About the Surface Gravity Calculator
This surface gravity calculator works out the gravitational acceleration at the surface of a planet, moon or star using Newton’s law g = GM/R². Pick a body from the solar system or enter your own mass and radius — in kilograms, Earth masses or Jupiter masses, and kilometres or Earth radii — and it returns g in m/s², as a multiple of Earth’s gravity and in ft/s².
It is useful for astronomy and physics students checking homework, science-fiction writers designing believable worlds, and anyone curious how heavy they would feel on Mars or a super-Earth exoplanet. Enter your own mass to see what a bathroom scale calibrated on Earth would read there, plus the weight in newtons, the escape velocity and the mean density of the body.
The result is the pure gravitational pull at the mean radius of a non-rotating sphere. Real surface gravity varies slightly with latitude, altitude and spin — Earth’s works out to 9.82 m/s² here versus the conventional standard 9.80665 m/s², and on fast-spinning gas giants the centrifugal effect lowers the felt gravity noticeably.
With the default inputs, the surface gravity is 9.82 m/s². Change any value above to recalculate instantly.
How to use the surface gravity calculator
- 1Choose a planet, moon or the Sun — or pick Custom world.
- 2For a custom world, enter its mass and radius and choose the units.
- 3Optionally enter your own mass to see your weight there.
- 4Read surface gravity in m/s², in Earth g and in ft/s².
- 5Compare with the bar chart of solar-system bodies.
Formula and method
Surface gravity follows from Newton’s law of universal gravitation: a mass m at distance R from the centre of a body of mass M feels a force GMm/R², so its acceleration is g = GM/R². Doubling the mass doubles g, while doubling the radius at the same mass cuts g to a quarter.
The calculator uses G = 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻² (CODATA 2018) with NASA fact-sheet masses and volumetric mean radii, and treats the body as a non-rotating sphere. The “scale reading” is your mass × g ÷ 9.80665, i.e. what an Earth-calibrated scale would show. Escape velocity is √(2GM/R) and density is M divided by the sphere’s volume.
- g
- Surface gravitational acceleration (m/s²)
- G
- Gravitational constant, 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²
- M
- Mass of the planet, moon or star (kg)
- R
- Mean radius of the body (m)
Worked examples
Surface gravity of Earth
g = 6.6743e-11 × 5.9722e24 ÷ 6,371,000² ≈ 9.820 m/s², slightly above the 9.80665 standard because Earth’s spin and equatorial bulge are ignored. Mean density comes out at 5.51 g/cm³.
Gravity on Mars for a 70 kg person
Mars has 10.7% of Earth’s mass but a radius of 3,389.5 km, giving g ≈ 3.73 m/s² — about 38% of Earth. A 70 kg person’s scale would read only about 26.6 kg.
A super-Earth: 5 Earth masses, 1.5 Earth radii
Gravity scales with M/R², so 5 ÷ 1.5² = 2.22 times Earth’s 9.82 m/s² ≈ 21.8 m/s². Escape velocity scales with √(M/R) = √3.33, giving about 20.4 km/s.
Jupiter (cloud-top mean radius) for an 80 kg person
With 1.898 × 10²⁷ kg inside a 69,911 km mean radius, g ≈ 25.9 m/s², 2.6 times Earth. Jupiter’s rapid 10-hour spin lowers the felt value at the equator to roughly 23 m/s².
Frequently asked questions
How do you calculate surface gravity?+
Multiply the gravitational constant G (6.6743 × 10⁻¹¹) by the body’s mass in kilograms and divide by the square of its radius in metres: g = GM/R². For Earth that gives about 9.82 m/s².
Which planet has the strongest surface gravity?+
Jupiter, at roughly 24.8–25.9 m/s² depending on the radius used — about 2.5 times Earth. Neptune (about 11 m/s²) and Saturn (10.4–11.2 m/s², depending on whether the equatorial or mean radius is used) come next, followed by Earth (9.8), Venus (8.9) and Uranus (8.7–9.0).
Why is Saturn’s gravity similar to Earth’s if it is 95 times more massive?+
Because gravity falls with the square of the radius. Saturn is about 9.1 times wider than Earth, so 95 ÷ 9.1² ≈ 1.1 — its cloud-top gravity is only slightly above Earth’s.
Is mass the same as weight on another planet?+
No. Your mass (kilograms of matter) never changes; your weight is the force gravity exerts on that mass, mass × g. A scale calibrated for Earth will show a lower or higher number elsewhere because it really measures force.
Why does the calculator give 9.82 m/s² for Earth instead of 9.81?+
It computes pure gravitation at the mean radius of a non-rotating sphere. Earth’s rotation and equatorial bulge reduce measured gravity to between 9.78 m/s² at the equator and 9.83 m/s² at the poles; 9.80665 m/s² is a defined standard value.