Universal Gravitation Calculator

How it works

1. 1Enter the two masses m₁ and m₂ in kilograms. Scientific notation (e.g. 5.972e24 for Earth) is supported.
2. 2Enter the centre-to-centre separation r in metres. The calculator applies Newton’s inverse-square law: F = G·m₁·m₂ ÷ r².
3. 3The result shows the gravitational force in newtons, with kilonewtons alongside for larger values.

Use cases

• Verify surface gravity — Earth’s mass and radius with a 70 kg person gives ≈ 688 N.
• Orbital mechanics — the force between a satellite and Earth to cross-check centripetal requirements.
• Astrophysics homework — the force between any pair of bodies at any separation.

Frequently asked questions

What is the formula used by this calculator?

Newton’s law of universal gravitation: F = G·m₁·m₂ ÷ r², where G = 6.674×10⁻¹¹ N·m²/kg², m₁ and m₂ are the masses in kg, and r is the centre-to-centre distance in metres. Earth (5.972×10²⁴ kg) and a 70 kg person at Earth’s radius give F ≈ 688 N.

Why does the force decrease so rapidly with distance?

Because of the inverse-square law — r is squared in the denominator. Double the separation and the force falls to a quarter; triple it and it drops to a ninth. That is why gravity from distant stars is negligible despite their huge mass.

Is the force the same on both objects?

Yes. By Newton’s third law the force is mutual and equal: the Earth pulls you with the same force you pull it. The difference in acceleration (a = F ÷ m) is what makes the Earth appear stationary.