Surface Gravity Calculator
Find the acceleration due to gravity at a body’s surface with g = GM ÷ r².
That is 1× Earth’s gravity (one g = 9.80665 m/s²). G = 6.674×10⁻¹¹ N·m²/kg²; enter M in kg and r in metres (use e-notation, e.g. 5.972e24).
Surface gravity is the acceleration a falling object feels at a body’s surface: g = GM ÷ r², with G = 6.674×10⁻¹¹ N·m²/kg². For Earth (M = 5.972×10²⁴ kg, r = 6.371×10⁶ m) that is about 9.8 m/s². The Moon has far less mass, so its surface gravity is only about 1.62 m/s² — roughly one-sixth of Earth’s.
What surface gravity means
Surface gravity is the gravitational acceleration measured right at the surface of a planet, moon, or star. It follows from Newton’s law of gravitation applied to a single body: the force on a small mass m sitting on the surface is F = GMm ÷ r², and dividing by m (since weight = mass × acceleration) leaves the acceleration g = GM ÷ r². Here M is the body’s mass, r is its radius, and the small object’s own mass cancels out entirely — a feather and a rock accelerate at the same rate.
Because r is squared in the denominator, radius matters more than you might expect: shrinking a body while keeping its mass fixed raises g sharply, since the surface sits closer to the centre of mass.
G = 6.674×10⁻¹¹ N·m²/kg², M is the body’s mass in kg, r its radius in metres, g in m/s²
Worked example
What is Earth’s surface gravity? Use M = 5.972×10²⁴ kg and r = 6.371×10⁶ m (Earth’s mean radius).
- 1 Write the formula. g = GM ÷ r², with G = 6.674×10⁻¹¹ N·m²/kg².
- 2 Substitute the values. g = 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ (6.371×10⁶)².
- 3 Work out GM and r². GM ≈ 3.986×10¹⁴ and r² ≈ 4.059×10¹³ m².
- 4 Divide. g ≈ 3.986×10¹⁴ ÷ 4.059×10¹³ ≈ 9.82 m/s² — that is 1.00× Earth gravity.
Surface gravity of common bodies
Computed from each body’s mass and mean radius with g = GM ÷ r²; one g = 9.80665 m/s².
| Body | Surface gravity (m/s²) | Multiple of Earth g |
|---|---|---|
| Moon | 1.62 | 0.166 |
| Mars | 3.73 | 0.380 |
| Earth | 9.82 | 1.00 |
| Jupiter | 25.9 | 2.64 |
Why the numbers look the way they do
It depends on both mass and radius. A body with more mass pulls harder, but a larger radius pushes its surface farther from the centre, weakening g by the square of the distance. That trade-off is why Jupiter — over 300 times Earth’s mass — has a surface gravity of only about 2.6× Earth’s: its enormous radius partly offsets its mass.
A small, dense body can rival a larger one. Because g scales with density × radius, a compact rocky world can match or beat the surface gravity of a much bigger but puffier body. Mercury and Mars, for instance, end up with almost the same surface gravity despite different sizes, because their masses and radii balance out.
Weight changes, mass does not. Surface gravity sets your weight, not your mass. Your mass — the amount of matter in you — is the same everywhere, but your weight (mass × g) shrinks on the Moon and grows on Jupiter, because g differs from body to body.