Formula

In mathematics and science, a formula is a formal rule or statement that is usually written in mathematical notation. The plural of formula can be written in two ways: formulae (the Latin convention) or formulas (the English convention). Both plurals are used, and it is normally up to personal or editorial preference.

In mathematics

Formally, a mathematical formula is a generalized version of the idea of an equation. A formula combines expressions and relations to make some statement about the mathematical objects involved.

The most important type of formula is a mathematical theorem. Theorems are formulae that relate expressions and other formulae by using logical operators like if and only if. Some key formulas under this category include the Pythagorean theorem, binomial theorem, Euler's formula and De Moivre's formula.

Many familiar mathematical statements are types of formula defined by a specific relation. An equation is a formula that uses the relation $=$, equality. An inequality instead uses one of the relations $<,>,\leq ,\geq$. Other equivalence classes have formulae similar to equations, like similarity and congruence in geometry, or congruence in modular arithmetic. Order theory looks at formulae that generalise inequalities similarly to how equivalence classes generalise equalities.

Physical sciences

In the physical sciences, the term "formula" is generally used for an equation that gives some quantity in terms of other quantities.

The expression $V=lwh$, gives the volume $V$ of a rectangular prism to its length $l$, width $w$, and height $h$. This would then be called a formula for the volume of the prism.

In science, one of the most well known formulas is Albert Einstein's formula for rest energy, $E=mc^{2}$. Here, $m$ is the mass of an object, which is a variable, and $c$ is a physical constant, the speed of light in a vacuum. Einstein's equation shows that the rest energy of a massive particle depends only on its mass.

Chemistry

In chemistry, "formula" usually refers to a chemical formula: a short expression showing what a chemical is made of, and maybe part of its structure.

Related pages

• Inequality
• Scientific law