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Work–Energy Theorem

Also known as net work equals change in kinetic energy

W=12m(v2−v02)W = \tfrac{1}{2} m \left(v^{2} - v_0^{2}\right)
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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. Change any unit and the answer follows.

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See also

Conservation of Mechanical Energy (½mv² + mgh): The special case where the net work is done by gravity alone, so the total energy never changes and the mass drops out.Displacement from Average Velocity: Both use final speed and initial speed.Final Velocity (Uniform Acceleration): Both use final speed and initial speed.Velocity-Displacement Relation (v² = v₀² + 2ad): Both use final speed and initial speed.Work from Force and Displacement Components: Both use net work.Displacement (Uniform Acceleration): Both use initial speed.
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The energy swap →

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Work–Energy Theorem explained

mv0vW

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

W=12m(v2−v02)W = \tfrac{1}{2} m \left(v^{2} - v_0^{2}\right)
Where
  • WW= Net work (J)
  • mm= Mass (kg)
  • vv= Final speed (m/s)
  • v0v_0= Initial speed (m/s)
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Work, energy and power

8 formulasWork, the two stores of mechanical energy, the theorem that connects them to speed, and the two ways of writing power.

Revised 16 October 2026
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formula.expert. (2026, October 16). Work–Energy Theorem Formula & Calculator. https://formula.expert/solvers/work-energy-theorem

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