Work
Energy transferred by this force; the angle determines its sign.
Physics · Mechanics · Motion & Energy
Work of a force calculator
Find the work of a constant force from force magnitude, displacement length and their angle. Positive work supplies energy; negative work removes it.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Relation and numerical substitution
W = F × d × cos(θ)—
Constant force and angle; F,d ≥ 0; 0° ≤ θ ≤ 180°.
01Formulas and symbols
Formulas used
W
W = F × d × cos(θ)Energy transferred by this force; the angle determines its sign.02Assumptions and limits
Scope of validity
- Constant force and angle; F,d ≥ 0; 0° ≤ θ ≤ 180°.
03Validation example
Reference numerical case
- F = 100 N, d = 5 m, θ = 60° = π/3 rad: W = 100 × 5 × cos(60°) = 250 J. At 180°, the same magnitudes give −500 J.
04References
Technical references
- University Physics Volume 1, §7.1 Work — OpenStax
FAQ
Why is work zero when force is perpendicular to displacement?
Mechanical work is the dot product W = Fd cosθ. At 90°, cosθ = 0, so the force has no component along the displacement and does no work on that motion.
Can mechanical work be negative?
Yes. Work is negative when the force component along the path points opposite the displacement, such as a braking or friction force. In the dot-product formula this occurs when cosθ is negative.
05How it works
Only the component of force parallel to displacement contributes. At 0° the work is Fd; at 90° it is zero; at 180° it is −Fd. The angle is between the vectors, not necessarily between the force and the ground.
06Limits of the model
A constant force over a straight displacement with a fixed angle. Variable forces generally require integration. This gives work by one force, not net work unless F is the constant resultant.
07Common mistakes
Enter nonnegative magnitudes for F and d and encode direction through θ from 0° to 180°. Select degrees or radians explicitly. Do not interpret work as force: its unit is the joule.