Work & Energy Calculator

W = F x d x cos(theta)

Work Calculator

Calculate work done

Formula
W = F x d x cos(theta)

What Is Work in Physics?

In physics, work is done when a force causes displacement of an object in the direction of the force. Work is not simply applying a force — if you push against a wall and it doesn't move, no work is done. Work is the transfer of energy via force acting over a distance.

Work is measured in joules (J), the same unit as energy, because work is a form of energy transfer. The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE. This principle connects mechanics and energy conservation in a fundamental way.

How to Use the Work-Energy Calculator

  1. Enter the force (F) applied to the object in Newtons (N).
  2. Enter the displacement (d) of the object in meters (m).
  3. Enter the angle (θ) between the force direction and the direction of motion in degrees.
  4. Click Calculate to get the work done in joules (J).

Formula & Explanation

W = F × d × cos(θ) W = work done (J) F = applied force (N) d = displacement (m) θ = angle between force and displacement Work-Energy Theorem: W_net = ΔKE = ½mv₂² − ½mv₁²

When θ = 0° (force parallel to motion), W = Fd (maximum). When θ = 90° (force perpendicular to motion), W = 0. When θ = 180° (force opposing motion), work is negative.

Worked Examples

Pulling a Sled

A child pulls a sled with 50 N at 30° above horizontal, moving it 10 m. W = 50 × 10 × cos(30°) = 500 × 0.866 = 433 J. The vertical component of force does no work — only the horizontal component contributes to displacing the sled.

Braking a Car

A 1200 kg car braking from 20 m/s to rest. W_net = ΔKE = 0 − ½ × 1200 × 20² = −240,000 J. The brakes do −240 kJ of work (negative because force opposes motion), converting kinetic energy to heat in the brake pads.

Lifting a Box

A 20 kg box is lifted 2 m vertically. Force = mg = 20 × 9.81 = 196.2 N (upward). Displacement = 2 m upward. θ = 0°. W = 196.2 × 2 × cos(0°) = 392.4 J of work done against gravity, stored as gravitational potential energy.

Frequently Asked Questions

What is the work-energy theorem?▾
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv₂² − ½mv₁². It bridges Newton's second law and energy conservation, letting you find speed changes from work or work requirements from speed changes.
Can work be negative?▾
Yes. Negative work occurs when force opposes displacement (θ > 90°). Friction always does negative work on sliding objects; brakes do negative work on wheels; gravity does negative work when you lift an object. Negative work removes kinetic energy from the system.
What is power vs. work?▾
Work is the total energy transferred; power is the rate of energy transfer: P = W/t (watts). A weightlifter doing 500 J of work in 2 seconds generates 250 W. An elevator motor doing the same work in 0.5 s generates 1000 W (1 kW). Same work, different power.
Does gravity do work on a satellite?▾
For a satellite in a circular orbit, gravity acts perpendicular to the velocity at every instant, so θ = 90° and gravity does zero net work per orbit. The satellite's speed stays constant. In elliptical orbits, gravity does positive work (speeding up near Earth) and negative work (slowing down far away).
What is the difference between work and torque?▾
Both are measured in N·m, but work (joules) is a scalar — energy transferred. Torque (N·m) is a vector — rotational force tendency. Work done by a torque: W = τ × θ, where θ is the rotation angle in radians. Rotational work-energy theorem: W_net = ΔKE_rotational = ½Iω₂² − ½Iω₁².