Practice

½mv² Formula – How to Calculate Kinetic Energy (Practice)

KE = ½mv² — Translational kinetic energy

Kinetic energy is the energy of motion. For a single mass moving as a whole, KE = ½ m v². Double the speed and KE becomes four times larger.

Guide — how to use this formula

1. 1. Convert mass to kg and speed to m/s.
2. 2. Square the speed, multiply by mass, then take half.
3. 3. Or rearrange: v = √(2KE/m), m = 2KE/v².
4. 4. Pair with PE = mgh for drop / conservation problems.

Derivation

From the work–energy theorem, net work equals the change in kinetic energy. Starting from rest:

1. Constant net force F accelerates mass m through distance d:
   W = Fd = mad
2. With v² = u² + 2ad and u = 0:
   v^{2} = 2ad \Rightarrow ad = \tfrac{1}{2}v^{2}
3. So the work (and gained KE) is
   KE = \tfrac{1}{2}mv^{2}

Units: kg · (m/s)² = J. Use speed relative to your chosen frame.

Examples

Example: 2 kg at 4 m/s

KE = ½(2)(4)² = 16 J.

Example: find speed from 50 J

m = 4 kg, KE = 50 J → v = √(2×50/4) = √25 = 5 m/s.

Practice on the interactive page

Calculator · All practice formulas