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
- Use Earth's mass: 5.972 × 10²⁴ kg.
- Use Earth's mean radius: 6.371 × 10⁶ m.
- Apply g = GM / r².
- 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
Continue your gravity analysis
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.