🎯 Solve for:
Enter force.
Enter displacement.
0° = force parallel to motion
Enter angle (0-180°).
Work Done
—
💡
ℹ️ W = F × d × cos(θ) gives work done by a single constant force. For varying forces, integration is required. Net work on an object equals its change in kinetic energy (work-energy theorem).
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Sources & Methodology
Work formula per classical mechanics; Serway & Jewett Physics for Scientists and Engineers and NIST SI units.
Serway & Jewett — Physics for Scientists and Engineers, 10th Ed.
Standard university reference for work, energy, power, and the work-energy theorem.
NIST — SI Units: Joule Definition
1 J = 1 N·m = 1 kg·m²/s². physics.nist.gov
Halliday, Resnick & Krane — Physics, 5th Ed.
Comprehensive treatment of work, kinetic energy, and conservative forces.
W = F × d × cos(θ) [N, m, joules]
Work-energy theorem: W_net = ΔKE = ½mv² − ½mv&sub0;²
Power: P = W / t (watts = J/s)
1 J = 1 N·m = 0.7376 ft·lb = 0.2388 cal
Work-energy theorem: W_net = ΔKE = ½mv² − ½mv&sub0;²
Power: P = W / t (watts = J/s)
1 J = 1 N·m = 0.7376 ft·lb = 0.2388 cal
W = F × d × cos(θ)
Example: 50 N force, 10 m displacement, θ = 30°.
W = 50 × 10 × cos(30°) = 500 × 0.866 = 433.0 J
At θ = 0°: W = 50 × 10 = 500 J (maximum work)
W = 50 × 10 × cos(30°) = 500 × 0.866 = 433.0 J
At θ = 0°: W = 50 × 10 = 500 J (maximum work)
Last reviewed: April 2026
How Is Work Calculated in Physics?
In physics, work is done when a force causes an object to move through a displacement. The formula W = F × d × cos(θ) incorporates the angle between the force vector and the displacement direction. Only the component of force parallel to the displacement does work — the perpendicular component does nothing.
The SI unit of work is the joule (J). One joule equals one newton of force applied over one meter of displacement in the direction of the force. Work is a scalar quantity — it has magnitude but no direction, though it can be positive or negative.
Work at Different Angles
| Angle θ | cos(θ) | Work (F=50N, d=10m) | Description |
|---|---|---|---|
| 0° | 1.000 | 500 J | Force fully parallel — maximum work |
| 30° | 0.866 | 433 J | Partial component — typical pushing |
| 60° | 0.500 | 250 J | Half of maximum work |
| 90° | 0.000 | 0 J | Force perpendicular — zero work |
| 180° | −1.000 | −500 J | Force opposes motion — negative work |
💡 Work-Energy Theorem: The net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv&sub0;². To accelerate a 1500 kg car from 0 to 100 km/h (27.78 m/s): W = ½ × 1500 × 27.78² − 0 = 578,704 J ≈ 579 kJ. This is the work the engine must do, minus friction losses.
Frequently Asked Questions
W = F × d × cos(θ). F = force (N), d = displacement (m), θ = angle between force and displacement. When θ = 0°, W = F × d (simplest case).
Joules (J) in SI. 1 J = 1 N·m = 1 kg·m²/s². Also: kJ, ft·lb, cal, BTU, kWh. The calculator converts between these.
W_net = ΔKE = ½mv² − ½mv&sub0;². Net work done on an object equals its change in kinetic energy. Positive net work accelerates the object; negative net work decelerates it.
Work is zero when: F = 0, d = 0, or θ = 90° (force perpendicular to motion). Example: carrying a box horizontally — the upward support force does zero work because it is perpendicular to horizontal displacement.
Work is negative when force opposes displacement (90° < θ ≤ 180°). Friction always does negative work. Negative work removes kinetic energy from the object (slows it down).
Work (J) = total energy transferred. Power (W) = rate of doing work = W/t. Same work done faster requires more power. 1 watt = 1 J/s.
Work done against gravity = gain in GPE: W = mgh. Work done against spring = gain in elastic PE: W = ½kx². Extended work-energy theorem: W_net = ΔKE + ΔPE.
cos(θ) extracts only the component of force parallel to displacement. At 0°: full force contributes. At 90°: zero contribution. At 180°: force fully opposes motion.
1 J = work done by 1 N force over 1 m in the direction of force. Also the KE of a 2 kg object at 1 m/s. Equivalent: 0.2388 calories, 0.7376 ft·lb, 2.778×10−&sup7; kWh.
No. Work requires displacement. Holding a weight stationary does zero mechanical work (no displacement) even though the body expends metabolic energy. Physics work = 0 when d = 0.
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