Work–Energy Theorem
Also known as net work equals change in kinetic energy
Worked example: 2 kg from rest to 10 m/s → 100 J — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
The energy swap →
Grade 11Grade 11 Physics
Work becomes speed →
Grade 12Grade 12 Physics
The work–energy theorem →
UniversityEngineering Mechanics
Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning. Find 2 more lessons on this formula.
share your results
Work–Energy Theorem explained
Whatever the forces, the net work done on an object shows up entirely as a change in its kinetic energy: W = ½m(v² − v₀²). Accelerate a 2 kg mass from rest to 10 m/s and exactly 100 J went in, no matter whether it took 1 m of huge force or 100 m of gentle push. Gaspard-Gustave de Coriolis formalised both "work" and the ½mv² form of kinetic energy in 1829, precisely so factory owners could compare what different machines actually delivered.
The theorem's power is that it skips time entirely, making it the fastest route to braking distances: a 1360 kg car slowing from 26.8 m/s to 13.4 m/s sheds about 367 kJ, and dividing that by the braking force gives the stopping distance directly. Sign discipline is the trap — friction and braking do negative work, so W comes out negative whenever the object slows, and this calculator will happily return a negative number to tell you so.
Work–Energy Theorem formula
- = Net work (J)
- = Mass (kg)
- = Final speed (m/s)
- = Initial speed (m/s)
Missing one of these? Work it out first, then come back
- Net work — Work (W = Fd cos θ), Power (P = W/t)
- Mass — Newton's Second Law, Kinetic Energy
- Final speed — Speed, Distance & Time, Kinetic Energy
- Initial speed — Speed at Natural Roll, Slide Distance Before Natural Roll