 J — negative, energy removed.
A second example — the same work, different power. Doing that 3,000 J over 10 seconds needs 300 W. Doing it in 2 seconds needs 1,500 W — five times the power for identical work. This is the whole distinction between strength and speed.
The work-energy theorem, numerically
A 1,200 kg car reaching 27 m/s has gained 437,400 J of kinetic energy. The net work done on it by the driving force must equal exactly that figure — which is why you can skip acceleration entirely and reason straight from energy when it is convenient.
How Angle Changes the Work Done
200 N over 15 m, angle varying:
| Angle | Work done | Effect |
|---|---|---|
| 0° | 3,000 J | Energy added |
| 30° | 2,598 J | Energy added |
| 45° | 2,121 J | Energy added |
| 60° | 1,500 J | Energy added |
| 90° | 0 J | No transfer |
| 120° | -1,500 J | Energy removed |
| 180° | -3,000 J | Energy removed |
Keep going
- Work is force times distance, so the force is the first thing you need; the force calculator solves for it from mass and acceleration. Force Calculator
- Net work done on an object equals its change in kinetic energy — the work-energy theorem; the kinetic energy calculator quantifies that change. Kinetic Energy Calculator
Frequently Asked Questions
What is work in physics?
Work is energy transferred by a force acting through a distance: W = F·d·cos θ. It is measured in joules, the same unit as every other energy. The everyday and physics meanings differ sharply — holding a heavy box still is exhausting but does zero physics work, because nothing moves.
Why does carrying something horizontally do no work?
Because the force you apply is vertical (holding it up) while the motion is horizontal, so θ is 90° and cos 90° is zero. Your muscles burn energy maintaining tension, but no energy is transferred to the box — its speed and height are unchanged.
Can work be negative?
Yes. When the force opposes the motion, θ exceeds 90°, cos θ goes negative, and the force removes energy rather than adding it. Friction and braking always do negative work, which is exactly how they bring things to a stop.
What is the work-energy theorem?
The net work done on an object equals its change in kinetic energy. Push a stationary object and whatever work you do appears as motion; brake it and the negative work removes exactly that energy again. It is one of the most useful shortcuts in mechanics, because it lets you skip the intermediate acceleration entirely.
How is work related to power?
Power is work per unit time, P = W ÷ t, measured in watts. The same job done twice as fast needs twice the power but exactly the same work. A 100 W lightbulb consumes 100 joules every second it stays on.
Related Calculators
- Kinetic Energy Calculator — Energy, Work & Power
- Potential Energy Calculator — Energy, Work & Power
- Acceleration Calculator — Motion & Kinematics
- Velocity Calculator — Motion & Kinematics