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Solve Newton's law of gravitation F = Gm₁m₂/r² for any variable, or find the gravitational field strength g = GM/r² at any distance from a planet.
Also covers: Newton's law of gravitation · Universal gravitation calculator · Gravitational field strength · Surface gravity calculator
F = G m₁ m₂ / r²
G = 6.6743 × 10⁻¹¹ N·m²/kg² (CODATA 2018). r is the distance between the centres of the two masses. The defaults are Earth and a 70 kg person on its surface.
Gravitational force (F)
687.39814 N
In other units
Working
Choose Newton's law of gravitation or gravitational field strength and which variable to solve for; the form asks only for the others.
Each input has its own unit picker, so you can mix km, cm, µC or MHz without converting first.
You get the result in your chosen unit and every other unit, plus the rearranged equation with your numbers in SI units.
G = 6.6743 × 10⁻¹¹ N·m²/kg², the CODATA 2018 recommended value.
The distance between the centres of the two masses. For an object on a planet's surface, that's the planet's radius, e.g. 6,371 km for Earth.
A 70 kg person on Earth's surface feels F = Gm₁m₂/r² ≈ 687 N, the same as m × g with g ≈ 9.8 m/s². That's the law of gravitation and weight agreeing.
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