Work Calculator
Calculate work, force, distance, angle, and power using W = F × d
W = F × d × cos(θ)
Work = Force × Distance × cos(angle)
Work Quick Reference
Formula:
W = F × d × cos(θ)
SI Unit:
Joule (J) = N·m
Power:
P = W / t (Watts)
1 kJ =
1000 J
Understanding Work in Physics
In physics, work is the energy transferred to or from an object when a force acts on it over a distance. Work is done when the force causes displacement in the direction of the force.
The Work Formula
The basic formula for work is W = F × d, where W is work, F is force, and d is displacement. When the force is applied at an angle to the direction of motion, the formula becomes W = F × d × cos(θ).
When is Work Done?
- Positive work: Force and displacement are in the same direction (θ < 90°)
- Negative work: Force opposes the displacement (θ > 90°)
- Zero work: Force is perpendicular to displacement (θ = 90°)
Work and Energy
Work and energy are closely related. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: Wnet = ΔKE.
Power
Power is the rate at which work is done: P = W / t. It measures how quickly energy is transferred. The SI unit of power is the Watt (W), where 1 W = 1 J/s.
Common Examples
- Lifting a weight against gravity
- Pushing a box across the floor
- Pulling a wagon with a rope at an angle
- A car engine doing work to accelerate the vehicle
Units of Work
- SI unit: Joule (J) = Newton × meter (N·m)
- CGS unit: Erg = dyne × centimeter
- Other: Kilowatt-hour (kWh), Calorie, BTU
Conversion Factors
- 1 kJ = 1000 J
- 1 kWh = 3,600,000 J
- 1 Calorie = 4.184 J