Mechanics
Work-Energy Theorem
Net work equals the change in kinetic energy.
Variables
WnetJ
Net work
Total work done
In SI units: kg·m²/s²
ΔKEJ
Change in KE
Final minus initial KE
In SI units: kg·m²/s²
mkg
Mass
Object mass
Allowed values: 0 or more
vfm/s
Final velocity
Final speed
vim/s
Initial velocity
Initial speed
Derivation
Integrate F = ma over displacement.
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.
- m = 2 kg (Mass)
- vf = 3 m/s (Final velocity)
- vi = 4 m/s (Initial velocity)
Result: Wnet = -7 J
Other mechanics formulas with the same quantities
- Gravitational Potential Energy (Work & Energy) shares Mass
Where this formula is listed
- Mechanics formulas, under Work & Energy, alongside Spring Potential Energy, Power and Conservation of Mechanical Energy.
- In the mechanics list it comes after Power and before Conservation of Mechanical 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-Energy Theorem formula?
Work-Energy Theorem is written W_net = ΔKE = (1/2)mv_f² − (1/2)mv_i². Net work equals the change in kinetic energy. It belongs to Mechanics, under Work & Energy.
What are the units in W_net = ΔKE = (1/2)mv_f² − (1/2)mv_i²?
In SI units, W_n et is net work, measured in kg·m²/s²; ΔKE is change in ke, measured in kg·m²/s²; m is mass, measured in kg; v_f is final velocity, measured in m/s; v_i is initial velocity, measured in m/s.
How is the Work-Energy Theorem formula derived?
Integrate F = ma over displacement. The result is W_net = ΔKE = (1/2)mv_f² − (1/2)mv_i².