Gravitational physics tool

Acceleration Due to Gravity Calculator

Calculate gravitational acceleration from planetary mass and radius using g = GM / r².

Enter planetary values

Calculate gravitational acceleration

Free tool

Enter the mass of the planet or celestial body.

Use the distance from the body's center.

Optional. When entered, this value is returned directly instead of using mass and radius.

Try an example:

Your result will appear here

Enter mass and radius, or provide a direct gravity override, then select calculate.

Physics overview

What is acceleration due to gravity?

Acceleration due to gravity is the acceleration experienced by an object because of a body's gravitational field. Near Earth's surface, its magnitude is approximately 9.81 m/s².

Formula

Gravitational acceleration formula

Gravityg = GM / r²

  • g is gravitational acceleration in m/s².
  • G is the universal gravitational constant.
  • M is the mass of the celestial body in kilograms.
  • ris distance from the body's centre in metres.

Worked example

Calculate gravity near Earth's surface

  1. Use Earth's mass: 5.972 × 10²⁴ kg.
  2. Use Earth's mean radius: 6.371 × 10⁶ m.
  3. Apply g = GM / r².
  4. The result is approximately 9.82 m/s².

Distance effect

Why gravity changes with altitude

Gravity becomes weaker as distance from a planet's centre increases. Because radius is squared in the denominator, even modest increases in distance reduce gravitational acceleration.

Applications

Where this calculation is used

  • Planetary science calculations.
  • Satellite and orbital analysis.
  • Free-fall and projectile problems.
  • Spacecraft mission planning.
  • Comparing gravity on planets and moons.

Related tools

Use the Free Fall Calculator to calculate falling distance, time, and final velocity.

Use the Gravitational Potential Energy Calculator to calculate energy associated with height.

Model limits

Assumptions and limitations

The calculation assumes a spherical gravitating body and uses distance from its center. It also treats the body mass as fixed and ignores local variations caused by rotation, altitude, terrain, and density differences.

The result is an ideal gravitational-field estimate. It may differ from locally measured acceleration and is not suitable for relativistic conditions or locations inside a nonuniform body.

Questions and answers

Acceleration due to gravity FAQ

What formula calculates acceleration due to gravity?

The calculator uses g = GM / r², where G is the universal gravitational constant, M is the mass of the celestial body, and r is the distance from its center.

What is the acceleration due to gravity on Earth?

The standard value near Earth's surface is approximately 9.81 metres per second squared, although the exact value varies slightly with altitude and location.

Why does gravity decrease with distance?

Gravitational acceleration follows an inverse-square relationship, so increasing the distance from the centre reduces gravity in proportion to the square of that distance.

Can this calculator be used for other planets?

Yes. Enter the mass and radius of any planet, moon, star, or other spherical celestial body to estimate its surface gravitational acceleration.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the Science Lab Tools Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Learn more about our formula-review and correction process, or read about Science Lab Tools.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently