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Work Calculator

Physics

Calculate mechanical work using W = F × d × cos(θ). Enter force, distance, and the angle between them to get work done in joules instantly.

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Work Done

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This calculator computes your Work Done from the values you enter.

Inputs
ForceDistanceAngle Between Force and Displacement
Outputs
Work Done

What is a Work?

The Work Calculator computes mechanical work using W = F × d × cos(θ) — the energy transferred when a force acts on an object over a distance. Enter a force in newtons, a distance in meters, and the angle between the force and the direction of motion (defaulting to 0° for force and motion in the same direction), and the calculator instantly returns the work done in joules.

Work is a central concept in mechanics, linking force and distance to energy, and forming the basis of the work-energy theorem that connects work directly to changes in kinetic energy. The angle term makes this calculator more general than a simple force-times-distance tool, correctly handling cases where the force isn't perfectly aligned with the motion.

If you need the resulting rate of energy transfer, use the Mechanical Power Calculator to divide this work value by the time it took.

How to use this Work calculator

  1. Enter the force — the magnitude of the applied force in newtons.

  2. Enter the distance — the distance over which the force acts, in meters.

  3. Enter the angle — the angle between the force direction and the direction of motion, in degrees (0° if they're aligned).

  4. Read the work result — the highlighted result shows the work done in joules, correctly accounting for the angle.

  5. Check the step-by-step breakdown — expand the calculation steps to see the exact formula substitution, then use the Mechanical Power Calculator if you also know the time taken.

Formula & Methodology

Work formula:
W = F × d × cos(θ)

Variable definitions:
- F — applied force (newtons)
- d — distance moved (meters)
- θ — angle between force and displacement direction (degrees)
- W — work done (joules)

Worked example:

A 150 N force is applied at a 30° angle to move an object 8 meters.

Step 1 — Apply the formula: W = 150 N × 8 m × cos(30°) = 150 × 8 × 0.866 = 1,039.2 J

This means about 1,039 joules of work were done on the object — less than the 1,200 J that would result if the force were perfectly aligned with the motion (θ = 0°), because part of the force acts perpendicular to the direction of travel.

Note: This calculator computes work done by a single force. If multiple forces act simultaneously, calculate the work done by each (with its own angle) and sum the results for total work.

Frequently Asked Questions

Mechanical work is calculated as W = F × d × cos(θ), where F is the applied force in newtons, d is the distance moved in meters, and θ is the angle between the force direction and the direction of motion. The result is expressed in joules (J). This calculator applies that formula directly to whatever values you enter.
Only the component of force that acts in the direction of motion does work — the cos(θ) term accounts for this. When force and displacement point in exactly the same direction (θ = 0°), cos(θ) = 1 and all the force contributes to work. When they're perpendicular (θ = 90°), cos(θ) = 0 and no work is done at all, regardless of how large the force is.
Negative work occurs when the angle between force and displacement is greater than 90°, meaning the force has a component acting opposite to the direction of motion — like friction or braking force. Negative work indicates energy being removed from the object's motion, rather than added to it.
When the angle is exactly 90°, cos(90°) = 0, so the formula gives zero work regardless of the force or distance values. A classic example is carrying a bag horizontally at constant height — gravity acts downward while you move horizontally, so gravity does zero work on the bag even though gravitational force is present.
Power is the rate at which work is done — once you know the work done using this calculator, divide it by the time taken to find power using the [Mechanical Power Calculator](/mechanical-power-calculator/). Work tells you the total energy transferred; power tells you how quickly that transfer happened.
Force is entered in newtons (N), distance in meters (m), and angle in degrees (°), producing work in joules (J) — the SI unit of energy. If your force or distance values are in other units, convert them to newtons and meters first for an accurate result.
Pushing a 200 N force over a 10-meter distance in the same direction as motion (θ = 0°) does 2,000 J of work — roughly the energy needed to lift a 20 kg object about 10 meters against gravity, illustrating how work connects force, distance, and energy.
The work-energy theorem states that the net work done on an object equals its change in kinetic energy. If you calculate work done by a net force here, that value tells you exactly how much the object's kinetic energy changed — check the result against the [Kinetic Energy Calculator](/kinetic-energy-calculator/).
No — this calculator computes the work done by a single specified force over a given distance and angle. If multiple forces act on an object simultaneously, you'd need to calculate the work done by each force separately (each with its own angle relative to displacement) and sum the results to find total work.
Lifting an object straight up against gravity is a special case where force equals the object's weight (mass × gravity) and the angle is 0° (force and displacement both point upward). This equals the object's gain in gravitational potential energy — verify it against the [Potential Energy Calculator](/potential-energy-calculator/).
The most common mistake is forgetting to account for the angle between force and displacement, effectively assuming θ = 0° when the force isn't actually aligned with the direction of motion. This overestimates the work done whenever the force has any perpendicular component.
Work calculations are foundational to energy conservation problems, machine design (calculating energy input needed for a task), structural engineering (work done against friction or gravity), and any scenario connecting force, distance, and energy transfer.
Also known as
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