A Gravitational Force Calculator

Every pair of masses in the universe pulls on each other, and the strength of that pull is one multiplication, one division and one constant.

First massIn kilograms. Earth is 5,972,000,000,000,000,000,000,000.Second massIn kilograms. The Moon is 73,480,000,000,000,000,000,000.Centre-to-centre distanceIn metres. Earth to the Moon is about 384,400,000.

Gravitational force

1.982111e+20

Field strength: 0.0026974833
Energy to separate: 7.619234e+28
Reduced mass: 7.258688e+22

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

The formula this calculator uses

F = G x m1 x m2 / r squared

F: Gravitational force
G: Gravitational constant
m1, m2: The two masses
r: Centre-to-centre distance

How to check the result by hand

1
Get both masses in kilograms
Convert to kilograms if the problem quotes tonnes or grams. Earth is about 5.972 times 10 to the 24 kilograms, which is written as 5,972,000,000,000,000,000,000,000.
2
Get the centre-to-centre distance in metres
Add the radii if the problem gives altitudes. Earth and the Moon are about 384,400,000 metres apart centre to centre.
3
Square the distance
Multiply the distance by itself. This is where the inverse square law bites, and it is also the easiest place to drop a factor of a million.
4
Multiply and divide
Multiply the gravitational constant by both masses, then divide by the squared distance. The result is in newtons.

For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Gravitational Force page.