Acceleration Due to Gravity Calculator - Surface Gravity From g = GM/r2
This acceleration due to gravity calculator finds the gravitational acceleration at the surface of any planet or moon, or at a chosen altitude above it, using g = G*M/r^2. Results show in m/s2, ft/s2, and g.
Acceleration Due to Gravity Calculator
Results
What Is Acceleration Due to Gravity?
An acceleration due to gravity calculator tells you the rate at which an unsupported object speeds up as it falls near a massive body. On Earth that value is close to 9.8 m/s2, meaning a dropped object gains about 9.8 metres per second of speed for every second it falls, neglecting air resistance. The same idea applies to every planet, moon, and star: anything with mass bends spacetime and pulls nearby objects toward its centre.
The number is not the same everywhere. It depends on the body's mass and how far you are from its centre, which is why the Moon pulls at only about 1.62 m/s2 while Jupiter pulls at roughly 24.8 m/s2 near its cloud tops. This calculator turns that physics into a single number for any body you pick.
Surface gravity is what you actually feel as weight: your mass times g gives the force pressing you against the floor. Because g changes from place to place, the same mass weighs less on Mars than on Earth even though the mass itself is unchanged. Engineers and students use this value whenever they convert between mass and weight or compare planetary environments.
The value also sets how quickly things fall and how high a projectile can rise, which is why the same launch speed sends a ball higher on the Moon than on Earth. Rockets, satellites, and even the path of a thrown ball all depend on the local g, so knowing it for a given world is the first step in any trajectory or orbit problem.
A related idea is ordinary acceleration, the general rate of change of velocity. Gravity is just one source of acceleration, but because it acts on everything equally it is the most universal example in introductory physics. Measuring g is also one of the classic ways to estimate a planet's mass, since the same equation solved for M gives the body's mass from a measured surface gravity and radius.
How Acceleration Due to Gravity Calculator Works
This acceleration due to gravity calculator evaluates Newton's law for whatever body and altitude you choose. The formula and its variables are below, followed by two worked examples. The same equation underpins satellite orbits, planetary science, and the design of anything that must leave the ground.
- Gravitational constant G: The fixed 6.67430 x 10^-11 m3 kg^-1 s^-2 that sets the strength of gravity; it is the same everywhere in the universe.
- Body mass M: More mass pulls harder, so g grows in direct proportion to M.
- Distance r: Gravity weakens with the square of the distance from the centre, so doubling r cuts g to one quarter.
- Altitude h: Height above the surface adds to the radius, so r = R + h in the denominator.
- Surface gravity: The special case h = 0, giving g0 = G*M/R^2 at the body's surface.
Earth at the surface
M = 5.9722 x 10^24 kg, R = 6.371 x 10^6 m, h = 0.
g = (6.67430 x 10^-11)(5.9722 x 10^24) / (6.371 x 10^6)^2 = 9.820 m/s2.
Surface gravity: 9.820 m/s2, or 1.001 g.
Earth at 100 km altitude
r = 6.371 x 10^6 + 1.00 x 10^5 = 6.471 x 10^6 m.
g = (6.67430 x 10^-11)(5.9722 x 10^24) / (6.471 x 10^6)^2 = 9.518 m/s2.
Gravity at 100 km: 9.518 m/s2, down from 9.820 m/s2.
According to NIST Special Publication 330, the SI Brochure defines standard gravity as exactly 9.80665 m/s2 and documents the CODATA value of G used in these calculations.
The force behind this acceleration is computed directly by the Gravitational Force Calculator, which pairs this g with a test mass through F = m*g.
Key Concepts Explained
Inverse-square law
Gravity falls with 1/r^2, so moving twice as far from a body's centre quarters the pull. This is why altitude matters even in low orbit.
Standard gravity g0
The exact reference 9.80665 m/s2 used to define weight and to express accelerations as multiples of g. It is a convention, not a measured local value.
Surface vs altitude
Surface gravity uses the body radius R; altitude gravity adds h to R. The two can differ by several percent only a few hundred kilometres up.
Measured in g
Dividing a result by 9.80665 turns it into multiples of Earth gravity, the unit pilots, astronauts, and roller-coaster designers quote as g.
According to Hyperphysics - Gravity, Newton's law of universal gravitation gives g = G*M/r^2 for the acceleration near a spherical body, the relation this calculator evaluates.
Dividing a result by standard gravity turns it into multiples of Earth gravity, the unit pilots and astronauts quote as g-force.
How to Use This Calculator
The acceleration due to gravity calculator needs only a body and an optional altitude, so most results take a few seconds. Changing any field re-runs the formula right away, which makes it easy to explore how mass, radius, and height trade off.
- 1 Pick a body: Choose Earth, Moon, Mars, Jupiter, Saturn, or Sun from the dropdown to load its mass and radius.
- 2 Choose Custom if needed: Select Custom body and enter your own mass in kilograms and radius in metres for an asteroid or exoplanet.
- 3 Set the altitude: Enter height above the surface in metres. Leave it at 0 to find surface gravity.
- 4 Read the results: The output shows gravity in m/s², ft/s², and multiples of g, plus the surface gravity at zero altitude.
- 5 Compare bodies: Re-run with a different body or altitude to see how mass, radius, and height change the pull.
For a falling object the time it takes to reach the ground follows from this same g, which the Free Fall Time Calculator works out from height and gravity.
Benefits of Using This Calculator
A quick g value saves the repeated algebra of Newton's law and keeps your numbers consistent with the standard gravity reference, which matters when several steps of a problem build on the same result.
- • Compact comparison: See how gravity differs across worlds in seconds instead of hand-cranking G*M/r^2 for each body.
- • Three unit systems: Get the same value in m/s², ft/s², and g so you can match the units your course or report uses.
- • Altitude awareness: Watch gravity fade with height, which matters for orbit, sounding rockets, and high-altitude physics problems.
- • Custom bodies: Extend beyond the presets to asteroids, moons, or hypothetical planets by entering any mass and radius.
- • Physics foundation: The output feeds weight, force, and trajectory questions, linking to the broader mechanics toolkit.
That weight relation comes straight from Newton's Second Law Calculator, where force equals mass times this acceleration.
Factors That Affect Your Results
Four things decide what the acceleration due to gravity calculator returns for a given body and height.
Body mass
Gravity is directly proportional to mass, so a body twice as heavy pulls twice as hard at the same radius.
Body radius
Because g scales with 1/R^2, a smaller radius raises surface gravity sharply even when mass is similar.
Altitude above surface
Every metre of height adds to r, so gravity drops. The effect is small near the ground but large in orbit.
Non-uniform shape and spin
Real bodies are lumpy and rotating, so local gravity varies by a few percent from the ideal sphere model used here.
- • This calculator models each body as a uniform sphere; it ignores equatorial bulge, local density variations, and centrifugal effects from rotation, so quoted values are idealised rather than the exact local reading at a specific site.
- • It gives gravitational acceleration only, not the smaller apparent weight you would measure on a scale that already accounts for spin and the slight lift from the body's own rotation.
- • For extreme altitudes near another body, the dominant gravity can switch to that neighbour, which a single-body model does not capture, so close to a moon or planet the result is only approximate.
According to NASA Earth Fact Sheet, Earth's mean radius and mass are the source values behind the preset used for our surface-gravity result.
A pendulum's swing rate depends on local gravity, so the Pendulum Period Calculator uses this same g to find how long each swing takes.
Frequently Asked Questions
Q: What is the acceleration due to gravity on Earth?
A: Mean surface gravity on Earth is about 9.82 m/s2, while the standard gravity value g0 used in physics and engineering is exactly 9.80665 m/s2. The small difference comes from Earth's rotation and its slightly squashed, non-uniform shape. At the poles gravity is closer to 9.83 m/s2 and at the equator closer to 9.78 m/s2.
Q: How do you calculate acceleration due to gravity?
A: Use Newton's law: g = G*M/r^2. G is the gravitational constant 6.67430 x 10^-11 m3 kg^-1 s^-2, M is the body's mass, and r is the distance from its centre. For gravity a height h above the surface, set r = R + h where R is the body radius. This calculator does both steps for you.
Q: Does gravity change with altitude?
A: Yes. Gravity falls with the square of the distance from the centre, so at altitude h it is g = G*M/(R + h)^2. At 100 km above Earth the value drops from about 9.82 to 9.52 m/s2, and at one Earth radius up it is one quarter of the surface value because the distance has doubled.
Q: What is standard gravity (g0)?
A: Standard gravity g0 is defined exactly as 9.80665 m/s2 by the International Committee for Weights and Measures. It is a reference value for converting between mass and weight (force) and for normalising accelerations into multiples of g. It is not the exact gravity anywhere on Earth, just a single agreed reference.
Q: How does gravity compare across planets?
A: It scales with mass divided by radius squared. The Moon gives about 1.62 m/s2, Mars about 3.73 m/s2, and Jupiter about 24.8 m/s2 at the cloud tops. Surface gravity depends far more on radius than on overall size, because bringing mass closer to the surface raises g quickly.