Potential Energy Calculator

1. Enter any two of energy, mass and height.
2. Leave the one you want to find blank.
3. Adjust gravity g if you are not on Earth (it defaults to 9.81).
4. Read the result and the formula used.

Here is what each result means:

Gravitational potential energy is the energy an object has because of its height in a gravitational field. Lift something up and you store energy in it; let it fall and that energy is released as motion. The higher the object and the heavier it is, the more energy it holds. A 2 kilogram object raised 10 meters on Earth stores about 196 joules.

The energy depends on three things: the mass, the height above some chosen reference level, and the strength of gravity. On Earth the field strength is about 9.81 meters per second squared, but it is weaker on the Moon and stronger on Jupiter, which is why this calculator lets you change it. In SI units potential energy is measured in joules.

Potential energy is always measured relative to a reference height, usually the ground or the lowest point of interest. Only differences in height matter, so you are free to choose where zero sits. When an object drops, its lost potential energy turns into kinetic energy, which is the principle behind everything from roller coasters to hydroelectric dams.

It rearranges one relation to solve for whichever value you leave blank.

1. For energy, multiply mass by gravity by height.
2. For mass, divide energy by gravity times height.
3. For height, divide energy by mass times gravity.

Potential energy converts into motion; see the kinetic energy calculator and work calculator.

A 2 kilogram object is raised 10 meters on Earth, where gravity is 9.81.

Calculation: PE = m g h = 2 x 9.81 x 10 = 196.2 joules. To find the height that stores 490.5 joules for a 2 kilogram mass, divide: 490.5 over 2 times 9.81 is 25 meters.

One relation, rearranged for whatever you need to find.

All three come from PE equals m g h, so any two of energy, mass and height give the third once gravity is fixed. Because gravity is nearly constant near the surface of the Earth, the energy is set almost entirely by how heavy the object is and how high it sits.

The two are the main forms of mechanical energy, and one turns into the other.

As an object falls, its potential energy drops and its kinetic energy rises by the same amount, so the total mechanical energy stays constant when friction is ignored. This exchange is why a pendulum swings and why water stored behind a dam can drive a turbine at the bottom of the drop.

The Mass

A heavier object stores more potential energy at the same height, in direct proportion.

The Height

Raising an object higher stores more energy. Doubling the height doubles the energy.

The Gravity

A stronger gravitational field stores more energy for the same object. The Moon holds far less than the Earth for the same lift.

Physics Homework

Solve for potential energy, mass or height in a mechanics problem.

Engineering

Estimate the energy stored by a raised load, a reservoir or a counterweight.

Other Planets

Change gravity to compare stored energy on the Moon, Mars or elsewhere.

1. Forgetting a Reference Level

Height is measured from a chosen zero. Only the difference in height matters.

2. Using Weight for Mass

Enter mass in kilograms, not weight in newtons. Gravity is already in the formula.

3. Wrong Gravity

Use 9.81 on Earth, but change it for the Moon or another planet.

4. Mixing Units

Use kilograms, meters and joules together for a consistent result.

5. Zero Divisor

Solving for mass or height cannot divide by a zero height, mass or gravity.

The relation is exact; only the displayed decimals are rounded.

Gravitational potential energy is the energy an object has because of its height. It equals mass times gravity times height. A 2 kilogram object 10 meters up on Earth stores about 196 joules.

Multiply the mass by gravity by the height. For a 2 kilogram object 10 meters up on Earth, that is 2 times 9.81 times 10, which is 196.2 joules.

Divide the energy by mass times gravity. Leave the height field blank and enter energy and mass, and the calculator solves for it.

Use 9.81 meters per second squared on Earth. It is about 1.62 on the Moon and 3.7 on Mars, so change the gravity field to match the body you are on.

Height is measured from a zero level you choose, usually the ground. Only differences in height matter, so where you place zero does not change the physics.

The SI unit is the joule, when mass is in kilograms, gravity in meters per second squared and height in meters. Keep the units consistent for a correct result.

It turns into kinetic energy. As the height drops the stored energy is released as motion, so the object speeds up as it falls.

No. This calculator covers gravitational potential energy from height. Elastic potential energy stored in a spring uses a different formula based on the spring constant.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Potential energy (Wikipedia).
• Gravitational energy (Wikipedia).
• Potential energy explained (Maths Is Fun).