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Gravitational Potential Energy Calculator

A 10 kilogram mass raised 5 meters stores 490.5 joules, a tiny fraction of a kilowatt-hour, which shows how little energy gravity storage holds by household standards: lifting a ton 100 meters stores under 0.3 kilowatt-hours. Falling objects convert this energy to kinetic energy, and the potential energy at the top equals the kinetic energy at the bottom, ignoring air resistance.

Gravitational Potential Energy Calculator: inputs

Calculated result
Potential energy (J)490.5
Potential energy (kWh)0.00014

Gravitational Potential Energy Calculator: Mass (kg) sensitivity

Gravitational Potential Energy Calculator: Mass (kg) and Potential energy (J)5 calculations vary the “Mass (kg)” input while holding the other entered inputs constant.8392.49441.510490.511539.612588.6

Gravitational Potential Energy: formula

Gravitational potential energy = m × g × h

OpenStax University Physics: potential

Enter the mass in kilograms, the gravitational acceleration and the height in meters. Gravitational potential energy is mass times gravity times height, with 9.81 meters per second squared on Earth, 1.62 on the Moon and 3.71 on Mars. The height is measured above a chosen reference level, such as the ground or the bottom of a fall.

The result is in joules, with kilowatt-hours shown for scale.

Gravitational Potential Energy: worked example

Mass (kg)10
Gravity (m/s²)9.8
Height (m)5
Potential energy (J)490.5
Potential energy (kWh)0.00014

Only differences in height matter, so the reference level is arbitrary. Near the surface gravity is nearly constant, but over large heights it decreases. Real systems lose energy to friction and air.

Elastic and chemical energy are separate forms.

Gravitational Potential Energy: changing Mass (kg)

Mass (kg)Potential energy (J)Potential energy (kWh)
8392.40.00011
9441.50.00012
10 (example)490.50.00014
11539.60.00015
12588.60.00016

Gravitational Potential Energy: compare input ranges

InputTested fromToPotential energy (J): low inputPotential energy (J): high inputSwing
Mass (kg)911441.5539.698.1 (20%)
Height (m)4.55.5441.5539.698.1 (20%)
Gravity (m/s²)911450550100 (20%)

Gravitational Potential Energy: individual input comparisons

InputValuePotential energy (J)Potential energy (kWh)
Mass (kg)8392.40.00011
9441.50.00012
10490.50.00014
11539.60.00015
12588.60.00016
Gravity (m/s²)84000.00011
94500.00013
105000.00014
115500.00015
126000.00017
Height (m)4392.40.00011
4.5441.50.00012
5490.50.00014
5.5539.60.00015
6588.60.00016

Gravitational Potential Energy: combined input changes

Mass (kg) / Gravity (m/s²)81012
8320400480
9360450540
10400500600
11440550660
12480600720

Gravitational Potential Energy: which assumptions move the result?

Gravitational Potential Energy: Potential energy (J) as Mass (kg) changesPotential energy (J) starts at 392.4. Moving Mass (kg) from 8 to 12 changes it to 588.6, with Gravity (m/s²) 9.8; Height (m) 5 kept fixed.8392.49441.510490.511539.612588.6
Chart quantityDisplayed settings
Mass (kg)8 → 12
Potential energy (J)392.4 → 588.6
Gravity (m/s²)9.8
Height (m)5
Gravitational Potential Energy: Potential energy (J) as Height (m) changesPotential energy (J) starts at 392.4. Moving Height (m) from 4 to 6 changes it to 588.6, with Mass (kg) 10; Gravity (m/s²) 9.8 kept fixed.4392.44.5441.55490.55.5539.66588.6
Chart quantityDisplayed settings
Height (m)4 → 6
Potential energy (J)392.4 → 588.6
Mass (kg)10
Gravity (m/s²)9.8

Gravitational Potential Energy: values and definitions

Quantity and definitionValue used
Mass (kg)10
Gravity (m/s²) — 9.81 on Earth. About 1.62 on the Moon.9.8
Height (m)5
Potential energy (J)490.5
Potential energy (kWh)0.00014

Gravitational Potential Energy: half and double Mass (kg)

Mass (kg)Potential energy (J)
5245.3
10490.5
20981

Common error: Using the mass in pounds. The formula wants kilograms, and pounds without conversion overstate the energy by more than double.

Physics & Mechanics calculators: Work and Power Calculator, Wavelength and Frequency Calculator, Projectile Motion Calculator, Free Fall Calculator, Centripetal Force Calculator, Pendulum Period Calculator.

Lifting a mass stores energy equal to its weight times the height. Ten kilograms raised 5 meters under standard gravity holds 490.5 joules, which is what it would release if it fell. In kilowatt-hours that is a tiny 0.00014, which is why gravity storage needs enormous masses or heights to matter.

Measure the height as the vertical drop, not the path taken. A ramp changes the effort but not the stored energy.

See impact speed on the free fall calculator, the energy in motion on the kinetic energy calculator and the work on the work and power calculator. The force and Hooke's law pages cover related mechanics, and the pendulum period calculator shows energy exchange in a swing.

Does the reference height matter?

Only differences in height matter, so you can choose any level as zero, as long as you are consistent.

How does potential energy become kinetic energy?

As an object falls its height and potential energy drop while its speed and kinetic energy rise by the same amount, ignoring air resistance.

What is the formula for gravitational potential energy?

Mass times gravitational acceleration times height, so a 10 kilogram mass lifted 5 meters on Earth gains 490.5 joules.