Work Calculator (W = Fd cos θ)
Work Calculator (W = Fd cos θ)
Work is done whenever a force causes displacement, equal to the force times the distance times the cosine of the angle between them. Enter the force, distance, and angle, and this calculator computes the work, shown alongside a force-distance graph whose shaded area equals the work done.
The angle term is what trips people up most: if a force is applied perpendicular to the direction of motion (a 90° angle), the cosine term becomes zero and no work is done at all in the physics sense — this is exactly why carrying a bag horizontally while walking does zero work against gravity, even though it certainly feels tiring, because the force holding the bag up (vertical) is perpendicular to the walking motion (horizontal). A 50 N force applied in the same direction as a 10 m displacement (a 0° angle, where cosine equals 1) does the maximum possible 500 J of work for those magnitudes.
- W = F × d × cos(θ), so a 50 N force over 10 m in the same direction (θ = 0°) does 50 × 10 × 1 = 500 J of work.
- If the force is perpendicular to the motion (θ = 90°), no work is done - this is why carrying a bag horizontally while walking does no work against gravity, even though it feels tiring.
- Work is measured in joules (J), the same unit used for all forms of energy, since doing work on an object transfers energy to it.
How do I calculate work done by a force?
Multiply the force by the distance and by the cosine of the angle between them: W = F × d × cos(θ).
How much work is done by a 50 N force pushing something 10 m?
W = 50 × 10 × cos(0°) = 500 J.
Work Calculator (W = Fd cos θ)
Work is done whenever a force causes displacement, equal to the force times the distance times the cosine of the angle between them. Enter the force, distance, and angle, and this calculator computes the work, shown alongside a force-distance graph whose shaded area equals the work done.
The angle term is what trips people up most: if a force is applied perpendicular to the direction of motion (a 90° angle), the cosine term becomes zero and no work is done at all in the physics sense — this is exactly why carrying a bag horizontally while walking does zero work against gravity, even though it certainly feels tiring, because the force holding the bag up (vertical) is perpendicular to the walking motion (horizontal). A 50 N force applied in the same direction as a 10 m displacement (a 0° angle, where cosine equals 1) does the maximum possible 500 J of work for those magnitudes.
- W = F × d × cos(θ), so a 50 N force over 10 m in the same direction (θ = 0°) does 50 × 10 × 1 = 500 J of work.
- If the force is perpendicular to the motion (θ = 90°), no work is done - this is why carrying a bag horizontally while walking does no work against gravity, even though it feels tiring.
- Work is measured in joules (J), the same unit used for all forms of energy, since doing work on an object transfers energy to it.
How do I calculate work done by a force?
Multiply the force by the distance and by the cosine of the angle between them: W = F × d × cos(θ).
How much work is done by a 50 N force pushing something 10 m?
W = 50 × 10 × cos(0°) = 500 J.