Gravitational Force Calculator

Every two masses attract each other along the line joining their centers with force F = G x m1 x m2 / r^2, where G is the gravitational constant (6.6743 x 10^-11 N m^2 / kg^2), m1 and m2 are masses in kilograms, and r is center-to-center distance in meters.

Internally everything is SI. Inputs let you pick masses in kg, g, lb, Earth masses (5.972 x 10^24 kg), or solar masses (1.989 x 10^30 kg), and distances in m, km, mi, astronomical units (1 AU = 1.496 x 10^11 m), or light-years. Output is shown in N, kN, and pound-force.

G is tiny: 6.6743 x 10^-11 N m^2 / kg^2. Two 1 kg masses 1 m apart attract each other with only 6.67 x 10^-11 N, roughly the weight of a single bacterium. Gravity only becomes obvious for very large masses like planets and stars.

Gravity follows an inverse-square law, so doubling r divides F by four, tripling r divides F by nine. That is why the Sun pulls Earth far harder than the much closer but much less massive Moon.

Newton's third law says both masses feel the same force, but they do not undergo the same acceleration because a = F / m. Earth and Moon attract each other with the same force (~1.98 x 10^20 N), but the Moon accelerates toward Earth at ~2.7 x 10^-3 m/s^2 while Earth only accelerates toward the Moon at ~3.3 x 10^-5 m/s^2.