Physics calculator
Work Calculator
Calculate mechanical work from force, displacement, and their angle.
0° produces maximum positive work, 90° produces zero work, and 180° produces negative work.
Work
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Mechanical work formula
In W = Fd cos(θ), W is work in joules, F is force in newtons, d is displacement in meters, and θ is the angle between the force and displacement vectors.
Worked examples
For 100 N over 5 m, the work is 500 J at 0°, 0 J at 90°, and −500 J at 180°. Near-zero cosine artifacts are normalized to zero.
Interpreting the sign
Positive work adds energy along the displacement, zero work occurs when force is perpendicular to displacement, and negative work removes energy or opposes the displacement. This simple formula assumes a constant force and angle.
Frequently asked questions
Why does a 90-degree force do no work?
Only the component of force parallel to displacement contributes to work. At 90°, that component is zero.
Can work be negative?
Yes. Work is negative when the force component points opposite the displacement, as at 180°.
Is a joule the same as a newton-meter?
For work and energy, 1 joule equals 1 newton-meter, although torque also uses newton-meters and represents a different quantity.