Gravitational Force Calculator

The Gravitational Force Calculator applies Newton's law of universal gravitation to work out the attractive force between any two masses — from an apple resting on the ground to the Earth orbiting the Sun. Enter two masses and the distance between them to find the force, or rearrange the equation to solve for a mass or the separation instead. Along with the answer you get an animated attraction diagram, an inverse-square force curve, the acceleration of each body, and a plain-language comparison that turns an abstract newton value into something you can picture.

Newton's Law of Universal Gravitation

In 1687 Isaac Newton proposed that every mass attracts every other mass with a force that grows with the product of the masses and shrinks with the square of the distance between them. The same single law governs a falling apple and the motion of the planets — which is why it is called universal.

where:

• \(F\) is the gravitational force between the two bodies, in newtons (N)
• \(m_1\) and \(m_2\) are the two masses, in kilograms (kg)
• \(r\) is the distance between their centres, in metres (m)
• \(G\) is the gravitational constant, \(6.6743 \times 10^{-11}\ \text{N·m}^2/\text{kg}^2\)

Rearranging the Formula

Because the law links four quantities, knowing any three lets you solve for the fourth. This calculator does the algebra for you:

Why Gravity Feels One-Sided

By Newton's third law the two bodies pull on each other with exactly the same force. Yet the Earth clearly does not lurch toward a dropped apple. The reason is acceleration: since \(a = F/m\), the identical force produces a huge acceleration on the tiny apple and an utterly negligible one on the enormous Earth. This calculator shows both accelerations so the asymmetry is obvious.

The Inverse-Square Law

The \(r^2\) in the denominator means gravity weakens very quickly with distance. Move twice as far apart and the force drops to one quarter; three times as far and it falls to one ninth. The force curve in the results panel plots exactly this drop-off, with your own scenario marked on it.

The Gravitational Constant G

\(G\) is one of the fundamental constants of nature and one of the hardest to measure precisely. Its tiny size — about \(6.67 \times 10^{-11}\) — is why gravity is by far the weakest of the four fundamental forces and only becomes dominant when astronomical masses are involved.

What Affects Gravitational Force?

How to Use This Calculator

1. Choose what to solve for: the gravitational force, one of the masses, or the distance between the bodies.
2. Enter the known values: type each mass and distance and pick its unit — anything from grams and metres to solar masses and light-years.
3. Click Calculate: the tool applies Newton's law and solves for the unknown quantity.
4. Review your results: see the attraction diagram, the inverse-square curve, each body's acceleration, and a plain-language weight comparison, plus a full step-by-step solution.

Frequently Asked Questions

What is the formula for gravitational force?

Newton's law of universal gravitation states that the force between two masses is F = G × m₁ × m₂ / r², where m₁ and m₂ are the two masses in kilograms, r is the distance between their centres in metres, and G is the gravitational constant, 6.6743 × 10⁻¹¹ N·m²/kg².

What is the gravitational constant G?

G is the universal gravitational constant, equal to about 6.6743 × 10⁻¹¹ newton metres squared per kilogram squared. It sets the strength of gravity throughout the universe and is the same everywhere, which is why the law is called universal.

Why is the gravitational force between everyday objects so small?

Because G is extremely small, gravity only becomes noticeable when at least one mass is enormous, like a planet or star. Two people standing a metre apart attract each other with a force of roughly 3 × 10⁻⁷ newtons, far too weak to feel, while the Earth pulls on you strongly only because it has a mass of about 6 × 10²⁴ kilograms.

Can this calculator solve for mass or distance?

Yes. Use the "Solve for" menu to rearrange Newton's law. You can find the gravitational force from two masses and a distance, or work backwards to find one of the masses or the separation distance when the force is known.

Does gravitational force depend on the size of the objects?

For the purpose of this formula the objects are treated as points, so only their masses and the distance between their centres matter, not their physical size or shape. This point-mass approximation is exact for spherically symmetric bodies such as planets and stars.

What units can I use?

Masses can be entered in grams, kilograms, tonnes, Earth masses, or solar masses, and distances in metres, kilometres, astronomical units, or light-years. The calculator converts everything to SI units internally, so you can freely mix scales such as kilograms with light-years.

Additional Resources

• Newton's Law of Universal Gravitation - Wikipedia
• Gravitational Constant - Wikipedia