Gravitational Force Calculator (Newton's Law of Gravitation)
By Santaji GadepatilinUpdated October 27, 2026
Every mass in the universe attracts every other mass. Newton's law of universal gravitation gives the strength of that pull, from an apple falling to the Moon orbiting Earth. This free gravitational force calculator solves for whichever value you leave blank and shows the formula and steps.
How to use the gravitational force calculator
Enter the two masses in kilograms (scientific notation like 5.972e24 works) and the distance between their centres. The default values are the Earth and the Moon.
Gravitational force formula
F = G × m₁ × m₂ ÷ r²
with G = 6.6743 × 10⁻¹¹ N·m²/kg².
Examples
| Pair | Masses | Distance | Force |
|---|---|---|---|
| Earth–Moon | 5.97 × 10²⁴ and 7.34 × 10²² kg | 384,400 km | 1.98e+20 N |
| Earth–Sun | 5.97 × 10²⁴ and 1.99 × 10³⁰ kg | 149.6 million km | 3.54e+22 N |
| Person on Earth | 70 kg and Earth | 6,371 km | 687 N |
| Two people | 70 kg each | 1 m | 3.3e-07 N |
Inverse-square law
Double the distance and the force falls to a quarter; triple it and it falls to a ninth. At the International Space Station’s altitude (about 400 km), gravity is still about 90% of its surface value.
Gravity at the surface
Setting m₂ as a small object gives the gravitational acceleration: g = G × M ÷ r². For Earth this gives about 9.82 m/s², close to the standard 9.81 m/s². See the weight calculator for other planets.
Measuring G
Henry Cavendish first measured G in 1798 with a torsion balance, using lead spheres. It remains one of the least precisely known fundamental constants.
Frequently asked questions
What is Newton's law of universal gravitation?
Every mass attracts every other mass with a force F = Gm₁m₂ ÷ r², where G = 6.674 × 10⁻¹¹ N·m²/kg².
What is the force between the Earth and the Moon?
About 1.98 × 10²⁰ N.
Why don't I feel gravity from people near me?
Because G is tiny. Two 70 kg people 1 m apart attract each other with about 3.3 × 10⁻⁷ N — far too small to notice.
Do I use the surface distance?
No — use the distance between the centres of mass. For a person on Earth, that is Earth's radius.