Gravitational Force Calculator
F = G × m₁ × m₂ ÷ r²
Mass must be greater than 0.
Mass must be greater than 0.
Distance must be greater than 0.
Custom G must be greater than 0.
Quick summary
Enter m₁, m₂, and r, then click Calculate.
Results
Force
— N
Force
— lbf
Acceleration on m₂
— m/s²
Acceleration on m₁
— m/s²
All calculations are performed in SI units first.
Use this Gravitational Force Calculator to find the attractive force between two masses from their masses and center-to-center separation distance.
Calculation Method
Newton’s law of universal gravitation is:
F = G × m₁ × m₂ ÷ r²
Where:
- F = gravitational force in newtons
- m₁ and m₂ = masses in kilograms
- r = center-to-center distance in meters
- G = 6.67430 × 10−11 N·m²/kg²
The acceleration of either mass can also be calculated with:
a = F ÷ m
Example
For two 1 kg masses separated by 1 meter:
F = 6.67430 × 10−11 × 1 × 1 ÷ 1²
F = 6.67430 × 10−11 N
Important Note
The formula directly applies to point masses and works for spherically symmetric objects when the distance is measured between their centers. More complex mass distributions or strong-gravity systems may require more advanced models.