Work Calculator
With force 50 N, distance moved 10 m, angle between force and motion 30 °, time taken 4 s, work comes to 433.0127 J — work done. It is reached in 5 steps, the last of which is 43.30127 * 10, and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, not an approximation fitted to it.
Work done by a force over a distance, with the angle between them, plus the power if it took a given time and the same figure in calories.
Formula and sources checked · How we check
Force 50 N, Distance moved 10 m, Angle between force and motion 30 °, Time taken 4 s
433.0127 J
Work done for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Force along the motion
50 * cos(30 * pi / 180)43.301 N- Work done
43.30127 * 10433.013 J- Average power
433.0127 / 4108.253 W- Average power in horsepower
108.25318 / (550 * 0.3048 * 0.4535924 * 9.80665)0.145 hp- Work in food calories
433.0127 / 41840.103 kcal
Worked example
Pulling with 50 N at 30 degrees above the direction of travel puts 43.3013 N along the motion, so dragging something 10 m does 433.0127 joules of work. Over 4 seconds that is 108.2532 watts. Only the component along the motion counts: pull straight up on a sledge and the angle is 90 degrees, the cosine is zero, and no work is done on it at all.
How to work it out yourself
- 1.Measure the angle between the force and the direction the thing actually moves, not the angle to the ground.
- 2.A force at right angles to the motion does no work. Carrying a box across a level floor does no work on the box, however tired it makes you — the effort goes into your own muscles, not the load.
- 3.Past 90 degrees the cosine is negative and so is the work. That is friction and braking: energy taken out rather than put in.
The formula
- Force along the motion
50 * cos(30 * pi / 180) - Work done
43.30127 * 10 - Average power
433.0127 / 4 - Average power in horsepower
108.25318 / (550 * 0.3048 * 0.4535924 * 9.80665) - Work in food calories
433.0127 / 4184
Source: NIST Special Publication 811 — guide for the use of the SI, BIPM — the SI Brochure, base and derived units
Questions people actually ask
- Why does carrying something horizontally do no work?
- Because the force holding it up is vertical and the motion is horizontal, so the angle is 90 degrees and the cosine is zero. Physics is describing energy transferred to the load, and none is. Your muscles still burn energy holding the tension, which is a separate accounting.
- What is the difference between work and power?
- Work is the energy transferred; power is how quickly. The same 433 joules delivered in 4 seconds is 108 watts, and in 1 second it is 433 watts. A weaker motor can do any job, given time.
- Is a joule the same as a calorie?
- A food calorie is 4,184 joules — it is really a kilocalorie. The 433 joules in the example is about a tenth of a food calorie, which puts the energy accounting of manual work into perspective.
Related
- Velocity CalculatorFinal velocity from a starting velocity, a constant acceleration and a time, with the distance covered and the average velocity over the interval.
- Momentum CalculatorMomentum from a mass and a velocity, with the kinetic energy that goes with it and the impulse needed to stop the object in a given time.
- Kinetic Energy CalculatorKinetic energy from mass and speed, with the stopping distance it implies — because the square on the velocity is the part that surprises people.
- Mass-Energy CalculatorThe rest energy of a mass from E = mc², in joules, kilowatt-hours and kilotons of TNT, using the defined speed of light.
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