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Gravitational Force Calculator (Newton's Law of Gravitation)

Calculate the mutual gravitational attraction between two masses, F = G·m₁·m₂/r², using Newton's law of universal gravitation.

Gravitational force
198,211,072,907,925,200,000 N
Equivalent to the weight of
20,211,904,463,596,150,000 kg on Earth's surface

How it works

Newton's law of universal gravitation says any two masses attract each other with a force F = G·m₁·m₂/r², where G is the gravitational constant and r is the distance between their centers. The default values above are Earth's and the Moon's masses at their mean orbital distance, which this formula correctly predicts to be about 1.98×10²⁰ N — strong enough to raise ocean tides, despite the two bodies being hundreds of thousands of kilometers apart.

Because force drops off with the square of distance, doubling the distance between two masses cuts the force to a quarter, not a half — the same inverse-square relationship this site's Coulomb's Law calculator uses for electric charges, just with mass and G in place of charge and Coulomb's constant.

Mass and distance are converted to kilograms and meters before the formula runs (the standard convert-to-canonical-then-run pattern this site's other unit-toggled physics calculators use), and the resulting force is always reported in newtons. It's also translated into an 'equivalent weight' — the mass that force would be if it were that same object's weight sitting on Earth's surface — since a raw newton figure is often too small or too large a number to judge without a frame of reference.

FAQ

Why is the gravitational force between everyday objects so small?

Because G itself is tiny (6.674×10⁻¹¹ in SI units) and force scales with the product of the two masses — for G·m₁·m₂/r² to produce a force large enough to notice, at least one of the masses usually has to be planet-sized. Two 1 kg objects 1 m apart attract each other with a force of only about 6.674×10⁻¹¹ N, roughly a trillion times weaker than the weight of a feather, which is why gravity between ordinary objects is never something you'd feel.

Is this the same force that gives objects their weight?

Yes — an object's weight is exactly the gravitational force between it and the planet it's standing on, computed with this same formula using the planet's mass and the object's distance from the planet's center (its radius, for something at the surface). This calculator's 'equivalent weight' figure uses that same relationship in reverse, dividing the computed force by standard gravity to answer 'what mass would weigh this much on Earth?'

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