What is a dimensionless quantity? Give examples.

A dimensionless quantity is a physical quantity that has no units and no dimensions. It is usually a pure number obtained by taking the ratio of two similar quantities.

Definition

A quantity is called dimensionless if its dimensional formula is [M⁰L⁰T⁰], meaning it does not depend on mass, length, or time.

Examples of Dimensionless Quantities

1. Strain = Change in length / Original length
2. Refractive index = Speed of light in vacuum / Speed in medium
3. Relative density (specific gravity)
4. Coefficient of friction
5. Poisson’s ratio
6. Angle (in radians)
7. Percentage and ratios

Explanation

Since these quantities are ratios of similar physical quantities, their units cancel out.

Example:
Strain = (length / length) → no unit

Key Characteristics

• No unit
• Pure number
• Often represent comparisons or ratios

Practical Insight

Dimensionless quantities are widely used in:

• Physics formulas
• Engineering calculations
• Scientific analysis