Surface Gravity Calculator
Find the gravitational acceleration at the surface of any celestial body from its mass and radius.
Mass unit
Radius unit
Relative to Earth: 1.001 g
- 1
Radius squared R²
6,371,000 × 6,371,000 = 40,589,641,000,000 - 2
G × M (numerator)
6.674×10⁻¹¹ × 5,972,000,000,000,000,000,000,000 = 398,571,280,000,000G is the gravitational constant; M is the body mass in kg. - 3
Surface gravity g = G·M ÷ R²
398,571,280,000,000 ÷ 40,589,641,000,000 = 9.820
How does this calculator work?
Surface gravity is g = G·M/R², where G = 6.674×10⁻¹¹, M is the body's mass, and R its radius. Enter mass and radius in your chosen units to get g in m/s² and as a multiple of Earth's 9.80665 m/s². Larger mass raises g; larger radius lowers it by the square.
Formula
How this is calculated
Surface gravity is the gravitational acceleration felt by an object resting at the surface of a body. It follows directly from Newton's law of universal gravitation: the force on a unit mass is G·M/R², where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), M is the body's mass, and R is the distance from its centre to the surface (its radius).
Enter the mass M (in kilograms or Earth masses, where 1 Earth mass = 5.972×10²⁴ kg) and the radius R (in metres, kilometres, or Earth radii, where 1 Earth radius = 6.371×10⁶ m). The calculator converts both to SI units, computes g in m/s², and divides by the standard Earth value g₀ = 9.80665 m/s² to express the result as a multiple of Earth gravity.
The model assumes a spherically symmetric, non-rotating body, so g depends only on total mass and radius — not on internal density distribution. Real bodies that rotate quickly or are oblate have a slightly lower effective gravity at the equator. Radius and mass must both be positive; a zero or negative radius is rejected to avoid division by zero.
Frequently asked questions
Surface gravity scales with mass but falls off with the square of the radius. A large, low-density planet can have weaker surface gravity than a smaller, denser one because its surface sits farther from the centre of mass.
Using M = 5.972×10²⁴ kg and R = 6.371×10⁶ m gives about 9.82 m/s², very close to the standard reference value g₀ = 9.80665 m/s² used to define 1 g.
This calculator gives true gravitational acceleration. On a spinning body, centrifugal effects slightly reduce the measured weight at the equator, so the effective gravity there is a little less than G·M/R².
Also known as
TG we-Calculate Editorial Team. (2026). Surface Gravity Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/surface-gravity-calculator
TG we-Calculate Editorial Team. "Surface Gravity Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/surface-gravity-calculator.
TG we-Calculate Editorial Team, "Surface Gravity Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/surface-gravity-calculator
@misc{wecalculate_surface_gravity_calculator, title = {Surface Gravity Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/surface-gravity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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