Gravitational Field

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

Gravitational field strength at distance r.

Variables

Gravitational field

Field strength

m/s²

Gravitational constant

6.674×10⁻¹¹

In SI units: m³/(kg·s²)

Allowed values: greater than 0

N·m²/kg²

Mass

Source mass

Allowed values: 0 or more

Distance

From center of mass

Allowed values: greater than 0

Derivation

g = F/m = GM/r² from universal gravitation.

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 (Distance)

Result: g = 1.483178 × 10⁻¹¹ m/s²

Other mechanics formulas with the same quantities

Gravitational Potential Energy (General) (Gravitation) shares Gravitational constant, Distance
Escape Velocity (Gravitation) shares Gravitational constant, Mass
Surface Gravity (Gravitation) shares Gravitational constant, Mass
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 Universal Gravitation and before Gravitational Potential Energy (General).
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 Gravitational Field formula?

Gravitational Field is written g = GM/r². Gravitational field strength at distance r. It belongs to Mechanics, under Gravitation.

What are the units in g = GM/r²?

In SI units, g is gravitational field, measured in m/s²; G is gravitational constant, measured in m³/(kg·s²); M is mass, measured in kg; r is distance, measured in m.

How is the Gravitational Field formula derived?

g = F/m = GM/r² from universal gravitation. The result is g = GM/r².