Work Calculator

Work in physics is the energy transferred to or from an object when a force acts on it over a displacement. The formula is W = F × d × cos(θ), where F is force, d is displacement, and θ is the angle between the force and displacement vectors. Work is measured in Joules (J). Unlike everyday usage, physics work requires both force AND movement in the direction of that force.

The angle determines how much of the force contributes to work. When force is parallel to motion (θ = 0°), cos(0) = 1, so all force does work. At 45°, cos(45) ≈ 0.707, so about 71% of force does work. When perpendicular (θ = 90°), cos(90) = 0, meaning no work is done - the force doesn't help or hinder the motion. This is why carrying a heavy box horizontally does no physics work on the box.

The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½ mv²_final - ½ mv²_initial. This powerful principle connects work (force and distance) with motion (velocity). If positive net work is done, the object speeds up. If negative net work is done (like friction), the object slows down.

Friction always does negative work because it opposes motion. If you push an object with force F over distance d, and friction force f acts against it, the net work is W_net = (F - f) × d. Friction converts kinetic energy into heat. For example, pushing a 50 N object 10 m against 20 N friction: applied work = 500 J, friction work = -200 J, net work = 300 J.

Power is the rate of doing work: P = W/t, measured in Watts (W = J/s). A 100 W light bulb uses 100 Joules every second. Doing the same amount of work faster requires more power. Lifting a 10 kg box 2 m in 4 seconds takes 49 W, but doing it in 2 seconds takes 98 W. One horsepower (hp) equals about 746 Watts.

Yes, work is negative when the force opposes the direction of motion. Examples include: friction slowing an object, catching a ball (your hands apply force opposite to the ball's motion), and gravity doing negative work when you lift an object upward. Negative work removes energy from the system.

The SI unit is the Joule (J) = 1 N·m. Other units include: kilojoules (kJ = 1000 J), calories (cal ≈ 4.184 J), kilocalories/food calories (kcal = 4184 J), British Thermal Units (BTU ≈ 1055 J), foot-pounds (ft-lb ≈ 1.356 J), and electron volts (eV ≈ 1.6×10⁻¹⁹ J). Watt-hours (Wh) and kilowatt-hours (kWh) are common for electrical energy.

Work against gravity equals the weight times the vertical height: W = mgh, where m is mass, g is gravitational acceleration (9.81 m/s²), and h is height. This equals the change in gravitational potential energy. For example, lifting a 5 kg object 3 m: W = 5 kg × 9.81 m/s² × 3 m = 147.15 J.