How to Calculate Work, Power, and Energy
In physics, work has a precise definition: energy transferred when a force moves an object through a displacement. Power is the rate at which work is done. These concepts are foundational to mechanical engineering and everyday energy use.
Key Formulas
Work:
W = F × d × cos(θ)
Where F is force (N), d is displacement (m), and θ is the angle between force and displacement.
Power:
P = W / t = F × v
Kinetic Energy:
KE = ½ × m × v²
Potential Energy:
PE = m × g × h
Step-by-Step Examples
Work Example: You push a box 5 meters across the floor with 40 N of horizontal force. W = 40 × 5 × cos(0°) = 40 × 5 × 1 = 200 joules
Power Example: You do 200 J of work in 4 seconds. P = 200 / 4 = 50 watts
Ramp Problem: How much work to push a 100 kg crate 10 m up a 30° frictionless ramp? Height gained: h = 10 × sin(30°) = 5 m Work = change in PE = m × g × h = 100 × 9.81 × 5 = 4,905 J
Units
| Quantity | SI Unit | Common Equivalent |
|---|---|---|
| Force | Newton (N) | 1 kg·m/s² |
| Work/Energy | Joule (J) | 1 N·m |
| Power | Watt (W) | 1 J/s |
| 1 horsepower | 746 W | 550 ft·lb/s |
Conservation of Energy
In an ideal system: KE + PE = constant (total mechanical energy is conserved). Real systems lose energy to friction and heat, but total energy (including thermal) is always conserved.
Use our work and power calculator for any force, distance, and time.