Work Calculator
Calculate work, force, distance, angle, and power using W = F × d
W = F × d × cos(θ)
Work = Force × Distance × cos(angle)
Work Quick Reference
Formula:
W = F × d × cos(θ)
SI Unit:
Joule (J) = N·m
Power:
P = W / t (Watts)
1 kJ =
1000 J
Understanding Work in Physics
In physics, work is the energy transferred to or from an object when a force acts on it over a distance. Work is done when the force causes displacement in the direction of the force.
The Work Formula
The basic formula for work is W = F × d, where W is work, F is force, and d is displacement. When the force is applied at an angle to the direction of motion, the formula becomes W = F × d × cos(θ).
When is Work Done?
- Positive work: Force and displacement are in the same direction (θ < 90°)
- Negative work: Force opposes the displacement (θ > 90°)
- Zero work: Force is perpendicular to displacement (θ = 90°)
Work and Energy
Work and energy are closely related. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: Wnet = ΔKE.
Power
Power is the rate at which work is done: P = W / t. It measures how quickly energy is transferred. The SI unit of power is the Watt (W), where 1 W = 1 J/s.
Common Examples
- Lifting a weight against gravity
- Pushing a box across the floor
- Pulling a wagon with a rope at an angle
- A car engine doing work to accelerate the vehicle
Units of Work
- SI unit: Joule (J) = Newton × meter (N·m)
- CGS unit: Erg = dyne × centimeter
- Other: Kilowatt-hour (kWh), Calorie, BTU
Conversion Factors
- 1 kJ = 1000 J
- 1 kWh = 3,600,000 J
- 1 Calorie = 4.184 J
Worked Example: Pulling a Sled at an Angle
A person pulls a sled 20 m across snow with a 50 N force on a rope angled 30° above the horizontal. Only the horizontal component of the force does work, so W = F × d × cos(θ) = 50 × 20 × cos(30°) = 50 × 20 × 0.866 ≈ 866 J. If the pull took 10 seconds, the average power was P = W/t = 866 / 10 ≈ 86.6 W. Had the rope been horizontal (θ = 0°), the same pull would deliver the full 1,000 J — which is why angle is one of the calculator's solvable variables.
Frequently Asked Questions
How do I calculate work done by a force?+
Multiply force by the distance moved in the force's direction: W = F × d, with force in newtons and distance in meters giving joules. If the force acts at an angle θ to the motion, use W = F × d × cos(θ) — pulling a 100 N load 5 m gives 500 J straight-on but only about 433 J at a 30° angle.
Can this calculator solve for force, distance, or angle instead of work?+
Yes. It has five modes: work, force (F = W / (d cos θ)), distance (d = W / (F cos θ)), angle (θ = arccos(W / Fd)), and power (P = W / t). Enter the values you know and the tool rearranges the formula for the unknown automatically.
Why is no work done when carrying a box horizontally?+
The supporting force you apply points straight up while the displacement is horizontal, so the angle between them is 90° and cos(90°) = 0, giving W = 0 in the physics sense. Work is only done by the component of force along the direction of motion, even though carrying the box certainly feels like effort.
What is the difference between work and power?+
Work measures the total energy transferred (joules), while power measures how fast it is transferred (watts, where 1 W = 1 J/s). Lifting a 20 kg box 1 m takes about 196 J whether it takes one second or ten — but doing it in one second requires ten times the power.
Is the work calculator free and does it run on my phone?+
Yes. It is free, requires no registration, and all calculations execute in your browser without sending data anywhere. The responsive layout works on phones and tablets, so it is practical for homework checks and quick engineering estimates on the go.
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