Quick answer
Work done by a force is W = F d cos θ. A 100 N force over 5 m at 0° does 500 J of work, or 368.78 foot-pounds.
Enter the force, distance and the angle between the force and the motion. The calculator returns the work in joules and foot-pounds.
Related tools: Potential Energy Calculator: Gravitational potential energy from mass, height and gravity. Power Calculator: Mechanical power from work and time, or force and velocity. Solar Panel Output Calculator: Daily, monthly and yearly energy from a solar array.
How to use the Work Calculator
- Enter force (N).
- Enter distance (m).
- Enter angle between force and motion (°) (between 0 and 180). It starts at 0.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Force | A number, in N | — |
| Distance | A number, in m | — |
| Angle between force and motion | A number, in ° | ≥ 0, ≤ 180, starts at 0 |
Formula and method
Formula
W = F d cos θ
IEEE-754 double precision; shown to the decimals indicated.
Work is positive when the force has a component along the motion.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Force = 100; Distance = 5; Angle between force and motion = 0.
| Result | Value |
|---|---|
| Work | 500 J |
| In foot-pounds | 368.7811 |
Example 2
Inputs: Force = 50; Distance = 10; Angle between force and motion = 30.
| Result | Value |
|---|---|
| Work | 433.012702 J |
| In foot-pounds | 319.3738 |
Example 3
Inputs: Force = 200; Distance = 3; Angle between force and motion = 90.
| Result | Value |
|---|---|
| Work | 0 J |
| In foot-pounds | 0 |
The first line is the headline result (work). Below it the work Calculator lists in foot-pounds, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Worked example
At 0°, cos θ = 1, so W = 100 × 5 = 500 J. Pulling at 60° gives 100 × 5 × 0.5 = 250 J. Only the component of force along the motion does work.
Zero work
A 90° angle gives zero work: carrying a bag horizontally does no work on it against gravity. Work equals the change in kinetic energy (work-energy theorem). Negative work removes energy.
How the result changes with force
Holding every other input at the first worked example, this table changes only force. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Force | Work | In foot-pounds |
|---|---|---|
| 50 | 250 J | 184.3905 |
| 100 | 500 J | 368.7811 |
| 200 | 1,000 J | 737.5621 |
| 400 | 2,000 J | 1,475.1243 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Force: left empty shows "Enter force." beside that field and no result.
- Angle between force and motion: entering "200" shows "Angle between force and motion must be at most 180." beside that field and no result.
Choosing between the Work Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Potential Energy Calculator](/science/potential-energy-calculator/) | mass, height and gravitational acceleration | Potential energy |
| [Power Calculator](/science/power-calculator/) | use | Power |
| [Solar Panel Output Calculator](/science/solar-panel-output-calculator/) | panel rating, number of panels and peak sun hours per day | Energy |
| [Solar Payback Calculator](/science/solar-payback-calculator/) | system cost and annual savings | Payback period |
| [Wind Power Estimate Calculator](/science/wind-power-estimate-calculator/) | rotor diameter, wind speed and power coefficient | Power |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- A 90° angle gives zero work
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for force and angle between force and motion to confirm this.
Frequently asked questions
What is a joule?
A joule is the work done by a force of one newton over one metre; 500 J is 100 N over 5 m.
Does holding a weight do work?
Not in the physics sense.
How does work relate to power?
Power is work per second.
What does the Work Calculator calculate?
Work done by a force over a distance at an angle. It returns Work and In foot-pounds.
What formula does the Work Calculator use?
W = F d cos θ. Work is positive when the force has a component along the motion.
What do I need to enter in the work Calculator?
You enter Force (N), Distance (m) and Angle between force and motion (°).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. A 90° angle gives zero work.
What is an example of a work result?
With force 100, distance 5 and angle between force and motion 0, the work is 500 J.
Related calculators
- Potential Energy Calculator — Gravitational potential energy from mass, height and gravity.
- Power Calculator — Mechanical power from work and time, or force and velocity.
- Solar Panel Output Calculator — Daily, monthly and yearly energy from a solar array.
- Solar Payback Calculator — Simple payback period of an installation after incentives.
- Wind Power Estimate Calculator — Power from a wind turbine rotor at a wind speed.
- Work Hours Calculator — Hours worked between a start and end time minus breaks.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.