formula

A formula is a concise symbolic expression that describes a relationship, rule, or property. Formulas are used across disciplines to encode quantitative relationships in a compact form, often involving variables and constants, and they can be derived from theories or empirical observations. The term derives from Latin forma, meaning form or shape.

In mathematics and physics, a formula relates quantities and can be evaluated to compute a value. Examples include the area of a circle A = πr^2, the Pythagorean theorem a^2 + b^2 = c^2, and the quadratic formula x = [-b ± sqrt(b^2 - 4ac)]/(2a). Formulas may be algebraic, geometric, or physical, and they enable prediction and analysis without detailed derivations each time.

In chemistry, a chemical formula expresses the types and numbers of atoms in a substance, using chemical symbols and subscripts: H2O, CO2. Empirical formulas give the simplest whole-number ratios, while molecular formulas specify the actual numbers in a molecule. Structural formulas show how atoms are bonded and arranged, providing information beyond composition alone.

Formulas also appear in computing, where spreadsheet programs use them to calculate values, and in logic and finance, where formulas define logical expressions or financial quantities such as interest and payments. Across these uses, formulas function as compact rules that translate inputs into outputs, supporting computation, modeling, and communication of quantitative ideas.