Universal Gravitation Calculator

Formula

How this is calculated

Newton's law of universal gravitation states that every pair of point masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F = G·m1·m2/r². The gravitational constant G is 6.674×10⁻¹¹ N·m²/kg². Masses m1 and m2 are entered in kilograms and the separation r between centers of mass in meters; the resulting force F is in newtons.

Enter any three of the four quantities {F, m1, m2, r} and leave the fourth blank to solve for it. The force form is F = G·m1·m2/r²; rearranging gives m1 = F·r²/(G·m2), m2 = F·r²/(G·m1), and r = √(G·m1·m2/F). The chart plots F against separation ρ over a range around r, showing the characteristic inverse-square falloff — doubling the distance cuts the force to one quarter.

The law treats the bodies as point masses (or, equivalently for spherically symmetric bodies, as if all mass were concentrated at their centers). It is a classical approximation that breaks down in strong fields where general relativity applies. Edge cases such as zero separation, zero mass in a denominator, or a non-positive force when solving for r return no result, since they are physically undefined.