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.

Calculator guide

How this calculator works

Acceleration Due to Gravity Calculator determines gravitational acceleration created by a planet or celestial body. It helps physics students, engineers, astronomers, and laboratory users analyze gravitational fields, planetary motion, satellites, and scientific measurements using mass and radius values.

Formula explanation

Acceleration due to gravity describes the constant acceleration experienced by objects falling near Earth's surface.

Formula

Acceleration Due to Gravity = Gravitational Constant × Mass ÷ Radius²

Worked example

Example: Objects in free fall accelerate downward because of Earth's gravitational field.

Assumptions

  • Mass and radius measurements are accurate.
  • The celestial body is approximated as a spherical object.
  • Mass distribution is considered uniform.
  • Input values use compatible scientific units.

Examples

  • Example: Calculate gravitational acceleration using the mass and radius of a planet.
  • Example: Scientists compare gravity on Earth, planets, and moons using gravitational acceleration calculations.

Common mistakes

  • Using incorrect gravity values.
  • Ignoring air resistance effects.
  • Confusing mass with acceleration.

Variables

  • Mass of celestial body
  • Radius of celestial body
  • Gravitational constant
  • Gravitational acceleration
  • Planetary body properties
  • Measurement units

Limitations

  • Results assume a simplified spherical mass model.
  • Complex gravitational fields and irregular bodies require advanced physics models.

Scientific references

  • OpenStax University Physics: Gravitation
  • NIST SI Units and Measurement References
  • Newton's law of universal gravitation

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Planetary science calculations
  • Astronomy and space studies
  • Satellite and orbital analysis
  • Engineering and scientific research
  • Laboratory gravity experiments

Frequently asked questions

How is acceleration due to gravity calculated?

Acceleration due to gravity is calculated using the gravitational constant, the object's mass, and its distance from the center using g = GM ÷ r².

What is acceleration due to gravity?

Acceleration due to gravity is the acceleration experienced by an object because of the gravitational attraction of a planet or celestial body.

What is the SI unit of gravitational acceleration?

The SI unit of gravitational acceleration is meters per second squared (m/s²).

Why is gravity different on other planets?

Gravity differs between planets because gravitational acceleration depends on the mass and radius of each celestial body.

Accuracy and transparency

Created and maintained by our editorial team

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

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

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

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.

Use consistent SI units: enter mass in kilograms and radius or distance in metres to obtain gravitational acceleration in metres per second squared.

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.

Model boundaries

Assumptions and limitations

This calculation treats the celestial body as spherically symmetric and uses distance from the center of mass. It provides a Newtonian estimate for common educational and planetary calculations.

  • The model does not account for local mass distribution or terrain.
  • A measured surface value can vary with rotation, latitude, and altitude.
  • Use the distance from the center, not height above the surface, as radius.

Scientific references

Sources for constants and method

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.

Use the Weight Calculator to calculate weight from mass and local gravitational acceleration.

Questions and answers

Calculator FAQ

How is acceleration due to gravity calculated?

Acceleration due to gravity is calculated using the gravitational constant, the object's mass, and its distance from the center using g = GM ÷ r².

What is acceleration due to gravity?

Acceleration due to gravity is the acceleration experienced by an object because of the gravitational attraction of a planet or celestial body.

What is the SI unit of gravitational acceleration?

The SI unit of gravitational acceleration is meters per second squared (m/s²).

Why is gravity different on other planets?

Gravity differs between planets because gravitational acceleration depends on the mass and radius of each celestial body.