How to Calculate Work (W = Fd): Force, Distance & Energy

Calculate work with W = Fd or W = Fd cos θ. Work–energy theorem, joule units, worked examples, and a free work calculator.

What Work Asks

In physics, work is energy transferred when a force moves something along the direction of that force. It is not just “effort” — it is a precise quantity measured in joules.

When force F and displacement d point the same way, W = F × d. Force in newtons times distance in metres gives work in joules.

If you already have F and d (or W and one unknown), open the free work calculator first, then return here for angles, signs, and the work–energy link.

The Formulas

  • W = Fd — force parallel to displacement.
  • W = Fd cos θ — force at angle θ to displacement.
  • F = W / d — rearrange for force.
  • d = W / F — rearrange for displacement.

    • θ is the angle between the force vector and the displacement vector. cos 0° = 1 (maximum work), cos 90° = 0 (no work from that force).

    Work and Energy

    The work–energy theorem: net work on an object equals its change in kinetic energy, W_net = ΔKE.

    After net work, check kinetic energy with KE = ½mv². Lifting stores

    potential energy PE = mgh — the work done against gravity near Earth’s surface.

    Power is work per unit time: P = W/t. See the power calculator when the question includes seconds.

    Units

  • F → newtons (N).
  • d → metres (m).
  • W → joules (J). 1 J = 1 N·m.
  • Convert kN, cm, or kJ before substituting if the paper uses SI.

    • Worked Examples

    Example 1: push 50 N for 3.0 m

    W = (50)(3.0) = 150 J.

    Example 2: find force

    W = 120 J, d = 2.5 m. F = 120 / 2.5 = 48 N in the direction of motion.

    Example 3: force at 60°

    F = 20 N, d = 4.0 m, θ = 60°. W = Fd cos θ = (20)(4.0)(0.5) = 40 J.

    Common Mistakes

  • Using path length when displacement along the force is what matters.
  • Forgetting cos θ when force is not parallel to motion.
  • Confusing work (J) with power (W) or force (N).
  • Assuming you always do work when holding something still — no displacement means W = 0 for that force.

    • Check It on the Calculator

    Work calculator — W = Fd.

    Kinetic energy calculator.

    Potential energy calculator.

    Force calculator.

    Learn W = Fd and confirm every homework number on the calculator.

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