formulae

Formulae are compact notations that express rules for calculating quantities or describing relationships among quantities. The plural form is formulae in formal or traditional contexts, especially in British usage, while formulas is common in American English. They are used across mathematics, science, and engineering to convey how to obtain results from given inputs.

A formula is typically an algebraic expression that, with appropriate values for the variables, yields a result. It may also be a general rule linking several quantities. By contrast, an equation asserts that two expressions are equal; a formula is the rule or method used to compute a value, not merely a statement of equality.

In mathematics, formulae describe geometric measures (such as area and volume), kinematic relations (such as distance or velocity), and solution procedures (such as the quadratic formula). They can be simple, like A = πr^2 for the area of a circle, or more complex, involving multiple variables and constants.

In chemistry, a chemical formula denotes which atoms and how many of each are present in a substance. Molecular formulas show the actual composition, while empirical formulas reflect the simplest whole-number ratio. Ionic compounds may be represented by formulas that indicate the relative numbers of ions.

Notation for formulae relies on letters to represent variables, subscripts to indicate quantities, parentheses to group terms, and superscripts for powers or charges. Symbols and conventions vary by field, so clarity and context are important to avoid ambiguity. Formulae underpin quantitative reasoning, modeling, and the communication of scientific ideas.