⚡ Work Calculator
W = F × d × cos(θ) — Calculate work done, force, distance, or angle.
Result
How to Use This Calculator
Select what you want to find: work (J), force (N), or distance (m). Then enter the other values. The angle θ is between the force vector and the direction of displacement. It defaults to 0° (force parallel to motion) so that W = F × d in the simplest case.
Choose the quantity to solve for from the dropdown: Work, Force, or Distance.
Enter force in newtons. If you only know weight in kg, the weight force is mass × 9.81 N (e.g., 10 kg object weighs 98.1 N).
Enter displacement in metres. This is the distance the object actually moves, not the distance you push.
Adjust the angle θ. If you push a box at 30° below horizontal, θ = 30°. Friction acts at θ = 180° (opposing motion), so it does negative work.
Work Formula
Only the component of force in the direction of movement does work. When θ = 90°, cos(90°) = 0 and no work is done. This is why carrying a bag horizontally (force is vertical, motion is horizontal) does zero work against gravity, even though it feels tiring. The muscular effort is real, but in physics terms, gravity does no work on the bag during horizontal travel.
Worked Examples
Where This Comes Up in Real Life
The work-energy theorem connects work directly to kinetic energy: the net work done on an object equals the change in its kinetic energy. If a car applies a braking force of 8,000 N over 40 m to stop from some initial speed, the net work is -320,000 J. That means the car had KE = 320 kJ before braking, which tells you the initial speed was about 25.3 m/s (91 km/h).
In construction, calculating work helps size motors and hydraulic systems. A crane lifting a 5,000 kg steel beam by 20 m does W = 5000 × 9.81 × 20 = 981,000 J. If the lift must take no more than 60 seconds, the required power is 981,000 / 60 = 16,350 W, about 22 horsepower. Engineers add a safety margin, so they would likely specify a 30 kW motor.
Frequently Asked Questions
What is work in physics?
Work is done when a force displaces an object. W = F × d × cos(θ), where θ is the angle between the force and displacement vectors.
When is work zero?
Work is zero when: the object does not move (d=0), the force is perpendicular to motion (θ=90°), or both.
What is the unit of work?
Joules (J) in SI. 1 J = 1 N × 1 m. Same unit as energy — work is energy transfer.
What is negative work?
Negative work occurs when force opposes motion (θ > 90°). Friction does negative work, removing kinetic energy.
How does work relate to power?
Power = Work / Time (W = P×t). Doing the same amount of work faster requires more power.