Work Calculator

In physics, work means energy transferred by a force acting through a displacement — not the everyday sense of labor or employment. Pushing a crate across a floor, compressing a spring, and lifting a backpack all involve work. The work-energy theorem states net work equals change in kinetic energy, connecting forces to the energy calculators in this suite.

Work by a constant force:

W = F × d × cos θ

Where W is work in joules, F is applied force magnitude, d is displacement magnitude, and θ is the angle between force and displacement vectors. When force and motion align (θ = 0°), cos θ = 1 and W = Fd. Perpendicular force (θ = 90°) does zero work — centripetal force in circular motion never speeds or slows the object.

Vertical lifting against gravity: W = mgh, equivalent to increasing gravitational potential energy. Enter force, distance, and angle for general cases, or mass and height for pure lifting. Friction opposes motion — only the component of friction along displacement counts, which is why the friction calculator complements this tool on inclined planes.

Worked example: A worker pushes a 200 N crate 5 m across level ground with force parallel to motion. W = 200 × 5 × cos 0° = 1,000 J. If the same push is angled 30° below horizontal, only the horizontal component does work along the floor: W = 200 × 5 × cos 30° ≈ 866 J. Lifting a 15 kg box 2 m vertically: W = 15 × 9.81 × 2 = 294.3 J regardless of path if start and end heights differ by 2 m.

Relate results to kinetic and potential energy changes, and convert joules to kilowatt-hours for comparing human-scale work to electrical consumption. Power is work per unit time — divide work by duration to estimate watts during an activity.