Why the angle matters
Only the component of force in the direction of movement does mechanical work. A force applied at 60 degrees contributes half as much as the same force applied parallel to the movement because cos(60 degrees) = 0.5.
Example
A 50 N force moving an object 3 m in the same direction does 150 J of work. At a 60 degree angle, the same force and distance do 75 J.
Common mistakes
Use the angle between the force direction and displacement direction, not the angle from the ground unless that is the same reference.
Limitations
This simple formula assumes constant force and straight-line displacement. Variable forces, springs, curved paths, friction losses and energy conversion efficiency require more detailed modeling.
References
- BIPM SI Brochure, for joule and newton SI derived-unit context.
- NIST SI guidance, for consistent SI notation.
Last reviewed: 2026-05-17