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In mathematics, a formula (plural: formulae or formulas) is an entity constructed using the symbols and formation rules of a given logical language.
In science, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. Colloquial use of the term in mathematics often refers to a similar construct.
Such formulae are the key to solving an equation with variables. For example, determining the volume of a sphere requires a significant amount of integral calculus; but, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius for example). This particular formula is:
Having obtained this result, and knowing the radius of the sphere in question, we can quickly and easily determine its volume. Note that the quantities V, the volume, and r the radius are expressed as single letters. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate larger and more complex formulae.
Expressions are distinct from formulae in that they cannot contain an equals sign; whereas formulae are comparable to sentences, expressions are more like phrases.
In a general context, formulae are applied to provide a mathematical solution for real world problems. Some may be general: F = ma, which is one expression of Newton's second law, is applicable to a wide range of physical situations. Other formulae may be specially created to solve a particular problem; for example, using the equation of a sine curve to model the movement of the tides in a bay. In all cases however, formulae form the basis for all calculations.