The Physics of the Universe
HomeCalculators › Gravitational Force

Gravitational Force Calculator

Find the gravitational attraction between two masses with Newton's law F = G·m₁m₂/r² — or solve for a mass or the distance. Use kilograms and metres, or astronomy units like solar masses and AU.

 

Formula

$$ F = G\,\dfrac{m_1 m_2}{r^{2}} \qquad m_1 = \dfrac{F r^{2}}{G m_2} \qquad r = \sqrt{\dfrac{G m_1 m_2}{F}} $$
G = 6.674×10⁻¹¹ N·m²/kg²

Worked example

The Earth (5.972×10²⁴ kg) and Moon (7.35×10²² kg), 3.84×10⁸ m apart, attract with \( F = (6.674\times10^{-11})(5.972\times10^{24})(7.35\times10^{22})/(3.84\times10^{8})^2 \approx 1.98\times10^{20}\ \text{N} \).

How it works

Newton's law of universal gravitation says every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = G·m₁m₂/r², with G = 6.674×10⁻¹¹ N·m²/kg².

Because it is an inverse-square law, doubling the distance quarters the force. Gravity is extremely weak between everyday objects but dominates on astronomical scales, holding planets, stars and galaxies together.

Frequently asked questions

What is Newton's law of universal gravitation?

It states that the gravitational force between two masses is F = G·m₁m₂/r² — proportional to both masses and inversely proportional to the square of the distance between them.

What is the gravitational constant G?

G ≈ 6.674×10⁻¹¹ N·m²/kg². It sets the strength of gravity and is one of the most fundamental constants in physics.

How does distance affect gravitational force?

Force follows an inverse-square law: doubling the separation reduces the force to a quarter, and tripling it to a ninth.

Why is gravity so weak between everyday objects?

Because G is tiny. Two 1 kg masses 1 m apart attract with only about 6.7×10⁻¹¹ N — undetectable without sensitive instruments. Gravity only becomes strong with astronomical masses.

Related calculators