Mechanics
Work
Work is energy transferred by a force over a displacement.
Variables
WJ
Work
Energy transferred
In SI units: kg·m²/s²
FN
Force
Applied force
In SI units: kg·m/s²
dm
Displacement
Distance moved
θ°
Angle
Angle between F and d
In SI units: rad
Derivation
W = F⃗ · d⃗ = |F||d|cos θ (dot product).
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- F = 2 N (Force)
- d = 3 m (Displacement)
- θ = 4 ° (Angle)
Result: W = 5.9853843 J
Other mechanics formulas with the same quantities
Where this formula is listed
- Mechanics formulas, under Work & Energy, alongside Spring Potential Energy, Work-Energy Theorem and Conservation of Mechanical Energy.
- In the mechanics list it comes after Bulk Modulus and before Kinetic Energy.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Work formula?
Work is written W = Fd cos θ. Work is energy transferred by a force over a displacement. It belongs to Mechanics, under Work & Energy.
What are the units in W = Fd cos θ?
In SI units, W is work, measured in kg·m²/s²; F is force, measured in kg·m/s²; d is displacement, measured in m; θ is angle, measured in rad.
How is the Work formula derived?
W = F⃗ · d⃗ = |F||d|cos θ (dot product). The result is W = Fd cos θ.