Gravitational Potential Energy Calculator
The gravitational potential energy of two masses measures how tightly the pair is bound by gravity, taking the zero point at infinite separation. It is central to orbital mechanics, escape velocity, binding energy and any problem involving planets, moons or spacecraft. This calculator uses Newton's universal law of gravitation to compute the potential energy from the two masses and the distance between their centres. The result is negative, reflecting that work must be done to separate the masses, and its magnitude is also shown.
Gravitational potential energy formula
U = -G * M * m / r
G = 6.67430e-11 m3 / (kg * s2)
M, m = the two masses (kg)
r = centre-to-centre separation (m)
The energy is negative with the zero set at infinite separation. The magnitude line shows the absolute value, which equals the work needed to separate the masses to infinity.
Gravitation context
- The gravitational constant G is about 6.67430 times ten to the minus eleventh in SI units.
- Earth's mass is about 5.972 times ten to the twenty-fourth kilograms.
- Earth's mean radius is about 6,371 kilometres, useful as a surface separation.
- For a circular orbit, total energy equals half the gravitational potential energy.
- Escape from a body requires adding energy equal to the magnitude of its potential energy.
Gravitational potential energy: frequently asked questions
What is gravitational potential energy in orbit?
Gravitational potential energy is the energy stored in the gravitational attraction between two masses. For point masses or spheres separated by a distance r, it is U = -G * M * m / r. It is negative because energy must be added to pull the masses apart to infinity, where the energy is defined as zero.
Why is gravitational potential energy negative?
The zero of gravitational potential energy is conventionally set at infinite separation. Since gravity is attractive, bringing two masses from infinity closer together releases energy, leaving the system with less than zero. The closer the masses, the more negative and the more tightly bound the system is.
What is the gravitational constant?
The gravitational constant G is approximately 6.67430 times ten to the minus eleventh cubic metres per kilogram per second squared, recommended by CODATA. It sets the strength of gravity in Newton's law and is one of the least precisely known fundamental constants.
What units does this calculator use?
It uses SI units: masses in kilograms and separation in metres. The result is in joules. For astronomical bodies the masses are very large, so the energy is often an enormous negative number, which is normal and reflects how tightly bound large gravitating systems are.
How does this relate to orbital energy?
For a body in a circular orbit, the total mechanical energy is exactly half the gravitational potential energy, because kinetic energy equals minus half the potential energy. So once you have U you can find the binding energy and escape requirements of the orbit directly.
Official sources
- U.S. National Institute of Standards and Technology: Newtonian constant of gravitation.
- NASA Planetary Fact Sheet: Planetary masses and radii.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.