Work Calculator
This work calculator finds the work done by a force over a distance, using W = F d cos θ. Enter the force, the distance, and the angle between them and the work calculator returns the work in joules and kilojoules. It is the physics work calculator for any push or pull, whether the force lines up with the motion or acts at an angle.
Results
The Work Calculator is part of our Energy collection. Browse more energy to size, convert, and check your work alongside this tool.
What the work calculator shows
In physics, work is done when a force moves an object, and the work calculator measures how much. It multiplies the force by the distance moved and by the cosine of the angle between them, so a force that pushes straight along the motion does the most work. This work calculator returns joules, the unit of energy, since work and energy are the same quantity.
The formula behind the work calculator
The work calculator uses force times distance times the cosine of the angle:
F is the force, d is the distance, and θ is the angle between them. When the force is along the motion, cos 0 is 1 and the work is simply force times distance. At 90 degrees, cos is 0 and no work is done, which is why carrying a bag horizontally does no work against gravity. The work calculator applies the cosine for you.
Work calculator example
A 100 N force pushing an object 5 m straight along the motion. The work calculator gives:
So 500 joules of work is done, or 0.5 kJ. Change the angle to 60 degrees and the work drops to 250 J, since only part of the force acts along the path.
How to use the work calculator
Enter the force in newtons, the distance in meters, and the angle in degrees between the force and the motion, then the work calculator returns the work in joules and kilojoules. Use 0 degrees when the force pushes straight along the path, which is the most common case. The work done calculator handles angled forces too, since it applies the cosine of whatever angle you enter.
Reading the work done calculator result
The work in joules is the energy transferred to the object by the force. Positive work speeds an object up or lifts it; negative work, when the force opposes the motion, slows it down, as friction does. If the angle is 90 degrees the result is zero, since the force does not move the object along its line. Use the work done calculator result with a time to find power, or with mass to link it to a change in energy.
When to use the work calculator
- Solving physics problems with the work calculator
- Finding energy transferred by a force over a distance
- Handling angled forces with the work done calculator
- Setting up a power calculation from work and time
Common work calculator mistakes
- Ignoring the angle. A force at an angle does less work; enter the real angle, not always 0.
- Confusing force with weight. Use the force acting along the motion, not just the object weight.
- Mixing units. Force in newtons and distance in meters give joules; other units need converting first.
Tips for work problems
- Use 0 degrees when the force pushes straight along the path.
- Divide work by time to get power in watts.
- Remember that a force at 90 degrees does no work.
How the physics work calculator uses angle
The angle term is what makes the physics work calculator more than a simple multiply. Force is a vector, so only its component along the direction of motion does work, and that component is the force times the cosine of the angle. Push a lawnmower with the handle angled down and part of your effort presses into the ground, doing no useful work; only the horizontal part moves the mower. This is also why a satellite in a circular orbit has no work done on it by gravity, since gravity pulls at 90 degrees to the motion the whole way around. A work calculator with angle captures all of these cases with the single cosine factor, so entering the true angle keeps the energy honest.
Work done calculator and the sign of work
Whether work is positive or negative decides which way energy flows. When the force and the motion point the same way, the work is positive and energy goes into the object, speeding it up or raising it. When they oppose, as with braking or friction, the work is negative and energy leaves the object as heat or sound. A work done calculator with mass and distance links this to the change in kinetic energy through the work energy theorem: the net work equals the change in the object motion energy. That is why the same 500 joules can either accelerate a cart or, applied by a brake, bring it to rest.
Work calculator reference values
Work from the work calculator for several forces, distances, and angles:
| Force | Distance | Angle | Work |
|---|---|---|---|
| 100 N | 5 m | 0° | 500 J |
| 100 N | 5 m | 60° | 250 J |
| 200 N | 5 m | 0° | 1000 J |
| 100 N | 10 m | 90° | 0 J |
Work Calculator FAQ
What is the work formula?
The formula is W = F d cos θ, force times distance times the cosine of the angle between them. The work calculator applies it to give the work in joules.
Why does angle matter in the work done calculator?
Only the part of the force along the motion does work. The cosine of the angle scales the force, so a force at 90 degrees does zero work, which the work done calculator with angle shows.
What unit is work measured in?
Joules, the same unit as energy, since work is energy transferred. The physics work calculator also shows kilojoules for larger values.
Can work be negative?
Yes. When the force opposes the motion, such as friction, the angle is more than 90 degrees and the work is negative, meaning energy is taken from the object.