What is gravitational potential energy?

Gravitational potential energy is the energy an object has because of its height above a reference level. Raising an object requires work against gravity, and that work is stored rather than lost — release the object and every joule comes back as motion. The formula is PE = mgh, where m is mass in kilograms, g is gravitational acceleration and h is height above your chosen zero point.

How do I calculate potential energy?

Multiply mass by gravity by height, working in SI units. A 70 kg person standing on a 10 metre diving board has PE = 70 × 9.81 × 10 = 6,867 joules, about 6.9 kJ or 1.64 food Calories. The two commonest mistakes are leaving mass in grams or pounds, and measuring height from the wrong reference point — it must be the vertical distance to wherever you are treating as zero.

Where is the zero point for height measured from?

Wherever you choose — and that is genuinely allowed. There is no absolute zero of gravitational potential energy, so only differences in height are physically meaningful. A book on a table has one value relative to the tabletop and a larger one relative to the floor, and both are correct. Physicists pick whichever reference makes the problem simplest, usually the lowest point the object will reach.

How does potential energy turn into kinetic energy?

As an object falls, height decreases so PE falls, while speed increases so KE rises — and in the absence of air resistance the sum stays exactly constant. At the moment of impact all the potential energy has become kinetic energy, so mgh = ½mv², which rearranges to the familiar v = √(2gh). Mass cancels out of that result entirely, which is why every object dropped from the same height lands at the same speed.

Why is the halfway point 50/50 in energy but not in speed?

Because energy and speed are not proportional. Halfway down, exactly half the height remains, so exactly half the potential energy remains and half has become kinetic — a clean 50/50 split. But kinetic energy depends on v², so having half the kinetic energy means having √0.5 of the final speed, roughly 71 percent. The object is already travelling at over seven tenths of its landing speed when it is only halfway down.

How does potential energy differ from kinetic energy?

Potential energy is stored and depends on position; kinetic energy is active and depends on motion. They also scale differently, which matters more than people expect. PE is directly proportional to height, so doubling the height doubles the energy and the graph is a straight line. KE depends on the square of speed, so doubling the speed quadruples the energy and the graph curves upward. Both are measured in joules and both convert freely into one another.

Does gravity change the potential energy?

Yes, directly and proportionally, because g appears in the formula. Lifting a 70 kg person 10 metres stores 6,867 J on Earth but only 1,134 J on the Moon, where g is 1.62 m/s². On Jupiter, at 24.79 m/s², the same lift stores 17,353 J. This is why lifting things on the Moon feels so easy — you genuinely are storing far less energy for the same effort of movement.

What is elastic potential energy?

Elastic potential energy is stored in a stretched or compressed spring rather than by height, and it follows PE = ½kx², where k is the spring constant and x is the displacement from the natural length. It behaves like kinetic energy in that it depends on a squared quantity, so stretching a spring twice as far stores four times the energy. Rubber bands, bows and vehicle suspension all store energy this way.

How is potential energy used to generate electricity?

Hydroelectric dams are gravitational potential energy at industrial scale. Water held high behind a dam has PE = mgh, and letting it fall through turbines converts that store into motion and then into electricity. A single tonne of water dropping 100 metres releases about 981,000 joules, roughly 0.27 kilowatt-hours before losses. Pumped-storage plants run the process backwards, using surplus power to lift water uphill for later.

Potential Energy Calculator (PE = mgh)

Calculate gravitational potential energy, mass or height from PE = mgh — the energy an object holds simply because of where it is. Lift something up and you do work against gravity; that work does not disappear, it is stored, waiting. Let go and you get every joule of it back as motion. Enter any tw...

PE = m g h

SOLVE FOR

MASS

HEIGHT

GRAVITY — 9.81 m/s²

EVERYDAY EXAMPLES

POTENTIAL ENERGY

6,867.0 J

KILOJOULES

6.867

FOOD CALORIES

1.641

FOOT-POUNDS

5,064.8

Mass

70.000 kg

Height

10.000 m

Energy

6,867.00 J

If dropped, lands at

14.01 m/s

At double height

13,734.0 J

Weight (mg)

686.70 N

STEPS

Convert to SI: mass = 70.0000 kg, height = 10.0000 m, g = 9.81 m/s²

Multiply all three: PE = m × g × h

PE = 70.0000 × 9.81 × 10.0000 = 6,867.0000 J

STORED ENERGY BECOMING MOTION

HEIGHT

10.0 m

STORED

6,867 J

MOVING

0 J

SPEED

0.0 m/s

Conservation of energy. The gold band is energy still held in reserve by height, the black band is energy already turned into motion — and the line between them sits at exactly the object's current height, because each band measures a real distance: gold the height remaining, black the distance already fallen. One becomes the other as it falls and the total never changes. Halfway down the split is exactly 50/50, yet the speed there is not half the impact speed but about 71 percent of it, because speed depends on the square root of the energy.

HOW BIG IS THIS ENERGY?

THE SAME LIFT ELSEWHERE

Earth

6,867 J

Moon

1,134 J

Mars

2,604 J

Venus

6,209 J

Jupiter

17,353 J

WHAT THAT ENERGY IS WORTH

Food Calories

1.6413 kcal

Run a 60 W bulb for

114.5 s

A person climbing it

34.3 s

Impact speed

14.01 m/s

Climb time assumes a sustained 200 W of useful output, roughly what a fit adult manages on stairs.

Live simulation · updates as you type

Created with❤️byeaglecalculator.com

HOW TO USE

1
Choose what to find with the SOLVE FOR buttons: Energy, Mass or Height. The input fields change to ask for whichever two quantities are needed.
2
Enter your values and pick units beside each field. Mass in kilograms, grams, tonnes or pounds; height in metres, centimetres, feet or kilometres; energy in joules, kilojoules, megajoules, food Calories or kilowatt-hours.
3
Set gravity if you are not on Earth — the planet chips cover the Moon, Mars, Venus and Jupiter. Because g sits directly in the formula, changing it scales the stored energy in exact proportion.
4
Watch the conversion tower on the right: press PLAY to release the object and see the gold band of stored energy drain into the black band of motion, or drag the scrubber to freeze any point and read the exact split.

THE FORMULAS

Gravitational PEPE = m g h

Solve for massm = PE ÷ (g h)

Solve for heighth = PE ÷ (m g)

ConservationPE + KE = constant

Speed after fallingv = √(2gh)

Work done liftingW = m g Δh

Elastic PE (spring)PE = ½ k x²

Earth gravityg ≈ 9.81 m/s²

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Last updated: July 27, 2026 · Formula verified · Eagle-eyed accuracy for every calculation.