Answer first
What this calculator tells you
Calculate the work done by a force over a distance, and the power if you know the time. Find the energy a push or a pull transfers, and how fast it happens. Formula: Work = F × d × cos θ; power = work ÷ time; 1 horsepower = 745.7 W. At the worked-example inputs, the work done (j) is 519.6. Holding every other input steady, moving force (n) from 40 to 60 moves the result from 415.7 to 623.5.
Transparent method
The formula
Find the energy a push or a pull transfers, and how fast it happens.
Worked example
Example inputs
How to interpret the result
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.
At the worked-example inputs the work done (j) is 519.6. It rises with force (n) and distance (m) and falls as angle between force and motion (degrees) increases; time taken (s) does not move it.
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds).
Before you rely on it
What to check
Read the angle as the gap between the force and the direction of motion. Pushing straight along the path is zero degrees and gets full credit.
The common error
Where people go wrong with work and power calculator
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.
Sensitivity evidence
How force (n) changes the work done (j)
Holding every other input at the worked-example value, moving force (n) from 40 to 60 moves the work done (j) from 415.7 to 623.5: a spread of 207.8, or 40% of the worked-example result.
| Force (N) | Work done (J) | Power (W) | Power (horsepower) |
|---|---|---|---|
| 40 | 415.7 | 103.9 | 0.139 |
| 45 | 467.7 | 116.9 | 0.157 |
| 50worked example | 519.6 | 129.9 | 0.174 |
| 55 | 571.6 | 142.9 | 0.192 |
| 60 | 623.5 | 155.9 | 0.209 |
Every input, tested
Which input moves the work done (j) most
Of the 4 inputs, force (n) moves the work done (j) most (103.9 across the range tested) and angle between force and motion (degrees) moves it least (31.4). Time taken (s) does not change it at all.
| Input | Tested from | To | Work done (J) at each end | Swing |
|---|---|---|---|---|
| Force (N) | 45 | 55 | 467.7 to 571.6 | 103.9 (20%) |
| Distance (m) | 11 | 13 | 476.3 to 562.9 | 86.6 (17%) |
| Angle between force and motion (degrees) | 27 | 33 | 534.6 to 503.2 | 31.4 (6.0%) |
| Time taken (s) | 3.6 | 4.4 | 519.6 to 519.6 | none |
Two variables at once
Work done (J) by force (n) and distance (m)
Across the grid the work done (j) runs from 346.4 to 727.5. Moving force (n) from 40 to 60 shifts it by 207.8 at the middle column, and moving distance (m) from 10 to 14 shifts it by 173.2 at the middle row, so force (n) is the bigger lever here.
| 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 |
The highlighted cell is the worked example: 519.6.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Force (N) | 50 | Enter the force (n) used in this calculation. |
| Distance (m) | 12 | Enter the distance (m) used in this calculation. |
| Angle between force and motion (degrees) | 30 | Enter the angle between force and motion (degrees) used in this calculation. |
| Time taken (s) | 4 | Enter the time taken (s) used in this calculation. |
| Work done (J) | 519.6 | |
| Power (W) | 129.9 | |
| Power (horsepower) | 0.174 | |
Inputs, definitions and assumptions
Force (N)
Enter the force (n) used in this calculation. The prefilled worked-example value is 50.
Distance (m)
Enter the distance (m) used in this calculation. The prefilled worked-example value is 12.
Angle between force and motion (degrees)
Enter the angle between force and motion (degrees) used in this calculation. The prefilled worked-example value is 30.
Time taken (s)
Enter the time taken (s) used in this calculation. The prefilled worked-example value is 4.
How to use this calculator
- 1Verify the inputs. Gather force (n), distance (m), angle between force and motion (degrees) and time taken (s) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the work done (j) at 519.6. Store your own version of it as Scenario A.
- 3Test one change. Start with force (n), the input with the biggest effect here: moving force (n) from 45 to 55 takes the work done (j) from 467.7 to 571.6, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example force (n) (25) the work done (j) is 259.8; at double (100) it is 1,039.2.
People also ask
Frequently asked questions
How do you calculate work and power?
Work = F × d × cos θ; power = work ÷ time; 1 horsepower = 745.7 W. At the worked-example inputs the work done (j) is 519.6.
What does the work and power result mean?
Find the energy a push or a pull transfers, and how fast it happens. At the worked-example inputs the work done (j) is 519.6. It rises with force (n) and distance (m) and falls as angle between force and motion (degrees) increases; time taken (s) does not move it.
How much does force (n) change the work done (j)?
Holding every other input at the worked-example value, moving force (n) from 40 to 60 moves the work done (j) from 415.7 to 623.5, a spread of 207.8.
What are the limits of this work and power calculator?
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds). The tables on this page test force (n) only from 40 to 60; a value outside that range is not tabulated here.
Which input moves the work done (j) most in the work and power calculator?
Ranked by how far each moves the work done (j) across the range tested: force (n) (103.9, 20%), distance (m) (86.6, 17%) and angle between force and motion (degrees) (31.4, 6.0%). Time taken (s) does not change it.
If I double force (n) in the work and power calculator, does the work done (j) double?
Doubling it from 50 to 100 takes the work done (j) from 519.6 to 1,039.2, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 25 gives 259.8.
How much does distance (m) matter in the work and power calculator?
The worked example uses 12. With the other inputs left at the worked example, moving distance (m) from 11 to 13 takes the work done (j) from 476.3 to 562.9, a swing of 17% of the worked-example figure.
How much does angle between force and motion (degrees) matter in the work and power calculator?
The worked example uses 30. With the other inputs left at the worked example, moving angle between force and motion (degrees) from 27 to 33 takes the work done (j) from 534.6 to 503.2, a swing of 6.0% of the worked-example figure.
How much does time taken (s) matter in the work and power calculator?
The worked example uses 4. The work done (j) does not depend on time taken (s); it moves the power (w) from 144.3 to 118.1 instead when time taken (s) goes from 3.6 to 4.4.
Which inputs change the power (w) in the work and power calculator?
At the worked-example inputs it is 129.9. Force (n) takes it from 116.9 to 142.9, distance (m) takes it from 119.1 to 140.7, angle between force and motion (degrees) takes it from 133.7 to 125.8 and time taken (s) takes it from 144.3 to 118.1.
Which inputs change the power (horsepower) in the work and power calculator?
At the worked-example inputs it is 0.174. Force (n) takes it from 0.157 to 0.192, distance (m) takes it from 0.16 to 0.189, angle between force and motion (degrees) takes it from 0.179 to 0.169 and time taken (s) takes it from 0.194 to 0.158.
Why does a projectile launched at 45 degrees go farthest?
On level ground with no air resistance, the range is greatest at 45 degrees, because that angle balances the time in the air against the forward speed. Angles equally far above and below 45 give the same range.
Sources and evidence
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