Gravitational Constant (G): Meaning, Formula, Value & Unit

Gravity is one of the forces we experience every day. It keeps us on the ground, holds planets in their orbits and governs the motion of objects in space. But how do we quantify the strength of gravitational attraction between two objects?
This is where the universal gravitational constant, represented by G, comes in. It is a fundamental constant used in Newton's law of universal gravitation. In this article, we will understand the define gravitational constant g concept, its value, SI unit, formula and dimensional formula.

The gravitational constant G is the constant of proportionality in Newton's universal law of gravitation. It relates the gravitational force between two masses to their masses and the distance between them.
Newton's law of gravitation is written as:
F = Gm₁m₂/r²
Here, G represents the universal gravitational constant, m₁ and m₂ are the two masses and r is the distance between their centres.
The gravitational constant is called universal because its value is considered the same throughout the universe. It is also a scalar quantity. NCERT gives G as approximately 6.67 × 10⁻¹¹ N m² kg⁻².

The gravitational constant formula can be obtained from Newton's law of universal gravitation:
F = Gm₁m₂/r²
Rearranging the equation:
G = Fr²/(m₁m₂)
This equation can also be used to determine the unit and dimensions of G.
The gravitational force depends on the masses of the two objects and the distance between them. G itself does not change according to the masses or distance involved.

The si unit of gravitational constant is:
N m² kg⁻²
The unit can be derived from:
G = Fr²/(m₁m₂)
Since force is measured in newtons, distance in metres and mass in kilograms, the SI unit becomes N m² kg⁻².
It can also be expressed using fundamental SI units as:
m³ kg⁻¹ s⁻²
Both forms represent the same SI unit.

The standard value of G used in school-level Physics is approximately:
G = 6.67 × 10⁻¹¹ N m² kg⁻²
The value is extremely small. This is one reason why the gravitational attraction between ordinary objects around us is usually not noticeable.
The value of G was experimentally determined by Henry Cavendish using a sensitive balance. His experiment provided an experimental determination of the gravitational constant.

The dimensional formula of gravitational constant can be derived from Newton's law of gravitation.
We know:
G = Fr²/(m₁m₂)
The dimensions of force are:
[F] = [MLT⁻²]
The dimensions of distance are:
[r] = [L]
Therefore:
[G] = [MLT⁻²][L²]/[M²]
So,
[G] = [M⁻¹L³T⁻²]
Therefore, the dimension of gravitational constant is:
[M⁻¹ L³ T⁻²]
This is an important result to remember for questions involving dimensional analysis. NCERT's Class 11 material gives the same dimensional formula for G.

A common question is the gravitational constant depends upon what factors.
The value of G does not depend on the masses of the objects, the distance between them, the material of the objects or their location. It is treated as a universal constant.
This is different from gravitational force. The gravitational force changes when the masses or distance between the objects changes, according to Newton's law of gravitation. G remains constant in the equation.

Do not confuse G with g.
G is the universal gravitational constant and has the same value everywhere under the usual Newtonian framework. Its SI unit is N m² kg⁻².
g represents acceleration due to gravity. Near Earth's surface, its commonly used value is approximately 9.8 m/s². Its value can vary with location and distance from Earth.
The two quantities are related by:
g = GM/R²
where M is the mass of Earth and R is its radius.

Use this table for a quick revision of the most important facts about G. It brings together the symbol, formula, value, SI unit and dimensions in one place.

The easiest way to keep G clear in your mind is to connect its three essentials: its role in Newton's law of gravitation, its very small numerical value and its dimensions. Once these are linked, questions on units and dimensional analysis become much easier to solve.