Formulas

Formulas are compact expressions that describe quantitative relationships. They typically involve variables, constants, operations, and functions, and are used to compute a value or express a law.

Mathematical formulas express geometric, algebraic, or numeric relationships. Examples include the area of a rectangle A = l × w, the area of a circle A = πr^2, and the volume V = l × w × h. They also appear as solution formulas, for instance the quadratic formula x = [-b ± sqrt(b^2 - 4ac)]/(2a).

Chemical formulas encode composition of substances. A chemical formula lists the elements and their relative numbers, with subscripts indicating atom counts, as in H2O, CO2, and NaCl. Molecular formulas show exact counts; empirical formulas reflect the simplest whole-number ratio. Ionic compounds are described by formula units, for example CaCl2; formula notation does not convey bonding geometry.

Notation and use. Formulas rely on consistent notation, symbols for quantities, units, and operations. They are manipulated symbolically, substituted with known values, and rearranged to solve problems or derive new relationships. They are fundamental in science, engineering, economics, and computer science, but models represented by formulas are simplifications and rely on assumptions.

Etymology and scope. The word formula comes from Latin formula, meaning a prescribed method or rule. In everyday mathematics, science, and engineering, formulas codify laws, rules, or conventions and are tested for validity under defined conditions.