This calculator applies Newton’s law of universal gravitation to find the attractive force between two masses. Enter two masses and the distance between them and it returns the force in newtons — useful for physics study, orbital intuition, and checking how an object’s weight arises from Earth’s mass.
How it works
Every pair of masses attracts along the line joining them with a force:
F = G × m₁ × m₂ / r²
where m₁ and m₂ are the masses in kilograms, r is the centre-to-centre distance in metres, and G is the gravitational constant, 6.674×10⁻¹¹ N·m²/kg². The relationship is an inverse-square law: doubling the distance cuts the force to a quarter. Scientific notation (e.g. 5.972e24) is accepted for planetary masses.
Example
The default values reproduce a person’s weight on Earth:
- m₁ = Earth’s mass = 5.972×10²⁴ kg
- m₂ = 70 kg
- r = Earth’s radius = 6.371×10⁶ m
F = 6.674×10⁻¹¹ × 5.972×10²⁴ × 70 ÷ (6.371×10⁶)² ≈ 687 N
That matches the familiar 70 kg × 9.81 m/s² ≈ 687 N — the gravitational force is the person’s weight.
| Scenario | m₁ | m₂ | r | Force |
|---|---|---|---|---|
| Person on Earth | 5.972×10²⁴ kg | 70 kg | 6.371×10⁶ m | ≈ 687 N |
| Two 1 kg masses, 1 m apart | 1 kg | 1 kg | 1 m | ≈ 6.674×10⁻¹¹ N |
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