Energy

Energy calculator: kinetic E = mv²/2 and potential E = mgh, plus speed, mass and height from energy, with a solution.

What to find:

Gravitational acceleration on Earth g ≈ 9.8 m/s² (problems sometimes use 10 m/s²). Numbers can be decimals (2.5), fractions (1/3) or 1.5e3.

Test yourself

The kinetic and potential energy calculator finds the energy of a body, as well as speed, mass or height from a known energy. The solution is written step by step: given, conversion to SI, formula, substitution, answer.

Kinetic energy

E_k = m · v² / 2, v = √(2E_k / m), m = 2E_k / v²

The energy of motion grows with the square of speed: doubling the speed makes the kinetic energy 4 times larger.

Potential energy

E_p = m · g · h, h = E_p / (m · g), m = E_p / (g · h)

Here h is the height above the chosen zero level and g ≈ 9.8 m/s² is the gravitational acceleration. Below the zero level height and energy are negative.

By conservation of energy, a body falling without air resistance turns potential energy into kinetic: m · g · h = m · v² / 2, so v = √(2gh).

Example 1. A 2 kg ball moving at 3 m/s: E_k = 2 · 3² / 2 = 9 J.

Example 2. A 5 kg load raised 10 m: E_p = 5 · 9.8 · 10 = 490 J.