Classical Mechanics
Work & Power Calculator
Calculate work done (W = Fd cosθ) or power output (P = W/t). Enter angle between force and displacement.
Result
W = Fd cosθ
Power Output
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W
Step-by-Step Solution
What are Work and Power?
Work is done when a force causes displacement in the direction of the force. Power is the rate of doing work. If a force is applied at an angle θ to the direction of motion, only the component along the motion does work. This is why pushing a box at an angle is less efficient than pushing horizontally.
W = Fd cosθ | P = W/t
F = force (N) | d = displacement (m) | θ = angle between F and d | t = time (s) | P = power (W)
💡 If the force is perpendicular to motion (θ = 90°), no work is done. A centripetal force in circular motion does zero work because it is always perpendicular to velocity.
Real-World Applications
Power Stations
Rating in watts (W) or megawatts (MW) — the rate at which electrical energy is produced.
Weight Lifting
Work = force × distance lifted. Power = work/time. A faster lift needs more power even for the same work.
Train Engines
Traction force × speed = power output. More powerful engines can pull heavier loads at higher speeds.
Battery Capacity
Watt-hours (Wh) = power × time = energy stored. A 100 Wh battery can power a 10 W device for 10 hours.
Frequently Asked Questions
When is the work done by a force zero?
Work is zero when: (1) the object does not move (d = 0), (2) the force is perpendicular to motion (cos90° = 0), or (3) the force is zero. A person holding a heavy box stationary does no mechanical work, even though it feels tiring.
What is the difference between work and power?
Work (J) is the total energy transferred. Power (W) is the rate of energy transfer. Two people doing the same work but one does it twice as fast uses twice the power. Power = Work/Time.
How do I convert watts to horsepower?
1 horsepower (hp) = 745.7 watts. So 1 kW = 1.341 hp. Car engines are often rated in both kW and hp.