Work (Physics) Calculator
Total Work: 0 Joules (J)
In Kilojoules: 0 kJ
In Foot-Pounds: 0 ft-lb
Understanding How Work Works in Physics
In everyday language, "work" might mean your job or a difficult task. In the world of physics, however, work has a very specific mathematical definition. Work occurs when a force acts upon an object to cause a displacement. If you push a wall with all your might but the wall doesn't move, scientifically speaking, you have done zero work.
The Formula for Work
The standard formula used by this calculator to determine work done is:
W = F × d × cos(θ)
- W (Work): Measured in Joules (J). One Joule is the work done when a force of 1 Newton moves an object 1 meter.
- F (Force): The magnitude of the force applied to the object, measured in Newtons (N).
- d (Displacement): The distance the object moves while the force is being applied, measured in meters (m).
- θ (Theta): The angle between the force vector and the direction of motion. If you are pushing an object perfectly flat across the floor, the angle is 0°.
How to Use the Work Calculator
- Input Force: Enter the amount of force applied in Newtons. (Example: 50 N).
- Input Distance: Enter how far the object moved in meters. (Example: 10 m).
- Input Angle: If the force is applied at an angle (like pulling a wagon handle), enter that angle in degrees. If the force is in the same direction as the movement, leave this as 0.
- Calculate: Click the button to see the result in Joules, Kilojoules, and Foot-Pounds.
Real-World Examples of Work
Example 1: Lifting a Box
If you lift a box weighing 100 Newtons (about 10kg) vertically for 2 meters, and the force is applied in the same direction as the movement (0 degrees), the work done is:
100 N × 2 m × cos(0) = 200 Joules.
Example 2: Pulling a Suitcase
Imagine you pull a suitcase with a force of 50 N at an angle of 45 degrees for a distance of 20 meters. Because some of your force is directed upward rather than forward, the work is calculated as:
50 N × 20 m × cos(45°) ≈ 707.1 Joules.
Common Units of Work
| Unit | Description |
|---|---|
| Joule (J) | The SI unit of work and energy. |
| Kilojoule (kJ) | 1,000 Joules. |
| Foot-Pound (ft-lb) | The imperial unit of work used primarily in the United States. |
Frequently Asked Questions
Can work be negative?
Yes. Work is negative when the force acts in the opposite direction of the displacement. For example, friction does negative work on a sliding object because it acts to oppose the motion.
What if the object doesn't move?
If the displacement (d) is zero, the work done is always zero, regardless of how much force is applied. This is why holding a heavy barbell stationary over your head results in zero scientific work.
How does the angle affect the work?
The most efficient way to do work is to apply force at 0° (parallel to motion). As the angle increases toward 90°, the work decreases. At exactly 90° (perpendicular), the work done is zero because cos(90°) = 0.