Surface Gravity Calculator

Frequently Asked Questions

How do I enter a planet mass?

Use scientific notation, for example 5.97e24 kilograms for Earth and 6.371e6 meters for its radius.

Why does radius matter more than mass?

Gravity falls off with the square of the radius but rises only linearly with mass, so radius has a stronger effect on surface gravity.

What is Earth's surface gravity?

Earth's surface gravity is about 9.81 meters per second squared. The calculator reports any body's gravity as a multiple of this value, so a result of 0.17 means about one-sixth of Earth's pull, close to the Moon.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Surface gravity is the acceleration that an object feels at the surface of a planet, moon, or star. It follows directly from Newton's law of gravitation: the gravitational constant times the body's mass divided by the square of its radius. A more massive body pulls harder, while a larger radius spreads that pull over a greater distance and weakens it.

Worked Example

Check the formula on Earth, with mass M = 5.97 × 10²⁴ kg and radius r = 6.371 × 10⁶ m, using G = 6.674 × 10⁻¹¹. First the numerator: GM = 6.674 × 10⁻¹¹ × 5.97 × 10²⁴ ≈ 3.984 × 10¹⁴. Then the denominator: r² = (6.371 × 10⁶)² ≈ 4.059 × 10¹³. Dividing gives g = 3.984 × 10¹⁴ ÷ 4.059 × 10¹³ ≈ 9.81 m/s², which is exactly Earth's surface gravity, so the relative value is 1.0.

How To Use It

Enter the body's mass in kilograms and its radius in meters. The calculator returns the surface gravity in meters per second squared, along with the value expressed as a multiple of Earth's surface gravity, which is about 9.81 meters per second squared. For the relative figure the calculator divides by the internationally defined standard gravity of 9.80665 m/s²; the rounded 9.81 used elsewhere on this page agrees with it to within about 0.03%.

Some Reference Values

Earth sits at roughly 9.81, the Moon at about 1.62, Mars near 3.7, and Jupiter at about 24.8 meters per second squared. Massive but diffuse bodies can have surprisingly low surface gravity, while small, dense ones can have very high values.

Tips

Use scientific notation for planetary masses, such as 5.97e24 for Earth.

Radius has a stronger effect than mass because it is squared.

The relative value tells you how heavy you would feel compared to Earth.

Surface Gravity Of Other Bodies

These values show how strongly radius and density shape surface gravity. The Sun is enormously massive yet only pulls about 28 times as hard as Earth because it is also huge; a white dwarf packs a Sun-like mass into an Earth-sized ball, and a neutron star crushes it into a city-sized sphere, sending gravity to extreme values.

Body

Mass (kg)

Radius (m)

g (m/s²)

Relative to Earth

Sun

1.99 × 10³⁰

6.96 × 10⁸

≈ 274

≈ 28

Venus

4.87 × 10²⁴

6.05 × 10⁶

≈ 8.87

≈ 0.90

Mercury

3.30 × 10²³

2.44 × 10⁶

≈ 3.70

≈ 0.38

White dwarf (Sirius B)

2.0 × 10³⁰

5.8 × 10⁶

≈ 4 × 10⁶

≈ 400,000

Neutron star

2.8 × 10³⁰

1.2 × 10⁴

≈ 1 × 10¹²

≈ 10¹¹

The neutron star figure is a Newtonian estimate; at that density general relativity matters, but it still shows the scale. Enter any of these mass and radius pairs above to reproduce the numbers.

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