W = F × d × cos(θ)Work in physics is the energy transferred when a force moves an object. Only the component of force along the direction of motion does work, which is why the cosine factor appears. When the angle is 90°, no work is done (the force does not push the object forward). When the angle is 180°, work is negative (braking).
Enter force, distance, and angle. Get work done in joules, kJ, and foot-pounds.
Enter a force in newtons, a distance in meters, and the angle between the two to get the mechanical work done in joules. Works for any direction of force, including pulling at an angle, pure horizontal pushing, lifting against gravity, or braking against motion.
When you push a shopping cart, lift a box, or drag a sled, you do mechanical work. Physics measures that work in joules. The amount depends on three things: how hard you push, how far the object moves, and whether you push in the same direction the object is moving. This calculator handles all three.
Definition
The computation, step by step
- 1Enter the force you apply to the object in newtons (1 kg ≈ 9.81 N of weight).
- 2Enter the distance the object moves in meters.
- 3Enter the angle between your force and the direction of motion.
- 4Use 0° for pushing in the direction of motion, 90° for sideways force.
- 5The calculator applies W = F × d × cos(θ).
Solved example
A worked solution
Example: Pulling a sled with a 100 N force at 30°
- 1F = 100 N, d = 10 m, θ = 30°
- 2cos(30°) = 0.866
- 3W = 100 × 10 × 0.866 = 866 J
Validity
Edge cases and pitfalls
- Forgetting the cosine factor: If you pull a wagon at 45°, only 71% of your force actually moves it forward. Using W = F × d without the angle overstates the work by up to 100%.
- Computing work for static forces: Holding a heavy object still requires force but does zero mechanical work. Work requires motion. A weightlifter holding a deadlock does no work in the physics sense.
- Confusing work with power: Work is total energy transferred. Power is the rate of doing work. Lifting 100 kg by 1 m in 1 second or 10 seconds does the same work but very different power.
- Using force in kg instead of newtons: Force in physics is measured in newtons. To convert mass in kilograms to weight in newtons, multiply by 9.81.
Adjacent topics
Related concepts
| Term | Definition |
|---|---|
| Joule | The SI unit of work and energy. One joule is the work done by a one-newton force moving one meter in the direction of the force. |
| Force | A push or pull measured in newtons. One newton accelerates one kilogram by one meter per second squared. |
| Cosine factor | cos(θ) projects the force onto the direction of motion. Forces perpendicular to motion do no work. |
| Negative work | When the force opposes motion (θ > 90°), work is negative. Brakes do negative work on a car. |
Applications
Where this calculation appears
- Physics problems: Solve standard work-energy problems with any combination of force, distance, and angle.
- Lifting calculations: Calculate the work to lift an object against gravity (angle = 0° when force is vertical and motion is vertical).
- Engine and machine specs: Convert force-distance specs into joules or kilowatt-hours for energy comparisons.
- Exercise science: Estimate the mechanical work done during lifts, rows, and other gym movements.
Implementation notes
Pro tips
- For vertical lifting, use F = m × g: When you lift, the force you apply equals the weight. A 10 kg box weighs 98.1 N. Lift it 2 m and the work is 196 J.
- Negative work removes energy: Brakes, friction, and air resistance all do negative work on a moving object. The energy lost shows up as heat.
- Convert to calories for food math: 1 food calorie = 4,184 J. Lifting 10 kg up 1 m burns about 0.025 calories. The exercise calorie cost is much higher because muscles are inefficient.
- Use the work-energy theorem: Net work on an object equals its change in kinetic energy. Useful when you do not have time or acceleration but you do have velocities.
Common questions
Frequently asked questions
Quick reference
Work Done in Common Scenarios
Reference values for everyday actions
| Action | Force | Distance | Work |
|---|---|---|---|
| Lift 1 kg by 1 m | 9.81 N | 1 m | 9.81 J |
| Lift 10 kg by 1 m | 98.1 N | 1 m | 98.1 J |
| Push grocery cart 100 m | 20 N | 100 m | 2,000 J |
| Climb one flight of stairs (70 kg)typical | 687 N | 3 m | 2,060 J |
| Carry 5 kg horizontally for 100 m | 49 N | 100 m | 0 J (force ⊥ motion) |
For related calculations, try the Kinetic Energy, Force Calculator, or Power Calculator. Browse all Calculator Online calculators for the full catalog.
Methodology
This calculator uses the standard work & energy calculator formula. Results match those from established financial, scientific, and health references.
Reviewed by
Calculator Online Editorial Team. All formulas verified against authoritative sources before publication.
Last updated
2026-05-24