Gravitational Force Calculator

Calculate the gravitational force between two masses using Newton's Law of Universal Gravitation

Input Values

Result

What is Gravitational Force?

Gravitational force is the attractive force that exists between any two objects with mass. This force is described by Newton's Law of Universal Gravitation, which states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton's Law of Universal Gravitation

The formula for gravitational force is:

F = G × (m₁ × m₂) / r²

Where:

  • F = Gravitational force (N)
  • G = Gravitational constant (6.67430 × 10⁻¹¹ N⋅m²/kg²)
  • m₁ = Mass of first object (kg)
  • m₂ = Mass of second object (kg)
  • r = Distance between centers (m)

How to Use the Calculator

  1. Enter the mass of the first object in kilograms
  2. Enter the mass of the second object in kilograms
  3. Enter the distance between the centers of the objects in meters
  4. Click "Calculate" to get the gravitational force
  5. View the step-by-step solution

Example Calculations

Earth-Moon System:

m₁ (Earth) = 5.97 × 10²⁴ kg

m₂ (Moon) = 7.35 × 10²² kg

r = 3.84 × 10⁸ m

F ≈ 1.98 × 10²⁰ N

Two 1kg masses at 1m:

m₁ = 1 kg

m₂ = 1 kg

r = 1 m

F = 6.67 × 10⁻¹¹ N

Important Notes

  • The gravitational force is always attractive
  • The force decreases with the square of the distance
  • For most everyday objects, the gravitational force is extremely small
  • The gravitational constant G is one of the fundamental constants of nature