Calculate kinetic energy (½mv²) or gravitational potential energy (mgh).
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How do you calculate kinetic and potential energy?
Kinetic energy KE = ½ · m · v² and gravitational potential energy PE = m · g · h, where m is mass (kg), v velocity (m/s), h height (m) and g gravity (m/s²). For example, a 2 kg object at 3 m/s has KE = ½ × 2 × 3² = 9 J; raised 10 m it has PE = 2 × 9.81 × 10 ≈ 196.2 J.
Understanding your result
Kinetic energy is the energy of movement and grows with the square of speed. Potential energy is stored by position in a gravitational field. One joule equals one kilogram-metre-squared per second-squared (kg·m²/s²).
Formula and method
Kinetic energy KE = ½ · m · v². Gravitational potential energy PE = m · g · h, where m is mass (kg), v velocity (m/s), h height (m) and g gravity (m/s²).
Assumptions and limitations
This tool computes kinetic energy from mass and speed and gravitational potential energy from mass and height, all in SI units, returning joules. Potential energy is always relative to the reference height you choose, not an absolute value. The model assumes a uniform gravitational field and ignores rotation, friction and relativistic effects.
Worked example
A 2 kg object at 3 m/s has KE = ½ × 2 × 3² = 9 J; raised 10 m it has PE = 2 × 9.81 × 10 ≈ 196.2 J.
How to use this tool
- Choose kinetic or potential energy.
- Enter the mass and the velocity or height.
- Read the energy in joules.
Common mistakes to avoid
- Forgetting to square the velocity for kinetic energy.
- Using grams instead of kilograms for mass.
About the Kinetic & Potential Energy Calculator
This calculator works out mechanical energy in joules. Find kinetic energy from an object’s mass and velocity, or gravitational potential energy from its mass and height above a reference point.
Who should use this tool
Physics students, teachers and engineers checking energy in motion or storage problems.
Benefits
- Kinetic and potential energy in one tool.
- Adjustable gravity for other planets.
- Shows the formula and the working.
- Results in joules and kilojoules.
Practical use cases
- Energy of a moving vehicle or ball.
- Stored energy of a raised mass.
- Checking conservation-of-energy homework.
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Frequently asked questions
What units does this use?
SI units: mass in kilograms, velocity in metres per second, height in metres and energy in joules.
Why does doubling speed quadruple the energy?
Because kinetic energy depends on velocity squared — 2² = 4 — so twice the speed means four times the kinetic energy.
What value of gravity does the potential energy use?
Gravitational potential energy uses g, the acceleration due to gravity, taken as about 9.81 metres per second squared for Earth's surface. This value varies slightly with latitude and altitude and differs on other bodies, such as roughly 1.62 on the Moon. Adjust g if you need results for a different location or planet.