Work and Power: formula
Enter the force in newtons, the distance moved in meters, the angle between the force and the direction of motion in degrees and the time taken in seconds. Work is force times distance times the cosine of the angle, so only the component of force along the motion does work. Power is the work divided by the time, in watts, and 745.7 watts make a horsepower.
Work and Power: worked example
| Force (N) | 50 |
|---|---|
| Distance (m) | 12 |
| Angle between force and motion (degrees) | 30 |
| Time taken (s) | 4 |
| Work done (J) | 519.6 |
| Power (W) | 129.9 |
| Power (horsepower) | 0.174 |
The formula assumes a constant force. Variable forces need integration or an average. Friction and losses mean the work you supply exceeds the useful work.
Work is a scalar and can be negative, when the force opposes the motion.
Work and Power: changing Force (N)
| Force (N) | Work done (J) | Power (W) | Power (horsepower) |
|---|---|---|---|
| 40 | 415.7 | 103.9 | 0.139 |
| 45 | 467.7 | 116.9 | 0.157 |
| 50 (example) | 519.6 | 129.9 | 0.174 |
| 55 | 571.6 | 142.9 | 0.192 |
| 60 | 623.5 | 155.9 | 0.209 |
Work and Power: compare input ranges
| Input | Tested from | To | Work done (J): low input | Work done (J): high input | Swing |
|---|---|---|---|---|---|
| Force (N) | 45 | 55 | 467.7 | 571.6 | 103.9 (20%) |
| Distance (m) | 11 | 13 | 476.3 | 562.9 | 86.6 (17%) |
| Angle between force and motion (degrees) | 27 | 33 | 534.6 | 503.2 | 31.4 (6.0%) |
| Time taken (s) | 3.6 | 4.4 | 519.6 | 519.6 | 0 |
Work and Power: individual input comparisons
| Input | Value | Work done (J) | Power (W) | Power (horsepower) |
|---|---|---|---|---|
| Force (N) | 40 | 415.7 | 103.9 | 0.139 |
| 45 | 467.7 | 116.9 | 0.157 | |
| 50 | 519.6 | 129.9 | 0.174 | |
| 55 | 571.6 | 142.9 | 0.192 | |
| 60 | 623.5 | 155.9 | 0.209 | |
| Distance (m) | 10 | 433 | 108.3 | 0.145 |
| 11 | 476.3 | 119.1 | 0.16 | |
| 12 | 519.6 | 129.9 | 0.174 | |
| 13 | 562.9 | 140.7 | 0.189 | |
| 14 | 606.2 | 151.6 | 0.203 | |
| Angle between force and motion (degrees) | 24 | 548.1 | 137 | 0.184 |
| 27 | 534.6 | 133.7 | 0.179 | |
| 30 | 519.6 | 129.9 | 0.174 | |
| 33 | 503.2 | 125.8 | 0.169 | |
| 36 | 485.4 | 121.4 | 0.163 | |
| Time taken (s) | 3.2 | 519.6 | 162.4 | 0.218 |
| 3.6 | 519.6 | 144.3 | 0.194 | |
| 4 | 519.6 | 129.9 | 0.174 | |
| 4.4 | 519.6 | 118.1 | 0.158 | |
| 4.8 | 519.6 | 108.3 | 0.145 |
Work and Power: combined input changes
| Force (N) / Distance (m) | 10 | 12 | 14 |
|---|---|---|---|
| 40 | 346.4 | 415.7 | 485 |
| 45 | 389.7 | 467.7 | 545.6 |
| 50 | 433 | 519.6 | 606.2 |
| 55 | 476.3 | 571.6 | 666.8 |
| 60 | 519.6 | 623.5 | 727.5 |
Work and Power: which assumptions move the result?
Work and Power: values and definitions
| Quantity and definition | Value used |
|---|---|
| Force (N) | 50 |
| Distance (m) | 12 |
| Angle between force and motion (degrees) | 30 |
| Time taken (s) | 4 |
| Work done (J) | 519.6 |
| Power (W) | 129.9 |
| Power (horsepower) | 0.174 |
Work and Power: half and double Force (N)
| Force (N) | Work done (J) |
|---|---|
| 25 | 259.8 |
| 50 | 519.6 |
| 100 | 1,039.2 |
Common error: Counting the whole force when it pulls at an angle. A sideways component does no work along the path, so the full force overstates the result.
Physics & Mechanics calculators: Wavelength and Frequency Calculator, Projectile Motion Calculator, Free Fall Calculator, Centripetal Force Calculator, Pendulum Period Calculator, Horsepower Calculator.
Work is force times the distance moved along the force, and only the part of the push that points along the motion counts. A 50 newton pull at 30 degrees to the direction of travel, over 12 meters, does about 520 joules of work. Power is how fast that work is done.
Finishing it in 4 seconds is about 130 watts, or roughly a sixth of a horsepower.
The force angle is measured relative to the direction of motion. Pushing straight along the path is zero degrees and gets full credit.
See the force on the force calculator, the energy on the kinetic and potential energy calculators and engine power on the horsepower calculator. The Hooke's law and uniform acceleration pages cover related mechanics, and the electricity cost calculator prices power over time.
Why can carrying a bag still require effort?
The ideal work from a purely vertical support force along a horizontal displacement is zero. That result does not measure the person's metabolic energy use or the work of other forces during walking.
How is work calculated in physics?
Multiply the force by the distance moved in the direction of the force, which is force times distance times the cosine of the angle.
Why does carrying a bag horizontally do no work?
Because the upward force is at 90 degrees to the motion, and the cosine of 90 degrees is zero.
What is the difference between work and power?
Work is the energy transferred, in joules, while power is how fast it is transferred, in watts, which are joules per second.