Gravitational Force Calculator

Calculate the gravitational attraction between two masses.

About Gravitational Force Calculator

Gravitational force follows an inverse-square law, so doubling the separation quarters the force. Potential energy is negative by convention, approaching zero at infinite separation. The inverse-square relationship is why orbital altitude changes gravity far less than intuition suggests — at 400 km, gravity is still about 89 per cent of its surface value.

Formula

Gravitational Force

F = G m₁ m₂ ÷ r²

G: Gravitational constant, 6.674 × 10⁻¹¹
r: Separation between centres of mass

Worked example

With the default values below, Gravitational Force Calculator returns Gravitational Force of 687.3672. Change any input above and every figure here is recalculated in your browser.

Inputs used

First massminimum 0 kg: 5,972,000,000,000,000,000,000,000 kg
Second massminimum 0 kg: 70 kg
Distance between centresminimum 0.001 m: 6,371,000 m

Results

Gravitational Force: 687.3672 N
Acceleration of the Second Mass: 9.8195 m/s2
Force at Double the Distance: 171.8418 N
Equivalent Weight in Kilogram-Force: 70.0680 kgf
Gravitational Potential Energy: -4,379,216,700.67 J

Step by step

1Values used
2Gravitational Force
3Gravitational Force= 687.3672 N
4Acceleration of the Second Mass= 9.8195 m/s2
5Force at Double the Distance= 171.8418 N
6Equivalent Weight in Kilogram-Force= 70.0680 kgf
7Gravitational Potential Energy= -4,379,216,700.67 J

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Gravitational Force calculated?

F = G m₁ m₂ ÷ r² Gravitational force follows an inverse-square law, so doubling the separation quarters the force. Potential energy is negative by convention, approaching zero at infinite separation.

Why does Gravitational Force matter?

The inverse-square relationship is why orbital altitude changes gravity far less than intuition suggests — at 400 km, gravity is still about 89 per cent of its surface value.

What values do I need to enter?

This calculator takes 3 inputs: First mass, Second mass, Distance between centres. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.