In physics, work is the energy transferred when a force moves an object over a distance. It is calculated as the product of the force applied in the direction of displacement and the distance moved. The standard formula is W = F × d × cos(θ), where θ is the angle between the force vector and the displacement vector. Work is measured in joules (J) in the SI system — 1 joule equals 1 newton of force moving an object 1 meter.

The cos(θ) term accounts for the fact that only the component of force parallel to the displacement does work. If you push at an angle, part of your force goes into moving the object (parallel component), and part pushes it into the ground or lifts it (perpendicular component).

• θ = 0° → cos(0°) = 1 → W = F × d (maximum positive work)
• θ = 90° → cos(90°) = 0 → W = 0 (no work — force is perpendicular)
• θ = 180° → cos(180°) = -1 → W = -F × d (negative work — force opposes motion, like friction)

Positive work occurs when the force has a component in the same direction as the displacement (θ < 90°). The force adds energy to the object — like pushing a cart forward.

Negative work occurs when the force has a component opposite to the displacement (θ > 90°). The force removes energy from the object — like friction slowing down a sliding box, or catching a ball. Negative work means the object is losing kinetic energy.

Common work/energy unit conversions:

• 1 kJ = 1,000 J
• 1 ft·lb ≈ 1.35582 J
• 1 calorie (cal) = 4.184 J
• 1 kcal = 4,184 J = 4.184 kJ
• 1 BTU ≈ 1,055 J
• 1 eV ≈ 1.602 × 10⁻¹⁹ J

This calculator handles all conversions automatically — just select your preferred result unit from the dropdown.

Lifting a 10 kg object 2 meters: F = m × g ≈ 98 N, d = 2 m, θ = 0° → W ≈ 196 J
Pushing a car with 300 N over 15 meters: W = 300 × 15 = 4,500 J = 4.5 kJ
Pulling a suitcase at 30° angle: If you pull with 100 N over 20 m at 30°, W = 100 × 20 × cos(30°) ≈ 1,732 J
Friction slowing a box: If friction applies 40 N opposite to 5 m of motion, θ = 180°, W = 40 × 5 × (-1) = -200 J

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Work measures the total energy transferred (in joules), while power measures the rate at which work is done (in watts). Power = Work ÷ Time.

For example, lifting 200 J of work in 2 seconds requires 100 W of power. The same work done in 0.5 seconds requires 400 W. Work tells you "how much energy," power tells you "how fast."

When θ = 90°, cos(90°) = 0, so W = 0. This means no work is done even if a force is applied. A classic example: carrying a heavy box horizontally at constant height — your arms apply an upward force, but the displacement is horizontal. The force is perpendicular to motion, so the upward force does zero work on the box (though your muscles certainly feel it — that's biological work, not mechanical work).

This tool eliminates conversion errors by handling all unit conversions automatically. You can mix and match force units (N, kN, lbf) with distance units (m, cm, ft, in) and angle units (degrees, radians), then get results instantly in joules, kilojoules, foot-pounds, or calories. The built-in formula display shows every step of the calculation, making it perfect for students, engineers, and physics enthusiasts who want to verify their work.