🌙 Gravitational Force Calculator

Every two objects in the universe pull on each other. Newton's law of universal gravitation states that the force between two point masses is F = G·m₁·m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between their centres. The law explains everything from a falling apple to the orbit of the Moon — the same force, just scaled by mass and distance.

The inverse-square behaviour is the crucial part: double the distance and the force drops to a quarter. That is why the pull of the Earth dominates your life even though the Sun is 333,000 times heavier — it is also about 23,500 Earth-radii away, and the inverse square crushes the comparison.

The calculator multiplies the two masses, divides by the square of the distance (converted to metres), and multiplies by the gravitational constant G. Because G is tiny — about 6.674×10⁻¹¹ — the force between everyday objects is imperceptible; you need at least one astronomically large mass for the result to be noticeable.

The derived weight on Earth (force divided by 9.80665 m/s²) converts the abstract newtons into the familiar kgf, and the force in dynes is handy for classroom physics. For the weight itself on Earth's surface you can also use our force converter to move between N, kgf and lbf.

1. Enter the first mass and pick its unit (kg, g, tons or Earth masses).
2. Enter the second mass and its unit.
3. Enter the distance between the centres and its unit (m, km, miles or radii).
4. Click Calculate to see the gravitational force in newtons, kgf and dynes.
5. Optionally use the weight-on-Earth output to check the result against everyday intuition.

Why is the force so tiny between ordinary objects?

Because the gravitational constant G is extraordinarily small — 6.674×10⁻¹¹. The force only becomes large when at least one mass is planet-sized. Between two 1 kg masses one metre apart, the force is about 6.67×10⁻¹¹ N — you could never feel it.

Does distance really matter that much?

It is an inverse-square law: doubling the distance quarters the force, tripling it drops the force to one-ninth. This is why standing on a mountain barely changes your weight, but moving from the surface to the orbit of the ISS (roughly 6,700 km from the centre instead of 6,371 km) drops it by about 10%.

Is the force on you from the Sun significant?

No. The Sun is so far away that its pull on you is about 0.42 N — roughly the weight of a small apple — even though it is 333,000 times more massive than Earth. Gravity's reach is enormous, but the inverse square makes nearby mass win every time.

What is the difference between mass and weight?

Mass is the amount of matter, measured in kilograms, and never changes. Weight is the gravitational force on that mass, F = mg, and changes with the local gravity. This calculator finds the mutual gravitational force; divide by local g to get the equivalent weight.

Can I use this for orbital mechanics?

For circular orbits, yes — the gravitational force equals the centripetal force, m·v²/r. Combining the two gives the orbital velocity formula. For elliptical orbits you need Kepler's laws, but every orbit problem starts with the same universal gravitation equation.

Why does the calculator include dynes?

The dyne (1 g·cm/s²) is the CGS unit of force used in many physics textbooks and older literature. Providing it avoids unit-conversion errors when comparing results with printed problems or lab manuals.

Use the centre-to-centre distance, never the surface gap — for objects on Earth's surface the relevant distance is the full planetary radius, not your altitude. The formula assumes point masses; for large bodies you can still use it if you measure r to the centres and both objects are spherically symmetric (a good approximation for planets). The gravitational constant is known to only about five significant figures, so do not expect the fifth digit of your result to be meaningful. At the scale of atoms, gravity is unbelievably weak compared with electromagnetism — which is why chemistry and electronics are not governed by it. When you need the weight of an object on another world, enter that world's mass and radius as the second body.