Work and Energy Calculator
Work in physics is done when a force moves an object through a distance in the direction of the force. This calculator computes work in Joules from force and displacement, and power in Watts from work and time elapsed.
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Formula
W = F × d × cos(θ)
Work (W) equals force (F) times displacement (d) times the cosine of the angle (θ) between the force direction and motion direction. When force and motion are parallel (θ = 0°), cos(0°) = 1 and W = F×d. When perpendicular (θ = 90°), cos(90°) = 0 and no work is done. Power = Work / Time, in Watts.
How to use the Work and Energy Calculator
- 1
Enter your force
Value should be in N.
- 2
Enter your displacement
Value should be in m.
- 3
Enter your angle between force and motion
Value should be in °.
- 4
Enter your time
Value should be in s.
- 5
Read your results instantly
Results update in real time as you type.
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When is work done in physics?
In physics, 'work' has a precise meaning: a force does work on an object only if the force has a component in the direction of motion. Holding a heavy box stationary does zero work (no displacement). Carrying it horizontally does zero work (force is vertical, displacement is horizontal). Only lifting it — force and displacement both upward — does positive work.
This definition sometimes surprises people. A waiter carrying a tray across a restaurant does no work on the tray in the physics sense, because the upward force and horizontal displacement are perpendicular. The waiter's muscles do biochemical work internally, but no mechanical work on the tray.
The work-energy theorem
The work-energy theorem connects work directly to kinetic energy: the net work done on an object equals its change in kinetic energy. W_net = ΔKE = ½mv₂² − ½mv₁². This powerful result means you can find the final speed of an object just by calculating the work done on it, without tracking force at every instant.
Example: a 1,000 N force pushes a 50 kg box 20 m across a frictionless floor. Work = 1,000 × 20 = 20,000 J. ΔKE = 20,000 J, so ½ × 50 × v² = 20,000, giving v = 28.3 m/s.
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Power: work over time
Power is the rate of doing work: P = W/t, measured in Watts (W). 1 Watt = 1 Joule per second. A 100 W light bulb consumes 100 J every second. A person climbing stairs might generate 200-400 W of mechanical power. A Tour de France cyclist sustains ~400 W for hours; elite sprinters can hit 1,500-2,000 W for a few seconds.
Horsepower is a common unit in engines: 1 hp = 746 W. A 200 hp car engine produces about 149 kW. Maximum power matters for acceleration; the engine's torque curve determines how that power is delivered across different RPM ranges.
Tips & Insights
Zero angle means maximum work
When force and displacement point in the same direction (angle = 0), all the force contributes to work. Any angle reduces work by the cosine factor.
Normal force does no work
The normal force from a surface is perpendicular to motion (for horizontal surfaces), so it does zero work. Only friction and applied horizontal forces do work on a horizontally moving object.
1 kWh = 3,600,000 J
A kilowatt-hour is the energy unit on your electricity bill. 1 kWh = 1,000 W × 3,600 s = 3.6 MJ. Lifting a 1,000 kg car 367 m would use about 1 kWh.
Worked Examples
Pushing a box up a ramp
Work = 200 × 5 × cos(30°) ≈ 866 J. Power = 866 ÷ 4 ≈ 217 W.
Lifting a weight
Work = 490 × 2 × cos(0°) = 980 J (lifting 50 kg by 2 m). Power = 980 ÷ 3 ≈ 327 W.
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Frequently Asked Questions
What is work in physics?
Work is done when a force moves an object through a displacement. W = F × d × cos(θ), where θ is the angle between force and motion.
What is the unit of work?
Joules (J). 1 J = 1 N × 1 m = 1 kg·m²/s².
Can work be negative?
Yes. When force opposes motion (angle > 90°), work is negative. Friction does negative work on a sliding object, removing kinetic energy.
What is power?
Power is the rate of doing work: P = W/t, measured in Watts. 1 Watt = 1 Joule per second.
Why does carrying a box horizontally do no work?
The upward support force is perpendicular to horizontal displacement. cos(90°) = 0, so W = 0. Muscles still burn energy internally, but no mechanical work is done on the box.
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