TheInfoList In
science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, testable explanations and predictions about the u ...
, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a
chemical formula A chemical formula is a way of presenting information about the chemical proportions of atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes ...
. The informal use of the term ''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 Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It has no generally ...
, 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) is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the
volume Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance ( solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI deri ...
of a
sphere of a sphere A sphere (from Greek language, Greek —, "globe, ball") is a Geometry, geometrical object in solid geometry, three-dimensional space that is the surface of a Ball (mathematics), ball (viz., analogous to the circular objects in two d ...
requires a significant amount of
integral calculus In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Deriv ...
or its geometrical analogue, the
method of exhaustion The method of exhaustion (; ) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas limit (mathematics), converge to the area of the containing shape. If the sequence is correctly constructed, the ...
. However, having done this once in terms of some
parameter A parameter (from the Ancient Greek language, Ancient Greek wikt:παρά#Ancient Greek, παρά, ''para'': "beside", "subsidiary"; and wikt:μέτρον#Ancient Greek, μέτρον, ''metron'': "measure"), generally, is any characteristic that ...
(the
radius In classical geometry, a radius 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'', meaning ray but al ...
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 expression, closed form. In Chemistry#Principles of modern chemistry, modern chemistry, a
chemical formula A chemical formula is a way of presenting information about the chemical proportions of atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes ...
is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical chemical symbols, element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O denotes an ozone molecule consisting of three oxygen atoms and a net negative charge. 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 : is an expression of Newton's laws of motion, Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the Tidal movement, movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations. Expression (mathematics), Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be liken to phrases the same way formulas can be liken to Sentence clause structure, grammatical sentences.

# Chemical formulas

A
chemical formula A chemical formula is a way of presenting information about the chemical proportions of atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes ...
identifies each constituent chemical element, element by its chemical symbol, 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 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, 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 molecules, chemical formulas often employ ways to suggest the structure of the molecule. There are several types of these formulas, including molecular formulas and condensed formulas. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for glucose 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 is a drawing that shows the location of each atom, and which atoms it binds to.

# In computing

In computing, a formula typically describes a calculation, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer Instruction (computer science), instruction such as. : ''Degrees Celsius'' = (5/9)*(''Degrees Fahrenheit''  - 32) In computer spreadsheet software, a formula indicating how to compute the value of a cell reference, 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.

# Formulas with prescribed units

A physical quantity can be expressed as the product of a number and a Units of measurement, physical unit, while a formula expresses a relationship between physical quantities. A necessary condition for a formula to be valid is the requirement that all terms Dimensional analysis#Commensurability, have the same dimension, meaning that every term in the formula could be potentially converted to contain the identical unit (or product of identical units). For example, in the case of the volume of a sphere ($\textstyle$), one may wish to compute the volume when $r= 2.0\text$, yielding that: :$V = \frac\pi\left(2.0 \mbox\right)^3 \approx 33.51 \mbox^.$ There is a vast amount of educational training about retaining units in computations, and converting units to a desirable form (such as the case of units conversion by factor-label). In most likelihood, the vast majority of computations with measurements are done in computer programs, with no facility for retaining a symbolic computation of the units. Only the numerical quantity is used in the computation, which requires the universal formula to be converted to a formula intended to be used with prescribed units only (i.e., the numerical quantity is implicitly assumed to be multiplying a particular unit). The requirements about the prescribed units must be given to users of the input and the output of the formula. For example, suppose that the aforementioned formula of the sphere's volume is to require that $V \equiv \mathrm~\mathbf$ (where $\mathbf$ is the Tablespoon#Traditional definitions, US tablespoon and $\mathrm$ is the name for the number used by the computer) and that $r \equiv \mathrm~\mathbf$, then the derivation of the formula would become: : $\mathrm~\mathbf = \frac \pi \mathrm^3~ \mathbf^3.$ In particular, given that $1~\mathbf = 14.787~\mathbf^3$, the formula with prescribed units would become : $\mathrm \approx 0.2833~\mathrm^3.$ Here, the formula is not complete without words such as: "$\mathrm$ is volume in $\mathbf$ and $\mathrm$ is radius in $\mathrm$". Other possible words are "$\mathrm$ is the ratio of $V$ to $\mathbf$ and $\mathrm$ is the ratio of $r$ to $\mathrm$." The formula with prescribed units could also appear with simple symbols, perhaps even with identical symbols as in the original dimensional formula: : $V = 0.2833~r^3.$ and the accompanying words could be: "where $V$ is volume ($\mathbf$) and $r$ is radius ($\mathrm$)". If the physical formula is not dimensionally homogeneous, it would be erroneous. In fact, the falsehood becomes apparent in the impossibility to derive a formula with prescribed units, as it would not be possible to derive a formula consisting only of numbers and dimensionless ratios.

## In science

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 ''S'' of an ideal gas to the quantity ''W'', which is the number of Microstate (statistical mechanics), microstates corresponding to a given macrostate: :$S = k \cdot \log W$           (1) S= k ln W where ''k'' is Boltzmann constant, Boltzmann's constant equal to 1.38062 x 10−23 joule/kelvin, and ''W'' is the number of Microstate (statistical mechanics), microstates consistent with the given macrostate.