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Work Calculator (W = F·d·cos θ)
Computes mechanical work W = F × d × cos(θ) done by forces along a displacement vector.
Mechanical Work Calculator
Work done by a constant force over displacement: W = F × d × cos(θ)
W = F·d·cos θ
Real-World Mechanical Scenarios:
Vector Direction & Angle Diagramcos(0°) = 1.000
Total Mechanical Work Done
3,000 Joules (J)
Kilojoules3.000 kJ
Foot-pounds2212.7 ft·lbf
Effective Parallel Force200.0 N
Step-by-Step Derivation
1. Formula: Mechanical Work W = F · d · cos(θ)
2. Angle Cosine: cos(0°) = 1.0000
3. Effective Parallel Force Component: F_parallel = 200 N × 1.0000 = 200.00 N
4. Total Work Done: W = 200.00 N × 15 m = 3000.00 Joules (J)
5. Equivalent Units: 3.000 kJ | 2212.7 ft·lbf
What is Work in Physics?
Work is energy transferred by a force acting through a displacement. If force is perpendicular to motion, work is zero.
Formula & Step-by-Step Calculation
W = F × d × cos(θ)
Dot product of force and displacement vectors.
Worked Step-by-Step Examples
Example 1
200 N force pulling a sled 15 meters along the ground
Solution: 3,000 Joules
• 200 × 15 × cos(0°) = 3,000 J
Common Real-World & Academic Use Cases
- ✓ Crane hoisting work
- ✓ Thermodynamic piston expansion
- ✓ Human physical exertion
How to Use the Work Calculator (W = F·d·cos θ)
1
Input Force, Distance, Angle
Enter N, m, and degrees.
2
Read Work
Inspect calculated Joules.
Frequently Asked Questions
Q: When is work negative?
When the angle θ > 90° (force opposes motion, such as friction).