Gravitational Force Calculator
Enter two masses and the distance between their centres to get the gravitational force in newtons — and see why gravity falls off so fast with distance.
Use SI units
Mass in kilograms and distance in metres give the force in newtons. The distance is measured centre-to-centre, not surface-to-surface.
What is gravitational force?
The mutual pull between masses
Gravitational force is the attraction that every mass exerts on every other mass. Newton's law of universal gravitation says the force grows with the product of the two masses and shrinks with the square of the distance between their centres. The gravitational force calculator turns three measurements — the two masses in kilograms and their separation in metres — into the force in newtons. It is the number behind your weight on Earth, the pull that keeps the Moon in orbit, and the faint attraction between any two everyday objects.
Enter two masses in kilograms and the distance between their centres in metres to get the gravitational force in newtons instantly.
The gravitational force is the gravitational constant G times the product of the two masses, divided by the square of the distance between their centres.
F = G × m₁ × m₂ ÷ r²The constant G = 6.674_30 × 10⁻¹¹ N·m²/kg² is tiny, so gravity is only noticeable when at least one mass is enormous. Because the distance is squared in the denominator, moving the objects twice as far apart cuts the force to a quarter. Use kilograms and metres and the force comes back in newtons.
Suppose a 70 kg person is standing at Earth's surface (Earth's mass 5.972 × 10²⁴ kg, Earth's radius 6.371 × 10⁶ m).
Multiply the two masses
5.972e24 × 70 = 4.1804e26 — the product of the masses.
Multiply by G
6.674_30e-11 × 4.1804e26 = 2.790e16 — the numerator.
Divide by the distance squared
(6.371e6)² = 4.059e13, and 2.790e16 ÷ 4.059e13 = about 687 N — the gravitational force, which is exactly what we call the person's weight.
The force you get back is the pull each object feels toward the other — and by Newton's third law it is equal and opposite, so both masses are tugged with the same number of newtons. For a person at Earth's surface, about 687 N, that force is simply their weight. The crucial insight is the inverse-square dependence on distance: the force drops with the square of how far apart the centres are. Double the separation and the force falls to one quarter; triple it and the force falls to one ninth. That is why gravity is overwhelming at a planet's surface yet fades quickly as you climb away, and why distant objects pull on each other only feebly. The masses matter too, but only in direct proportion — distance is the lever that moves the result the most. Between two everyday objects the force is vanishingly small (two 70 kg people one metre apart attract with under a millionth of a newton), which is why we never feel it.
The formula is exact for point masses, but a couple of practical points are worth keeping in mind.
Point masses, centre-to-centre distance, and consistent units
Newton's law treats each object as a point mass and uses the distance between their centres of mass — for a uniform sphere this is the centre, so use the radius, not the surface gap. The law is the classical (Newtonian) approximation and does not include the tiny corrections of general relativity, which only matter in very strong gravitational fields. Keep your units consistent — kilograms for mass and metres for distance — or the newtons will be wrong.