The Moon tugs on the oceans and raises the tides, and Newton's law of universal gravitation prices that pull exactly: gravitational force equals G times both masses divided by the distance squared. In symbols: F = G × m₁ × m₂ / r², with G ≈ 6.674 × 10⁻¹¹. The inverse square is the drama — double the distance, quarter the force — which is why the Sun, despite its enormity, tugs Earth's oceans less than half as hard as the nearby Moon.

Satellite engineers live inside this equation. A GPS satellite at 12,550 miles up must travel about 8,700 mph or gravity wins and it falls; go faster and it escapes into a higher orbit. The same formula weighed the Earth itself — Cavendish's 1798 torsion-balance experiment measured G in a London shed, and from it came our planet's 5.97 × 10²⁴ kg mass.

This calculator evaluates the full law from your four inputs. Type the two masses in kilograms in the Mass 1 (m1) and Mass 2 (m2) boxes and their center-to-center separation in meters in the Distance (r) box. The Gravitational Force (F) box reports newtons. Try Earth and a 150-pound person at Earth's radius: about 667 newtons — your weight, derived from first principles.

With the pre-filled defaults — Mass 1 (m1) 5,972,000,000,000,000,000,000,000 kg, Mass 2 (m2) 73,480,000,000,000,000,000,000 kg, Distance (r) 384,400,000 m — the Gravitational Force Calculator returns Gravitational Force (F) 198,211,072,907,925,200,000.0000 N. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.