The difference between Equation and Formula

An equation is a mathematical statement that asserts the equality of two expressions, while a formula is a rule or equation that expresses a relationship between two or more variables. Essentially, all formulas are equations, but not all equations are formulas. Formulas are specifically designed to express a relationship that can be used to calculate a specific value, whereas equations are broader and may simply state an equality without implying a calculative purpose. For example, "x + 2 = 5" is an equation, while "A = πr²" is a formula for calculating the area of a circle. 

While "equation" and "formula" are often used interchangeably, there's a subtle distinction:
Equation:

• Focuses on equality. An equation shows that two expressions are equal. It usually contains an equal sign (=).
• Solves for an unknown. Equations are often used to find the value of a variable.
• Examples: 2x + 5 = 11, y = mx + c (equation of a straight line)

Formula:

• Expresses a relationship. A formula shows a relationship between different quantities. It often involves constants and variables.
• Provides a calculation. Formulas are used to calculate a specific value based on known inputs.
• Examples: A = πr² (area of a circle), V = lwh (volume of a rectangular box)

In summary:

• Equations solve for unknowns.
• Formulas calculate specific values based on known quantities.

While an equation can be a formula, not all formulas are equations. A formula might not have an equal sign but still defines a relationship.