Gravitational Force Calculator

Newton's law of universal gravitation: the attraction between two masses at a given distance.

kg

Scientific notation works, e.g. 5.972e24 (Earth).

kg

Moon: 7.342e22

m

Earth–Moon average: 3.844e8 m

Gravitational force

1.9805e+20 N

Force
4.4523e+19 lbf
Acceleration of mass 2 toward mass 1
2.6975e-3 m/s²
Acceleration of mass 1 toward mass 2
3.3163e-5 m/s²

How it works

Every mass attracts every other mass with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centers.

The gravitational constant G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018) is tiny, so gravity between everyday objects is almost undetectable. It dominates only when at least one mass is enormous, like a planet or star.

The defaults show the Earth–Moon pull, about 1.98 × 10²⁰ N. Measure distance between centers of mass, not surfaces.

Formula

F = G × m₁ × m₂ ÷ r², G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²

Questions people ask

How strong is gravity between two people?

Two 70 kg people 1 m apart attract each other with about 3.3 × 10⁻⁷ N, roughly the weight of a few grains of dust.

Why does doubling distance quarter the force?

Gravity spreads over the surface of a sphere, whose area grows with r². Twice as far means the force is spread over four times the area.

Can I use this for weight on another planet?

Yes. Put the planet’s mass as mass 1, your mass as mass 2 and the planet’s radius as the distance. The acceleration of mass 2 is the surface gravity.