Mathematical Formulas

A mathematical formula is a concise statement of a relationship between quantities, written using symbols and operations. Formulas capture general rules so that they can be applied to many particular cases, and collecting them into reference tables gives a quick way to recall and apply established results. Such collections span the major branches of mathematics and are widely used in study, science, and engineering.

Algebraic formulas include rules for expanding and factorising expressions and for solving equations, such as the standard solution of a quadratic. Geometric formulas give the areas, perimeters, surface areas, and volumes of common shapes and solids, while trigonometric formulas relate the angles and sides of triangles and describe the behaviour of periodic functions. Calculus contributes formulas for differentiation and integration, which describe rates of change and accumulated quantities, and these are often listed in tables of standard derivatives and integrals.

Formulas also depend on a stock of mathematical constants and symbols. Fundamental constants such as the ratio of a circle’s circumference to its diameter appear throughout geometry and analysis, and many quantities are denoted by letters of the Greek alphabet. Clear, standard notation lets formulas be read and applied consistently across countries and disciplines. Reference tables that bring together formulas, constants, and symbols therefore serve as a practical toolkit for solving a wide range of problems.

Frequently asked questions

What is a mathematical formula?

It is a compact expression, written with symbols, that states a general relationship between quantities and can be applied to many specific cases.

Why keep tables of formulas?

Reference tables let established results be recalled and applied quickly without re-deriving them each time, across algebra, geometry, trigonometry and calculus.

What is a mathematical constant?

It is a fixed number with a special significance, such as the ratio of a circle’s circumference to its diameter, that appears in many formulas.