Work Calculator
In physics, work is done on an object when a force moves it through a displacement. It is not just the size of the force that matters but also the direction: only the component of the force acting along the direction of motion does work. The formula is W = Fd cos(θ), where F is the force in newtons, d is the displacement in metres, and θ is the angle between the force vector and the direction of motion. At zero degrees the force and motion are perfectly aligned and all of it goes into doing work. At 90 degrees the force is entirely perpendicular, no work is done at all, which is why a person carrying a heavy bag horizontally does no work on the bag, even though they are exerting a force. This calculator offers two modes. In the first you enter the force, the displacement, and the angle, and it returns the work in joules and kilojoules along with the effective force component along the direction of travel. In the second mode, applying the work-energy theorem, you enter the mass and the initial and final speeds, and it returns the net work done as the change in kinetic energy. The two modes reinforce each other: if you calculate work by one method and check it by the other you get the same number when all forces are accounted for. The default example uses F = 50 N, d = 10 m, and θ = 30 degrees, giving W = 50 times 10 times cos(30) = 433.01 J. Use this calculator for physics homework, for engineering problems involving force and displacement, or to understand the relationship between work and energy.
Work = force x displacement x cos(angle). At 0 deg full force acts; at 90 deg no work is done. Results in joules and kilojoules, rounded for display.
How it works
Work done by a force equals the dot product of force and displacement: W = Fd cos(θ). The cosine factor extracts the component of force along the direction of movement. When θ = 0 the force and motion align and all the force does work. When θ = 90 deg the force is perpendicular and does zero work. In the work-energy mode the net work equals the change in kinetic energy: W = 0.5mv² - 0.5mu².
Worked example
A force of 50 N is applied at 30 degrees to the direction of motion, moving an object 10 m. The effective force component is 50 times cos(30) = 43.30 N. Work done = 43.30 times 10 = 433.01 J (or 0.433 kJ). These match the default values pre-filled above.
Related calculators
- Kinetic Energy Calculator: energy of a moving object from mass and velocity.
- Force Calculator: net force from mass and acceleration.
- Torque Calculator: rotational work and turning force.
- Energy Converter: convert between joules, kJ, kWh, and calories.