Gravitational Force Calculator
Find the gravitational pull between any two masses using Newton's law of gravitation.
Newton's law of gravitation: every pair of masses pulls on each other with a force set by their masses and the square of the distance between them. Double the gap and the force drops to a quarter. The defaults show Earth tugging on a 70 kg person at the surface — about 686 N, which is that person's weight.
How it works
Newton's law of universal gravitation says every pair of masses attracts each other. The pull is F = G·m₁·m₂/r², where G is the gravitational constant (6.674 × 10⁻¹¹), the two masses are in kilograms, and r is the distance between their centers in meters.
The force grows in step with either mass but falls off with the square of the distance. Move the objects twice as far apart and the pull drops to a quarter; three times as far and it's a ninth.
The defaults model Earth pulling on a 70 kg person standing on the surface, which comes out to about 686 newtons — exactly that person's weight. Swap in any masses and separation to explore other pairings.
Frequently asked questions
What is the gravitational constant?
G is 6.674 × 10⁻¹¹ N·m²/kg². It's a fixed number that sets the strength of gravity throughout the universe and appears in every gravitational calculation.
Why is gravity between everyday objects so weak?
Because G is tiny. Two people standing a meter apart attract each other with a force far smaller than a millionth of a newton — real, but utterly swamped by friction and everything else. Gravity only becomes obvious when at least one mass is planet-sized.
What happens to the force as distance grows?
It follows an inverse-square law. Double the distance and the force becomes one quarter as strong; triple it and it's one ninth. This is why distant objects tug on each other so gently.