Gravitational Force Calculator

This calculator finds the gravitational force between any two masses using Newton's law of universal gravitation. The law states that every object with mass attracts every other object with mass, with a force that increases with the product of the masses and decreases with the square of the distance between their centres. Written as F = Gm1m2 / r2, it ties together two masses m1 and m2, the distance r between them, and the universal gravitational constant G = 6.674 x 10-11 N m2/kg2. This single equation explains the weight you feel on Earth, the Moon's orbit, tidal forces, and the motion of galaxies. The gravitational constant is tiny, which is why gravity is negligible between everyday objects but dominant on astronomical scales where masses are enormous. You enter the two masses in kilograms and the distance between their centres in metres. Scientific notation is fully supported: type 5.97e24 for the Earth's mass and 6.37e6 for Earth's radius. The calculator returns the gravitational force in newtons, the gravitational acceleration experienced by mass 2 (force divided by mass 2), and an easy-to-read note of the distance entered. The default example uses the mass of the Earth (5.97e24 kg), a 70 kg person, and the Earth's mean radius (6.37e6 m), which gives approximately 687.4 N, that person's weight, confirming surface gravity of about 9.82 m/s2. Use this tool for physics homework, orbital mechanics, or to explore how gravity weakens with distance.

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F = G x m1 x m2 / r², with G = 6.674 x 10⁻¹¹. Distance is between centres of mass. Scientific notation (e.g. 5.97e24) is supported. Rounded for display.