This calculator finds the gravitational force between any two objects using Newton's law of universal gravitation. Enter the two masses and the distance between their centres, and it returns the attractive force in newtons and other units. The gravitational constant G is filled in automatically.
What the symbols mean
- F — gravitational force (newtons).
- G — gravitational constant, 6.674×10⁻¹¹ N·m²·kg⁻² (auto-filled).
- m₁, m₂ — the two masses (kilograms).
- r — distance between the centres of the masses (metres).
Worked example
For the Earth (5.97×10²⁴ kg) and the Moon (7.34×10²² kg) separated by 3.84×10⁸ m, the force is about 1.98×10²⁰ N — the pull that keeps the Moon in orbit.
Want the full story behind this formula? Read our guide: Gravitational Force.
How the formula works
Newton's law of universal gravitation says the attractive force between two masses grows with the product of those masses and falls off with the square of the distance between their centres. The gravitational constant G sets the overall strength of the effect; because it is so tiny, gravity only becomes noticeable when at least one of the masses is very large, like a planet or star.
The inverse-square part — dividing by r² rather than r — reflects how the influence spreads out over the surface of an ever-larger sphere as distance increases. Double the distance and the force drops to a quarter; triple it and the force drops to a ninth.
Common mistakes to avoid
- Using the surface gap instead of centre-to-centre distance. For an object on Earth, r is the Earth's radius (about 6,371 km), not the small height above the ground.
- Forgetting to square r. The distance is squared, which has a dramatic effect on the result.
- Mixing units. Keep masses in kilograms and distance in metres for an answer in newtons.
Where it is used
This formula predicts planetary orbits, the tides raised by the Moon, the trajectories of spacecraft, and the gravitational pull that holds galaxies together. Near a planet's surface it simplifies to the familiar weight formula, force equals mass times g.