Work Calculator
Calculate mechanical work from force, distance, and the angle between them.
Work Done (W)
The Work Formula and the Role of the Angle
In physics, mechanical work measures the energy transferred when a force moves an object over a distance. It is calculated with the formula:
W = F · d · cos(θ)
- W - Work done, measured in joules (J)
- F - Force applied, in newtons (N)
- d - Distance moved, in metres (m)
- θ - Angle between the force and the direction of motion, in degrees
Only the component of the force aligned with the motion does work. When the force is parallel to the displacement (θ = 0°), cos(θ) = 1 and the work is maximised. As the angle grows, less of the force contributes to the motion.
Positive, Zero, and Negative Work
- Positive work (θ < 90°): the force has a component in the direction of motion, adding energy to the object.
- Zero work (θ = 90°): the force is perpendicular to the motion, so cos(90°) = 0 and no work is done.
- Negative work (θ > 90°): the force opposes the motion, removing energy from the object, as with friction.
The Work-Energy Theorem
The work-energy theorem states that the net work done on an object equals its change in kinetic energy:
W = ΔKE = ½mv² − ½mv₀²
This means doing positive work on an object speeds it up, while negative work slows it down. It links the concept of work directly to the energy of motion.
Related Calculators
Note: This calculator assumes a constant force and straight-line motion. Results are based on idealized physics equations and may differ from real-world scenarios.