What formula does this calculator use?

It uses Newton's law of universal gravitation: F = G x m1 x m2 / r^2, where m1 and m2 are masses in kilograms, r is the centre-to-centre distance in metres, and G is the gravitational constant 6.674e-11 N*m^2/kg^2 (CODATA 2018 value).

Can I solve for mass or distance instead of force?

Yes. Select "Mass m1", "Mass m2", or "Separation r" from the Solve For dropdown. The calculator rearranges the formula algebraically: m1 = F x r^2 / (G x m2), m2 = F x r^2 / (G x m1), and r = sqrt(G x m1 x m2 / F).

Why does the result show surface gravity as well as force?

Surface gravity g = G x m1 / r^2 is the gravitational acceleration that m1 produces at distance r. For the Earth preset the surface gravity comes out at about 9.81 m/s^2, confirming the standard value. It is useful for understanding how strongly a planet or star pulls objects at a given orbital radius.

Why is the gravitational constant G so small?

G = 6.674e-11 N*m^2/kg^2 is tiny because gravity is by far the weakest of the four fundamental forces. Two 1 kg masses placed 1 m apart attract with only about 6.7e-11 N — completely unmeasurable without laboratory-grade equipment. Gravity only dominates at astronomical mass scales.

Why does halving the separation quadruple the force?

The formula contains r^2 in the denominator, making gravity an inverse-square law. Halving r replaces r^2 with (r/2)^2 = r^2/4, so dividing by a quarter means multiplying the force by four. This rapid fall-off with distance also means that doubling the separation reduces the force to one-quarter.

What does centre-to-centre distance mean in practice?

Newton's shell theorem proves that the gravitational field outside a uniform sphere is identical to that of a point mass at the centre. So for two spherical bodies you measure r from centre to centre, not from surface to surface. For Earth and a person standing on the surface, r equals Earth's mean radius, 6.371e6 m.

Gravitational Force Calculator

This calculator applies Newton’s law of universal gravitation to find the attractive force between any two masses — or to work backwards and find an unknown mass or separation. It is designed for physics students, engineers, and anyone curious about orbital mechanics or planetary science. Four quick presets load real-world scenarios instantly, and the step-by-step panel shows every multiplication so you can follow or check the working.

The formula

Every pair of masses in the universe attracts every other pair with a force that depends on both masses and the square of the distance between them:

F = G x m1 x m2 / r^2

The symbols are:

F — gravitational force in newtons (N)
G — gravitational constant, 6.674 x 10^-11 N*m^2/kg^2 (CODATA 2018)
m1, m2 — the two masses in kilograms (kg)
r — the centre-to-centre separation in metres (m)

The formula is an inverse-square law: doubling the distance cuts the force to one-quarter; halving the distance quadruples it. This is why satellites in low Earth orbit experience much stronger gravity than those in geostationary orbit.

How to use the calculator

Select what you want to find from the Solve for dropdown. The matching input field disappears and becomes the unknown. Fill in the three known quantities — masses in kilograms and distance in metres — and the result appears immediately. Scientific notation is accepted in every field, so you can type 5.972e24 for Earth’s mass or 3.844e8 for the Moon’s orbital radius.

The Results panel shows the solved value alongside the surface gravity that m1 produces at distance r (g = G*m1/r^2) and how that compares to Earth’s standard 9.81 m/s^2. The Step-by-step working panel lists every arithmetic step, which you can copy to the clipboard with one click.

Worked example — a person’s weight on Earth

The default preset illustrates a familiar calculation:

m1 = Earth’s mass = 5.972 x 10^24 kg
m2 = 70 kg (the person)
r = Earth’s mean radius = 6.371 x 10^6 m

Substituting into F = G x m1 x m2 / r^2:

F = 6.674e-11 x 5.972e24 x 70 / (6.371e6)^2
F = 2.788e16 / 4.059e13
F ≈ 687 N

That matches the textbook result: 70 kg x 9.81 m/s^2 = 686.7 N. The gravitational force is the person’s weight.

Scenario	m1	m2	r	F
Person on Earth	5.972e24 kg	70 kg	6.371e6 m	687 N
Moon orbiting Earth	5.972e24 kg	7.342e22 kg	3.844e8 m	1.98e20 N
Two 1 kg masses, 1 m apart	1 kg	1 kg	1 m	6.674e-11 N

Understanding the gravitational constant G

G = 6.674 x 10^-11 N*m^2/kg^2 is extremely small, which is why gravity is the weakest of the four fundamental forces. Two 1 kg masses 1 m apart attract with only about 6.7 x 10^-11 N — far below the threshold of human perception. Yet at planetary scales the product G x m1 x m2 becomes enormous because the masses involved are on the order of 10^24 kg, making gravity the dominant force shaping the large-scale structure of the universe.

Surface gravity and orbital mechanics

The calculator also reports the surface gravity g = G*m1/r^2 at the given separation. This is the free-fall acceleration that m1 imparts to any object at distance r, regardless of that object’s mass. On Earth’s surface it equals 9.81 m/s^2; on Mars (mass 6.39 x 10^23 kg, radius 3.39 x 10^6 m) it is about 3.72 m/s^2, roughly 38% of Earth’s. The ratio column in the results panel lets you compare any body’s surface gravity directly to Earth’s.

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