Mechanical work and power equations
In physics, work is done when a force causes displacement of an object: Work W = F × d × cos(θ), where F is the applied force in Newtons (N), d is displacement in metres (m), and θ is the angle between the force vector and the direction of motion.
When force is in the exact direction of motion (θ = 0°), cos(0°) = 1 and W = F × d. When force is perpendicular to motion (θ = 90°), cos(90°) = 0, meaning no mechanical work is performed.
Power is the rate of doing work over time: Power P = W / t, measured in Watts (W = Joules per second), kilowatts (kW), or mechanical horsepower (1 hp ≈ 745.7 W).
Worked example: Lifting a crate
Lifting a 50 kg crate vertically by 2 metres requires overcoming gravity: Force F = m × g = 50 kg × 9.80665 m/s² = 490.33 N.
Work done = 490.33 N × 2 m × cos(0°) = 980.67 Joules (0.98 kJ or 723.3 ft·lbf).
If the lift takes 4 seconds, the average power expended is 980.67 J ÷ 4 s = 245.17 Watts (0.33 hp).
Inputs for the work calculator
Applied force
The magnitude of force in Newtons (N), kilonewtons (kN), or pounds-force (lbf).
Displacement
The distance moved by the object in metres or feet.
Angle
Angle between applied force and displacement direction in degrees (0° for parallel force).
CALCULATOR QUESTIONS
Mechanical work & energy calculator questions
What is the SI unit of work?
The SI unit of work is the Joule (J), which equals one Newton-metre (1 N·m = 1 kg·m²/s²).
Why is work zero when carrying an object on flat ground?
Because the lifting force is vertical (upward) while displacement is horizontal, creating a 90° angle. Since cos(90°) = 0, no mechanical work is done on the object against gravity.