Work & Power Calculator

Calculate work, power, force, distance, and time using fundamental physics formulas. Work measures energy transfer, while power measures the rate of energy transfer.

About Work & Power

Work

In physics, work is done when a force causes displacement of an object. Work is the energy transferred to or from an object via the application of force along a displacement. The formula is: W = F × d × cos(θ), where θ is the angle between the force and displacement vectors.

Power

Power is the rate at which work is done or energy is transferred over time. It measures how quickly work is performed. The formula is: P = W / t, where W is work and t is time. Power can also be expressed as P = F × v (force times velocity).

Key Formulas

• W = F × d × cos(θ) - Work equals force times distance times cosine of angle
• P = W / t - Power equals work divided by time
• F = W / d - Force equals work divided by distance (when θ = 0°)
• d = W / F - Distance equals work divided by force (when θ = 0°)

Angle Considerations

• θ = 0°: Force in same direction as motion → cos(0°) = 1 → maximum work
• θ = 90°: Force perpendicular to motion → cos(90°) = 0 → no work done
• θ = 180°: Force opposite to motion → cos(180°) = -1 → negative work (energy removed)

Units

• Work: J (Joules), where 1 J = 1 N·m; kJ (kilojoules); MJ (megajoules)
• Power: W (Watts), where 1 W = 1 J/s; kW (kilowatts); MW (megawatts); hp (horsepower, 1 hp ≈ 746 W)
• Force: N (Newtons), kN (kilonewtons), lbf (pound-force)
• Distance: m (meters), km (kilometers), ft (feet), mi (miles)
• Time: s (seconds), min (minutes), h (hours)

Examples

• Lifting a 10 kg box (98.1 N) 2 meters high: W = 98.1 × 2 = 196.2 J
• Pushing a car with 500 N force over 10 m: W = 500 × 10 = 5000 J
• Doing 1000 J of work in 5 seconds: P = 1000 / 5 = 200 W
• A 100 W light bulb uses 100 J of energy per second

Real-World Applications

• Lifting: Calculating energy needed to lift objects (elevators, cranes)
• Engines: Measuring engine power output (cars, generators)
• Exercise: Calculating calories burned and workout intensity
• Electricity: Power consumption of appliances and devices
• Machines: Efficiency calculations for mechanical systems

Common Power Ratings

• LED light bulb: 5-15 W
• Laptop computer: 50-100 W
• Microwave oven: 600-1200 W
• Electric car motor: 50-300 kW
• Small car engine: 75-150 kW (100-200 hp)
• Wind turbine: 1-5 MW