Surface Gravity Calculator
Find the gravitational acceleration at the surface of a planet or moon from its mass and radius.
How it works
g = G·M ÷ r² · Earth reference g₀ = 9.80665 m/s²
Surface gravity is just Newton’s law of gravitation evaluated at the body’s own radius: g = GM/r². Because radius is squared in the denominator, a body can be very massive yet have modest surface gravity if it is also large. That is why Uranus, far heavier than Earth, has almost the same surface gravity — its greater radius offsets its greater mass.
Worked example
For Earth, M = 5.972×10²⁴ kg and r = 6.371×10⁶ m: g = 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ (6.371×10⁶)² ≈ 9.82 m/s², matching the familiar 9.8 m/s².
Sources: Surface gravity — Wikipedia
Frequently asked questions
Why does surface gravity depend on radius squared?
Gravity spreads over a sphere whose area grows with radius squared, so the field weakens as 1/r². Measuring "at the surface" means using the body’s own radius as that distance.
Can two very different planets have the same gravity?
Yes. A small dense planet and a large low-density one can share a surface gravity if their mass-to-radius-squared ratios match. Mars and Mercury, for example, have nearly identical surface gravity despite Mercury being smaller and denser.
Is this the same as weight?
Weight is this gravity times an object’s mass (W = m·g). The g value here is the acceleration; multiply by a mass to get the force in newtons.
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This calculator is for educational purposes. Double-check important results before acting on them.