Surface Gravity

g = \frac{GM}{R^2}

Gravitational acceleration at the surface of a spherical body.

Variables

Surface gravity

Gravitational acceleration at surface

Allowed values: greater than 0

m/s²

Gravitational constant

6.674×10⁻¹¹

In SI units: m³/(kg·s²)

Allowed values: greater than 0

N·m²/kg²

Mass

Mass of planet/body

Allowed values: greater than 0

Radius

Radius of planet/body

Allowed values: greater than 0

Derivation

From g = GM/r², evaluated at r = R (surface).

Your notes

0/5000

Constants in this formula

Gravitational Constant

6.674 30 × 10⁻¹¹ ± 0.000 15 × 10⁻¹¹. Measured (CODATA 2018).

N·m²/kg²

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

G = 6.674 30 × 10⁻¹¹ N·m²/kg² (Gravitational constant)
M = 2 kg (Mass)
R = 3 m (Radius)

Result: g = 1.483178 × 10⁻¹¹ m/s²

Other mechanics formulas with the same quantities

Escape Velocity (Gravitation) shares Gravitational constant, Mass
Gravitational Potential Energy (General) (Gravitation) shares Gravitational constant
Orbital Velocity (Gravitation) shares Gravitational constant
Orbital Period (Gravitation) shares Gravitational constant
Geosynchronous Orbit Radius (Gravitation) shares Gravitational constant

Where this formula is listed

Mechanics formulas, under Gravitation.
In the mechanics list it comes after Escape Velocity and before Geosynchronous Orbit Radius.
Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Surface Gravity formula?

Surface Gravity is written g = GM/R². Gravitational acceleration at the surface of a spherical body. It belongs to Mechanics, under Gravitation.

What are the units in g = GM/R²?

In SI units, g is surface gravity, measured in m/s²; G is gravitational constant, measured in m³/(kg·s²); M is mass, measured in kg; R is radius, measured in m.

How is the Surface Gravity formula derived?

From g = GM/r², evaluated at r = R (surface). The result is g = GM/R².