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Work · Mechanics

Mechanical Work & Power Calculator

Calculate mechanical work from force, displacement, and their relative angle, then find average power over a selected time interval.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Constant force acting through a straight displacement over a measured interval

Mechanical work

W = Fd cos θ

Average power

Pavg = W/Δt

Parallel force

θ = 0° ⇒ W = Fd
Work and power

Resolve the force along the motion

Use magnitudes for force and displacement, then describe their relative direction with θ from 0° to 180°. Inputs accept up to three decimal places; displayed results are rounded to at most three decimal places.

W = Fd cos θ

Enter the force, motion, angle, and elapsed time.

Force and displacement vector diagramThe displacement vector points right. The force vector forms an angle of 30 degrees with it.dFθ = 30°
Vector direction updates with θ; vector lengths respond to the entered magnitudes.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Force and displacement are entered as non-negative magnitudes. Their relative angle determines the sign of work: acute angles produce positive work, 90° produces zero work, and obtuse angles produce negative work. Power is the average over the entered interval.

Worked examples

See the method in practice

01

Force partly along the motion

A 50 N force acting through 4 m at 30° performs about 173.205 J of work; over 5 s, its average power is about 34.641 W.

02

Opposing force

A friction force at 180° to displacement performs negative work because cos 180° = −1.

Questions

Frequently asked

Why is work zero at 90 degrees?

The force has no component along the displacement, so their scalar product is zero.

Can mechanical work be negative?

Yes. Negative work means the force component opposes displacement and removes mechanical energy from the object.

Is this instantaneous power?

No. W divided by a finite time interval gives average power. Instantaneous power requires the instantaneous velocity through P = F · v.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Work and Power

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology