formula.expert

Newton's Law of Universal Gravitation

Also known as gravity between two masses · F = Gm₁m₂/r²

F=Gm1m2r2F = \frac{G m_1 m_2}{r^2}

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Constant used — built into this formula, no need to enter
G=6.6743×10−11 m3/(kg⋅s2)G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}Newtonian constant of gravitation

Learning zone

Published in Newton's Principia in 1687, this law unified the heavens and the Earth: the same attraction that drops an apple holds the Moon in orbit. Every pair of masses pulls on each other with a force proportional to both masses and falling off with the square of the distance — double the separation and the pull drops to a quarter. The constant G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² is tiny, which is why gravity between everyday objects is unnoticeable; Henry Cavendish first measured it in 1798 with a delicate torsion balance, in effect "weighing the Earth".

A quick check: Earth's mass is 5.97 × 10²⁴ kg and its radius 6.37 × 10⁶ m, so the force on a 70 kg person works out to about 687 N — exactly the person's weight, as it must. Solving for r takes the principal positive square root, the only physically meaningful distance.

Newton's Law of Universal Gravitation
F=Gm1m2r2F = \frac{G m_1 m_2}{r^2}
Where
  • FF= Gravitational force
  • m1m_1= Mass 1
  • m2m_2= Mass 2
  • rr= Center-to-center distance
Missing one of these? Work it out first, then come back
Part of this formula set

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.