Work Calculator
The work calculator's example is a sled pulled 15 m with a 200 N pull on a rope held 30 degrees above the ground. The table shows the same pull at other angles.
Work done
- Work done W = Fd cos θ = 200 N × 15 m × cos 30° = 200 × 15 × 0.866 = 2,598 J.
- 2,598 J
- The unit algebra One joule is the work done by one newton acting through one meter. The cosine is a pure number, so it does not change the unit.
- N × m = J
- Force along the motion F cos θ. Only the part of the force pointing along the motion does work; the part at right angles to it does none.
- 173.2 N
- In other units
- 2,598 J 2.598 kJ 621 cal 0.621 kcal 0.0007217 kWh 1,916 ft-lbf
| Angle θ | cos θ | Force along the motion | Work |
|---|---|---|---|
| 0° | 1 | 200 N | 3,000 J |
| 30° | 0.866 | 173.2 N | 2,598 J |
| 45° | 0.7071 | 141.4 N | 2,121 J |
| 60° | 0.5 | 100 N | 1,500 J |
| 90° | 0 | 0 N | 0 J |
| 120° | -0.5 | -100 N | -1,500 J |
| 180° | -1 | -200 N | -3,000 J |
- Positive work adds energy to the object; a force with a component against the motion does negative work.
- This is the work done by one constant force over a straight path. Varying forces need W = ∫F·ds.
- Results are shown to four significant figures. Round to the precision of your least precise measurement.
How the Force Calculator works
W = Fd cos θ. The work done by a constant force is the force times the distance moved times the cosine of the angle between them. Newtons and meters give joules.
Worked example, the one above: a 200 N pull on a sled rope at 30 degrees to the ground, over 15 m. cos 30° = 0.8660, so W = 200 × 15 × 0.8660 = 2,598 J. If the rope were horizontal the same pull would do 3,000 J. The difference is the part of the pull that lifts the sled rather than moving it along (200 × sin 30° = 100 N upward), which does no work because the sled does not move upward.
Only the component along the motion counts. That is what the cosine does. At 0 degrees all of the force is along the motion; at 90 degrees none of it is, and the work is zero however hard you push. Carrying a heavy box across a level room does no work on the box in the physics sense: the force holding it up is vertical and the motion is horizontal. It certainly feels like work, because muscles burn energy just holding a load, but none of that energy goes into the box.
Negative work. Past 90 degrees the cosine is negative and so is the work. A force against the motion (friction, brakes, air resistance, your hands catching a ball) takes energy out of the moving object. At 180 degrees the force is directly opposed and W = −Fd. The work-energy theorem ties all this together: the net work done on an object equals its change in kinetic energy.
Units. A joule is one newton acting through one meter, N·m. Torque is also written N·m, but it is a different quantity: a force at a distance from an axis, not a force through a distance. The two are not interchangeable, and by convention torque is not written in joules. In US units, work is in foot-pounds (ft-lbf); 1 ft-lbf is 1.356 J.
What this does not cover. The formula is for one constant force over a straight path. A force that changes along the way (stretching a spring, where F = kx) needs the integral W = ∫F·ds, which for the spring gives ½kx². Lifting against gravity is a special case of this formula: the force is the weight mg, the angle is zero, and the work is mgh, the potential energy mode.
Work is energy transferred, not power. Doing the same 2,598 J in five seconds or five minutes is the same work; the rate is power, P = W / t, which the power mode works out.
Force Calculator FAQ
What is the formula for work in physics?
W = Fd cos θ: force times distance times the cosine of the angle between the force and the direction of motion. A 200 N pull at 30 degrees over 15 m does 200 × 15 × 0.866 = 2,598 J of work.
When is work zero?
When the object does not move, or when the force is at 90 degrees to the motion. A force holding a box up while you walk across a level floor does no work on the box, because the force is vertical and the motion horizontal.
What is the unit of work?
The joule, which is one newton acting through one meter (N·m, or kg·m²/s²). In US customary units work is measured in foot-pounds; one foot-pound-force is 1.356 J.
More from the Force Calculator
Sources
- NASA NSSDCA Moon Fact Sheet, bulk parameters table, row "Surface gravity (m/s2)", Moon column (page last updated January 11, 2024) (2026)
- NASA NSSDCA Mars Fact Sheet, bulk parameters table, row "Surface gravity (mean) (m/s2)", Mars column (page last updated May 19, 2025) (2026)