In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language.
In science, a specific formula is a concise way of expressing information symbolically as in a mathematical or chemical formula.
In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (–) signs.
The plural of formula can be spelled either formulae (like the original Latin) for mathematical or scientific senses, or formulas for more general senses. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
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.
Famous quotes containing the word formula:
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (17491827)
“Every formula which expresses a law of nature is a hymn of praise to God.”
—Maria Mitchell (18181889)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (18391894)