Work Calculator Formula
Understand the math behind the work calculator. Each variable explained with a worked example.
Formulas Used
Work Done
work = force * distance * cos(angle_rad)Variables
| Variable | Description | Default |
|---|---|---|
force | Force(N) | 50 |
distance | Distance(m) | 10 |
angle | Angle from Direction of Motion(degrees) | 0 |
angle_rad | Derived value= angle * pi / 180 | calculated |
How It Works
Work Done by a Force
Work is the energy transferred when a force moves an object through a displacement.
Formula
W = F * d * cos(theta)
When the force is parallel to motion (theta = 0), all of the force contributes to work. At 90 degrees, no work is done.
Worked Example
A 50 N force pushes a box 10 meters along the floor (angle = 0 degrees).
- 01W = F * d * cos(theta)
- 02W = 50 * 10 * cos(0°)
- 03W = 50 * 10 * 1
- 04W = 500 J
Frequently Asked Questions
Can work be negative?
Yes. When the angle between force and displacement exceeds 90 degrees, cos(theta) is negative, and the force removes energy from the object (e.g., friction).
What is the unit of work?
Work is measured in joules (J). One joule equals one newton-meter.
Is work a scalar or vector?
Work is a scalar quantity. It has magnitude but no direction, even though it is calculated from vector quantities.
Learn More
Guide
How to Calculate Force and Work
Learn how to calculate force (F = ma) and work (W = Fd) step by step. Covers net force, work-energy theorem, power, and real-world applications with clear examples.
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Open Work Calculator