BYTETOOLS

Potential Energy Calculator

Calculate gravitational potential energy PE = mgh or elastic spring energy ½kx², solving for any variable, with gravity presets and unit conversion.

490.3325 J
Energy
0.4903
Kilojoules
117.1923
Calories
361.6507
Foot-pounds

Working

PE = mgh = 10 × 9.80665 × 5 = 490.3325 J (m = 10 kg, g = 9.80665 m/s², h = 5 m). PE is measured relative to your chosen zero height. Earth preset uses standard gravity g = 9.80665 m/s².

What is the Potential Energy Calculator?

The ByteTools Potential Energy Calculator handles both kinds of mechanical potential energy taught in physics.

  • Gravitational PE = mgh solved for any of the four variables
  • Elastic spring mode PE = ½kx² solved for energy, k or x
  • Gravity presets: Earth (9.80665), Moon (1.625), Mars (3.721 m/s²)
  • Metric and imperial mass and height units
  • Energy output in J, kJ, cal and ft·lbf
  • 100% private — runs entirely in your browser

How to use the Potential Energy Calculator

  1. 1

    Pick gravitational (mgh) or elastic (½kx²) mode.

  2. 2

    Choose which variable to solve for and enter the others.

  3. 3

    In gravitational mode, pick a gravity preset or type a custom g.

  4. 4

    Read the result in joules plus kJ, calories and foot-pounds.

  5. 5

    Copy the answer with one click.

About the Potential Energy Calculator

The ByteTools Potential Energy Calculator handles both kinds of mechanical potential energy taught in physics. Gravitational mode solves PE = m × g × h for energy, mass, height or gravity, using standard gravity g = 9.80665 m/s² by default with presets for the Moon and Mars. Elastic mode solves the spring energy equation PE = ½ × k × x² for energy, spring constant or extension.

Mass can be entered in kilograms, grams or pounds, and height in metres, centimetres, feet or inches; energy is reported in joules, kilojoules, calories and foot-pounds. The substituted formula is printed under every answer so the working is transparent.

It is designed for students, teachers and engineers doing quick checks. All computation happens 100% locally in your browser — nothing is uploaded and it works offline.

Frequently asked questions

How do you calculate gravitational potential energy?

Multiply mass, gravitational acceleration and height: PE = mgh. Lifting a 10 kg mass 5 m on Earth stores PE = 10 × 9.80665 × 5 = 490.3 J. The energy is measured relative to your chosen reference height, usually the ground or a table top.

What is elastic potential energy?

It is the energy stored in a stretched or compressed spring: PE = ½kx², where k is the spring constant in N/m and x the displacement from natural length. A 200 N/m spring stretched 0.1 m stores ½ × 200 × 0.01 = 1 J. It assumes the spring obeys Hooke's law.

Does potential energy depend on the path taken?

No. Gravitational PE depends only on the height difference, not the route — carrying a box up a ramp or a ladder to the same shelf stores exactly the same energy. That is what makes gravity a conservative force and mgh so useful.

Can potential energy be negative?

Yes, if the object sits below your chosen zero level. A rock at the bottom of a 10 m well has PE = −mgh relative to ground level. Only differences in potential energy are physically meaningful, so the choice of zero is yours.

How is potential energy related to kinetic energy?

In the absence of friction they interconvert: a falling object's mgh becomes ½mv². Dropping from height h gives impact speed v = √(2gh) — about 9.9 m/s from 5 m on Earth. Our kinetic energy calculator handles the other side of that exchange.

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