formula

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In
science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...

, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
''. The informal use of the ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin).

# In mathematics

In
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula (often referred to as a ''
well-formed formula In mathematical logic Mathematical logic is the study of formal logic within mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they ar ...
'') is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

of a
sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

requires a significant amount of
integral calculus In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding ...
or its analogue, the
method of exhaustion The method of exhaustion (; ) is a method of finding the area of a shape by Inscribed figure, inscribing inside it a sequence of polygons whose areas limit (mathematics), converge to the area of the containing shape. If the sequence is correctly c ...

. However, having done this once in terms of some
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

(the
radius In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', ...

for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: : $V = \frac \pi r^3.$ Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume ''V'' and the radius ''r'' are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form. In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula : $F = ma$ is an expression of
Newton's second law Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
, and is applicable to a wide range of physical situations. Other formulas, such as the use of the
equation In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...

of a sine curve to model the movement of the tides in a , may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations. Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be likened to
phrases In syntax and grammar, a phrase is a group of words or singular word acting as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adjective phrase "very happy". ...
the same way formulas can be likened to grammatical sentences.

# Chemical formulas

In modern chemistry, a
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
is a way of expressing information about the proportions of
atom Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, l ...

s that constitute a particular
chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A homonuclear molecule, molecule co ...
, using a single line of chemical element symbols,
numbers A number is a mathematical object used to counting, count, measurement, measure, and nominal number, label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More u ...

, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...

, specifying that each
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

consists of two
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the chemical ...

(H) atoms and one
oxygen Oxygen is the chemical element with the chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...

(O) atom. Similarly, O denotes an
ozone Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic Allotropy, allotrope , breaking down i ...

molecule consisting of three oxygen atoms and a net
negative charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectiv ...
. A
chemical formula In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
identifies each constituent element by its
chemical symbol Chemical symbols are the abbreviations used in chemistry for chemical elements, functional groups and chemical compounds. Element symbols for chemical elements normally consist of one or two letters from the Latin alphabet and are written with th ...
, and indicates the proportionate number of atoms of each element. In empirical formulas, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound—as ratios to the key element. For molecular compounds, these ratio numbers can always be expressed as whole numbers. For example, the empirical formula of
ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...

may be written C2H6O, because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written as empirical formulas which contains only the whole numbers. An example is
boron carbide Boron carbide (chemical formula approximately B4C) is an extremely hard boron–carbon ceramic, a covalent compound, covalent material used in Tank armour, tank armor, bulletproof vests, engine sabotage powders, as well as numerous industrial ap ...
, whose formula of CBn is a variable non-whole number ratio, with n ranging from over 4 to more than 6.5. When the chemical compound of the formula consists of simple
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

s, chemical formulas often employ ways to suggest the structure of the molecule. There are several types of these formulas, including
molecular formula In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, str ...
s and condensed formulas. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for
glucose Glucose is a simple sugar with the Chemical formula#Molecular formula, molecular formula . Glucose is overall the most abundant monosaccharide, a subcategory of carbohydrates. Glucose is mainly made by plants and most algae during photosynthesis f ...

is C6H12O6 rather than the glucose empirical formula, which is CH2O. Except for the very simple substances, molecular chemical formulas generally lack needed structural information, and might even be ambiguous in occasions. A
structural formula The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are possibly arranged in the real three-dimensional space. The chemical bondi ...
is a drawing that shows the location of each atom, and which atoms it binds to.

# In computing

In
computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and development of both computer hardware , hardware and software. ...

, a formula typically describes a
calculation A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to th ...

, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer instruction such as. : ''Degrees Celsius'' = (5/9)*(''Degrees Fahrenheit''  - 32) In computer
spreadsheet A spreadsheet is a computer application for computation, organization, analysis and Data storage, storage of data in table (information), tabular form. Spreadsheets were developed as computerized analogs of paper accounting Worksheet#Accounting, ...

software, a formula indicating how to compute the value of a cell, say ''A3'', could be written as : ''=A1+A2'' where ''A1'' and ''A2'' refer to other cells (column A, row 1 or 2) within the spreadsheet. This is a shortcut for the "paper" form ''A3 = A1+A2'', where ''A3'' is, by convention, omitted because the result is always stored in the cell itself, making the stating of the name redundant.

# Units

Formulas used in science almost always require a choice of units. Formulas are used to express relationships between various quantities, such as temperature, mass, or charge in physics; supply, profit, or demand in economics; or a wide range of other quantities in other disciplines. An example of a formula used in science is Boltzmann's entropy formula. In statistical thermodynamics, it is a probability equation relating the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

''S'' of an ideal gas to the quantity ''W'', which is the number of
microstates A microstate or ministate is a sovereign state A sovereign state or sovereign country, is a polity, political entity represented by one central government that has supreme legitimate authority over territory. International law defines so ...
corresponding to a given
macrostate In statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energ ...
: :$S = k \cdot \log W$           (1) S= k ln W where ''k'' is
Boltzmann's constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
equal to 1.38062 x 10−23 joule/kelvin, and ''W'' is the number of
microstate A microstate or ministate is a sovereign state having a very small population or very small land area, usually both. However, the meanings of "state" and "very small" are not well-defined in international law.Warrington, E. (1994). "Lilliputs ...
s consistent with the given
macrostate In statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energ ...
.

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Formula editor A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: * They allow word processing and publication of technical content either for print ...
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Formula unit In chemistry, a formula unit is the empirical formula of any Ionic compound, ionic or covalent network solid compound used as an independent entity for stoichiometric calculations. It is the lowest whole number ratio of ions represented in an ioni ...
*
Mathematical notation Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations and any other mathematical objects, and assembling the ...
*
Scientific law Scientific laws or laws of science are statements, based on repeated experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experi ...
* Symbol (chemical element) *
Theorem In mathematics, a theorem is a statement (logic), statement that has been Mathematical proof, proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the th ...
*
Well-formed formula In mathematical logic Mathematical logic is the study of formal logic within mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they ar ...