Newton's Law of Universal Gravitation Calculator

About the Gravitation Force Calculator

This calculator finds the gravitational force of attraction between two masses using Newton's Law of Universal Gravitation, the inverse-square relationship that governs everything from falling objects to orbital mechanics. It's set up with default values for Earth and the Moon, making it easy to see how the same equation that describes tabletop physics also describes astronomical-scale forces.

How It Works

Enter the two masses in kilograms and the distance between their centers in meters. The calculator multiplies the two masses together, multiplies that by the gravitational constant G, and divides the result by the distance squared to return the force in newtons, displayed in scientific notation. It returns an error if the distance is zero or negative, since the equation would otherwise divide by zero.

F = G x m1 x m2 / d^2, where G = 6.6743 x 10^-11 N m^2/kg^2

Examples

Earth-Moon Attraction

Using Earth's mass of about 5.972 x 10^24 kg, the Moon's mass of about 7.342 x 10^22 kg, and their average center-to-center distance of 384,400,000 m, the calculator returns a gravitational force of roughly 1.98 x 10^20 N, the actual force that keeps the Moon in orbit.

Two Everyday Masses

Two 1000 kg masses, roughly the weight of a small car each, placed 1 m apart attract each other with a force of about 6.67 x 10^-5 N, far too small to feel or measure without sensitive lab equipment.

Advantages

Handles the full range from planetary-scale to everyday masses using the same formula and scientific notation output, without manual conversion.
Comes preloaded with real Earth-Moon values, letting you immediately see a physically meaningful result rather than an arbitrary example.
Isolates the inverse-square distance relationship clearly, since changing only the distance input shows directly how quickly gravitational force drops off.

Common Mistakes

Entering distance in kilometers or another unit instead of meters, which throws the squared term off by a large factor and produces a badly wrong force.
Forgetting that this is the mutual attractive force between the two masses, not the acceleration each mass experiences; converting to acceleration requires dividing this force by one object's own mass separately.
Assuming everyday-sized objects will show a noticeable force, when in fact G is so small that only astronomical masses or very sensitive instruments produce a measurable result.

Edge Cases to Watch For

Distance must be entered as a value greater than zero; the calculator returns an error instead of a result if distance is zero or negative, since the inverse-square term would be undefined.
The formula treats both masses as point masses (or uniform spheres) with distance measured center to center, so it's not accurate for irregularly shaped or very close-together objects where mass distribution matters.
Because the gravitational constant G is extremely small, everyday object masses produce forces too tiny to notice, which is why the default example uses astronomical masses like Earth and the Moon to give a result large enough to be meaningful.

Common Use Cases

Physics and astronomy students working through gravitation and orbital mechanics problems
Educators demonstrating the inverse-square law with real planetary or satellite distance data
Anyone curious about the actual gravitational pull between two known masses, from planets to everyday objects

Frequently asked questions

What is G in this formula?

G is the gravitational constant, 6.6743 × 10⁻¹¹ N·m²/kg² - it's the same fixed value everywhere in the universe, and combined with the two masses and the inverse square of distance between them, gives the attractive gravitational force per Newton's law, first published in 1687.

Conclusion

Newton's law of gravitation shows that every pair of masses attracts every other pair, with the force scaling directly with mass and falling off sharply with distance. This calculator applies that single equation across scales, from the negligible pull between two objects on a table to the force that keeps the Moon in orbit around Earth.