Newton's law of universal gravitation is one of the most consequential formulas in physics — it explains why apples fall, why the Moon orbits Earth, and why planets orbit the Sun, all with a single equation. This calculator applies that formula (F = Gm₁m₂/r²) to any two masses and any distance you supply, and can also solve backward for a missing mass or distance.
How the Gravitational Force Calculator works
The calculator multiplies the two masses together, divides by the square of the distance between their centers, and scales the result by the gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg². This single formula, published by Isaac Newton in 1687, describes the attractive force between any two masses in the universe — from subatomic particles to galaxy clusters — with no adjustment needed for what the objects are made of.
The force is always attractive (never repulsive) and acts along the line connecting the two masses' centers. Because G is such a small number, the gravitational force between everyday objects — two people standing near each other, for example — is far too small to notice. It only becomes significant when at least one of the masses is planet-sized or larger.
Inputs and what they mean
Mass 1 and mass 2 are both in kilograms and are interchangeable — the formula treats them symmetrically, so it doesn't matter which mass you call "1" and which you call "2". Astronomical masses are conveniently entered in scientific notation (5.97e24 for Earth, 1.989e30 for the Sun), which the calculator parses directly without needing to type out all the zeros.
Distance is measured center-to-center, not surface-to-surface. For a person standing on Earth, that means using Earth's radius (about 6,371 km), not zero — the surface-to-surface gap between a person and the ground is essentially zero, but gravity treats Earth's entire mass as if it were concentrated at its center, roughly 6,371 km below your feet.
Limits and edge cases
Newton's law of gravitation is a superb approximation for nearly every everyday and astronomical calculation, but it is not the final word on gravity. Einstein's general relativity, published in 1915, is more accurate in extreme conditions — very strong gravitational fields (near a black hole or neutron star), very high relative speeds, or when extreme precision is required (such as GPS satellite timing). For virtually all practical purposes — orbits, surface gravity, tides, spacecraft trajectories — Newton's formula is accurate to many decimal places.
The calculator also assumes both masses can be treated as point masses (or, equivalently, as uniform spheres) separated by the given distance. This is exact for spherically symmetric bodies like planets and stars, and a good approximation for most other shapes at typical astronomical distances.