Work Calculator
Calculate work, force, or displacement using the formula W = F × d. Select the calculation mode below.
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What is Work in Physics?
In physics, work is done when a force causes an object to move in the direction of the force. The scientific definition differs from everyday usage — if you push against a wall that doesn\'t move, no work is done in the physics sense. The formula is:
W = F × d × cos(θ)
Where W is work in joules (J), F is force in newtons (N), d is displacement in meters (m), and θ is the angle between force and displacement. For force aligned with motion (θ = 0°), W = F × d. Work is a scalar quantity that represents energy transfer.
Common Work Reference Values
| Activity | Work (J) |
|---|---|
| Lifting a 1 kg book 1 m | 9.81 |
| Pushing a car 10 m with 500 N | 5,000 |
| Climbing stairs (70 kg, 3 m up) | 2,059 |
| Cycling 1 km (typical effort) | 15,000 |
| Boiling 1 L water from 20°C | 334,720 |
| Human daily food energy (~2000 kcal) | 8,370,000 |
| Car at 100 km/h braking to stop | 578,703 |
| 1 kWh of electricity (typical) | 3,600,000 |
Related Calculators
Authoritative References
Frequently Asked Questions
What is work in physics?
In physics, work is done when a force causes displacement of an object. It is defined as the product of force and displacement in the direction of the force: W = F × d × cos(θ). The SI unit of work is the joule (J), which equals one newton-meter. Work is a scalar quantity and can be positive or negative depending on direction.
How do I calculate work?
Work is calculated using W = F × d × cos(θ), where F is force, d is displacement, and θ is the angle between them. When force aligns with displacement (θ = 0°), cos(θ) = 1 and W = F × d. For example, pushing a 20 kg box 5 m across a floor with 50 N of force does 250 J of work.
What is the relationship between work and energy?
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE. Work is a transfer of energy — when you do work on an object, you transfer energy to it. Conversely, when an object does work, it loses energy. Both work and energy share the same unit (joule).
What does it mean when work is negative?
Negative work occurs when the force opposes the direction of motion. For example, friction does negative work on a sliding box — it removes kinetic energy from the box, converting it to heat. When you lower an object slowly, gravity does positive work but your hand does negative work. Negative work reduces the object's energy.
How does angle affect work?
Work depends on the angle between force and displacement: W = Fd cos(θ). At θ = 0° (force in direction of motion), cos(θ) = 1, work is maximized. At θ = 90° (force perpendicular to motion), cos(θ) = 0, no work is done. At θ = 180°, cos(θ) = -1, work is fully negative. This is why carrying a box horizontally does no work — the upward force is perpendicular to horizontal motion.
What are everyday examples of work?
Everyday examples include: pushing a shopping cart (positive work), lifting groceries (work against gravity), brakes on a car (negative work removes kinetic energy), friction slowing a sliding object (negative work), a crane lifting steel beams (work increases potential energy), and pedaling a bicycle uphill (work against both gravity and friction).