Gravitational Acceleration Calculator Formula

Understand the math behind the gravitational acceleration calculator. Each variable explained with a worked example.

Use the Gravitational Acceleration Calculator

Formulas Used

Surface Gravity

gravity = 6.674e-11 * mass / pow(radius, 2)

In Earth g

gravity_g = (6.674e-11 * mass / pow(radius, 2)) / 9.80665

Variables

VariableDescriptionDefault
massBody Mass(kg)5.972e+24
radiusBody Radius(m)6371000

How It Works

Surface Gravitational Acceleration

Formula

g = G M / r²

  • *G* = 6.674e-11 N m² kg⁻²
  • *M* = body mass
  • *r* = body radius

    • Divide by 9.80665 m/s² to express in multiples of Earth's standard gravity.

    Worked Example

    Confirm Earth's surface gravity.

    mass = 5.972e+24radius = 6371000
    1. 01g = G M / r²
    2. 02G M = 6.674e-11 × 5.972e24 = 3.986e14
    3. 03r² = (6.371e6)² = 4.059e13
    4. 04g = 3.986e14 / 4.059e13 ≈ 9.82 m/s²

    Ready to run the numbers?

    Open Gravitational Acceleration Calculator