Enter the gravitational constant, the mass of the planet or celestial body, and radius into the calculator to determine the surface gravity. This calculator can also evaluate any of the variables given the others are known.
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Surface Gravity Formula
Surface gravity is the gravitational acceleration at the surface of a planet, moon, asteroid, or other celestial body. In the standard spherical-body model, surface gravity depends on two physical properties: the body’s total mass and its radius.
g = \frac{G M}{r^2}G = 6.67430 \times 10^{-11} \text{ m}^3\text{kg}^{-1}\text{s}^{-2}| Symbol | Meaning | Typical SI Unit | Notes |
|---|---|---|---|
| g | Surface gravity | m/s2 | The acceleration an object experiences at the surface |
| G | Universal gravitational constant | m3/(kg·s2) | A physical constant used in gravity calculations |
| M | Mass of the body | kg | Total mass of the planet, moon, or star |
| r | Radius of the body | m | Distance from the center to the surface |
If you already know the surface gravity and radius, you can solve for mass. If you know mass and surface gravity, you can solve for radius.
M = \frac{g r^2}{G}r = \sqrt{\frac{G M}{g}}How to Use the Surface Gravity Calculator
- Enter the mass of the celestial body.
- Enter the radius of the body measured from its center to its surface.
- Click calculate to find the surface gravity.
- If you already know the gravity, use the same relationship to solve for the missing mass or radius instead.
For the most reliable result, make sure mass and radius are entered with the correct units. In direct SI form, mass should be in kilograms and radius should be in meters, which produces gravity in m/s2.
What Surface Gravity Tells You
- How heavy objects feel: higher surface gravity means greater weight for the same object.
- How strongly the body pulls matter inward: this affects atmosphere retention, motion near the surface, and launch requirements.
- How mass and size interact: increasing mass raises gravity, while increasing radius lowers gravity at the surface.
- Why large planets do not always have extreme surface gravity: a very large radius can offset a large mass.
Example
Using Earth-like values gives a result very close to standard Earth gravity:
g = \frac{(6.67430 \times 10^{-11})(5.972 \times 10^{24})}{(6.371 \times 10^6)^2} \approx 9.82 \text{ m/s}^2A moon-sized body produces a much smaller value because its mass is lower and its radius is also smaller:
g = \frac{(6.67430 \times 10^{-11})(7.35 \times 10^{22})}{(1.737 \times 10^6)^2} \approx 1.62 \text{ m/s}^2Convert Surface Gravity to Earth Gravity
It is often useful to compare a result to Earth’s gravity.
g_{\text{rel}} = \frac{g}{9.80665}If your result is 19.6 m/s2, that is about 2 times Earth gravity. If your result is 4.9 m/s2, that is about 0.5 times Earth gravity.
Common Surface Gravity Values
| Body | Approx. Surface Gravity | Relative to Earth |
|---|---|---|
| Mercury | 3.70 m/s2 | 0.38 g |
| Venus | 8.87 m/s2 | 0.90 g |
| Earth | 9.81 m/s2 | 1.00 g |
| Moon | 1.62 m/s2 | 0.17 g |
| Mars | 3.71 m/s2 | 0.38 g |
| Jupiter | 24.79 m/s2 | 2.53 g |
| Saturn | 10.44 m/s2 | 1.06 g |
| Uranus | 8.69 m/s2 | 0.89 g |
| Neptune | 11.15 m/s2 | 1.14 g |
| Pluto | 0.62 m/s2 | 0.06 g |
Why Radius Matters So Much
Surface gravity does not depend on mass alone. Two bodies can have very different masses but similar surface gravity if the larger body also has a much larger radius. This is why some gas giants do not have surface gravity values as extreme as many people expect.
The radius term is especially important because it is squared in the denominator. That means moving the surface farther from the center weakens gravity quickly.
Accuracy and Assumptions
This calculator uses the ideal form of the surface gravity equation, which assumes the body is roughly spherical and that gravity is evaluated at the surface. In real-world astronomy and planetary science, local gravity can differ slightly from the ideal value because of rotation, shape, altitude, and internal density variation.
At an altitude above the surface, gravity decreases as distance from the center increases:
g(h) = \frac{G M}{(r + h)^2}- Rotation: fast-spinning bodies have slightly lower apparent gravity near the equator.
- Non-spherical shape: oblate planets and irregular asteroids do not have perfectly uniform surface gravity.
- Altitude: gravity becomes weaker as you move away from the surface.
- Mean radius vs. local terrain: mountains, basins, and density differences can change local values slightly.
Common Input Mistakes
- Using diameter instead of radius: the formula requires radius, not the full width of the body.
- Mixing units: if mass is entered in kilograms, radius should be converted consistently when doing manual checks.
- Confusing mass with weight: mass is the amount of matter in the body, while weight depends on gravity.
- Using altitude as radius: radius should be measured from the center to the surface, not from the surface upward.
Frequently Asked Questions
- Is surface gravity the same as gravitational force?
- No. Surface gravity is an acceleration field created by the celestial body. Gravitational force depends on that field and the mass of the object being acted on.
- Does a larger planet always have stronger surface gravity?
- No. A larger radius can reduce the surface gravity enough that the final value is not dramatically larger than Earth’s, even when the total mass is much higher.
- Can the same equation be used for planets, moons, and stars?
- Yes. The same relationship applies whenever the object can be approximated as spherical and its mass and radius are known.
- Why is Jupiter’s gravity not dozens of times higher than Earth’s?
- Jupiter is far more massive than Earth, but its radius is also much larger. Because surface gravity depends on both properties, the radius offsets a large portion of the mass effect.
