Gravitational Force Calculator Formula

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

Formulas Used

Gravitational Force

grav_force = 6.6743e-11 * m1 * m2 / pow(r, 2)

Variables

VariableDescriptionDefault
m1Mass 1(kg)5.972e+24
m2Mass 2(kg)70
rDistance Between Centers(m)6371000

How It Works

Newton's Law of Universal Gravitation

Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Formula

F = G * m1 * m2 / r²

where G = 6.6743 x 10^-11 N·m²/kg² is the gravitational constant.

Worked Example

Weight of a 70 kg person on Earth's surface (Earth mass = 5.972e24 kg, radius = 6,371,000 m).

m1 = 5.972e+24m2 = 70r = 6371000
  1. 01F = G * m1 * m2 / r²
  2. 02F = 6.6743e-11 * 5.972e24 * 70 / (6.371e6)²
  3. 03F = 6.6743e-11 * 4.1804e26 / 4.059e13
  4. 04F ≈ 687 N (close to 70 * 9.81 = 686.7 N)

Ready to run the numbers?

Open Gravitational Force Calculator