Surface Gravity Calculator
Enter a body's mass and radius to get its surface gravity in m/s² — plus how many Earth gravities that is — and see why a planet's size matters as much as its mass.
Gravity and Earth-ratio at once
This surface gravity calculator returns the gravitational acceleration (g = G·M/r²) in m/s² and how many Earth gravities that represents together.
Use SI units
Mass in kilograms and radius in metres give gravity in m/s² — use scientific notation (5.972e24) for the very large numbers astronomy involves.
What is surface gravity?
The pull you feel at the surface
Surface gravity is the gravitational acceleration an object feels standing on the surface of a planet, moon, or star. This surface gravity calculator turns two measurements — the body's mass in kilograms and its radius in metres — into that acceleration in metres per second squared, alongside how many Earth gravities it amounts to. It is the number behind your weight on the Moon, why astronauts bound across the lunar surface, and how heavy a rocket has to work to leave the ground. Crucially, gravity depends on radius as strongly as on mass: a body can be far heavier than Earth yet pull more gently at its surface if it is also much larger.
Enter a mass in kilograms and a radius in metres to get the surface gravity in m/s² and its ratio to Earth gravity instantly.
Surface gravity is the gravitational constant times the mass, divided by the radius squared. Dividing that by standard gravity (9.80665 m/s²) tells you how many Earth gravities it is.
g = G × M / r²The radius is squared in the denominator, so it pulls hard on the result: double a body's radius while keeping its mass and the surface gravity drops to a quarter. The gravitational constant G = 6.6743e-11 N·m²/kg² is the same everywhere in the universe. Use kilograms and metres and the gravity comes back in m/s²; divide by 9.80665 for the Earth ratio.
Suppose you take Earth's mass of 5.972e24 kg and its mean radius of 6.371e6 m.
Square the radius
(6.371e6)² ≈ 4.059e13 — the squared radius that sits in the denominator.
Multiply G by the mass
6.6743e-11 × 5.972e24 ≈ 3.986e14 — the gravitational pull of the mass.
Divide and compare to Earth
3.986e14 ÷ 4.059e13 ≈ 9.82 m/s² — the surface gravity. Dividing by 9.80665 gives about 1.00 g, just over one Earth gravity.
The formula is exact for a spherical body, but a few practical points are worth keeping in mind.
Spherical bodies and consistent units
This calculator treats the body as a uniform sphere and gives the gravity at its surface, ignoring rotation, equatorial bulge, and local terrain that nudge real surface gravity by a fraction of a percent. It assumes you stand on the surface, not above it. Keep your units consistent — kilograms for mass and metres for the radius — or the result in m/s² will be wrong.