Work CalculatorWork done · W = Fd cos θ
Work done is force times the distance moved in the direction of the force: W = Fd cos θ. It is measured in joules (1 J = 1 N·m). Find the work from a force pulled at an angle, from lifting a mass against gravity (W = mgh), or from a power running for a time (W = Pt). Results come in joules, kilocalories, watt-hours and foot-pounds.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Work inputs
θ is the angle between the force and the direction of motion.
Step-by-step working
What is work?
In physics, work is the energy transferred to or from an object when a force moves it through a distance. Only the part of the force acting along the direction of motion counts.
That makes physics “work” narrower than everyday effort. Pushing on a wall that doesn’t move, or carrying a tray across a level room, does no work on the object, even though your muscles are busy.
Quick answers
How do you calculate work done?
Multiply the force by the distance moved in the direction of the force: W = Fd cos θ. Pushing a cart 20 m with a steady 80 N horizontal force does 1,600 J of work.
How much work does it take to lift something?
W = mgh. Lifting a 15 kg suitcase 0.8 m onto a bed takes 15 × 9.81 × 0.8 ≈ 118 J. That energy is stored as potential energy until the case falls.
What does negative work mean?
The force acts against the motion, removing energy, as friction and brakes do. A car’s brakes do negative work equal to the kinetic energy they remove.
How many joules are in a food Calorie?
One food Calorie (kcal) is 4,184 J. Climbing a 3 m staircase at 70 kg does about 2,060 J of useful work, roughly 0.5 kcal, but your body burns about four times that.
Work formula
The work–energy theorem: the net work done on an object equals its change in kinetic energy.
| Symbol | Meaning | SI unit |
|---|---|---|
| W | Work done | J |
| F | Force | N |
| d | Distance moved | m |
| θ | Angle between force and displacement | ° |
| m, h | Mass and height lifted | kg, m |
| P, t | Power and time | W, s |
How to calculate work done
- Find the force acting on the object, in newtons.
- Measure the distance the object moves, in metres.
- Find the angle between the force and the motion, and take its cosine.
- Multiply F × d × cos θ to get joules.
Worked example: pulling a wagon at an angle
You pull a wagon 10 m with a 50 N force on a handle angled 30° above horizontal.
W = 50 × 10 × 0.866 = 433.0 J
Lifting a 20 kg box onto a 1.5 m shelf takes W = mgh = 20 × 9.807 × 1.5 = 294.2 J, about 0.07 kcal. Your body actually spends nearer 0.3 kcal, because muscles are inefficient.
Energy units for work
Work and energy share the same units. Here is 1 joule expressed in the units this calculator uses.
| Unit | Equals | Typical use |
|---|---|---|
| 1 joule (J) | 1 N·m | SI unit |
| 1 kilocalorie (kcal) | 4,184 J | Food labels (Calories) |
| 1 watt-hour (Wh) | 3,600 J | Batteries |
| 1 kilowatt-hour (kWh) | 3,600,000 J | Electricity bills |
| 1 foot-pound (ft·lbf) | 1.3558 J | US engineering |
| 1 BTU | 1,055 J | Heating and cooling |
Common mistakes to avoid
- Using the full force when it is applied at an angle. Multiply by cos θ.
- Counting work when nothing moves. Holding a heavy box still does no physical work on it, however tiring it feels.
- Confusing work with power. Work is energy (J); power is how fast work is done (W = J/s).
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Work Calculator: frequently asked questions
W = Fd cos θ, where F is the force, d the displacement and θ the angle between them. When the force is along the motion, W = Fd.
The joule (J), equal to one newton-metre. Other units are kWh, kcal, BTU and ft·lbf.
When the object doesn’t move, or when the force is perpendicular to the motion, as with a satellite’s gravity in a circular orbit.
No. Work is a scalar. It has magnitude and sign but no direction, even though force and displacement are both vectors.
The net work done on an object equals its change in kinetic energy: Wnet = ½mv² − ½mu².
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 7.1, Work
- HyperPhysics, Georgia State University — work and energy
- NIST Special Publication 811 — Guide for the Use of the SI — energy conversion factors
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.