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Formula
 
 
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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 and in the science
Science

In its broadest sense, science refers to any systematic knowledge or practice. In its more usual restricted sense, science refers to a system of acquiring knowledge based on scientific method, as well as to the organized body of knowledge gained through such research....
s, a formula (plural: formulae, formulę or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula
Chemical formula

A chemical formula is a way of expressing information about the atoms that constitute a particular chemical compound, and how the relationship between those atoms changes in chemical reactions....
), or a general relationship between quantities. One of many famous formulae is Albert Einstein
Albert Einstein

Albert Einstein was a Germany-born theoretical physics. He is best known for his theory of relativity and specifically mass?energy equivalence, expressed by the equation E = mc2....
's E = mc² (see special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
).

In mathematics, a formula is a key to solve an equation
Equation

An equation is a mathematics Proposition, in table of mathematical symbols, that two things are exactly the same . Equations are written with an equal sign, as in...
 with variables. For example, the problem of determining the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 of a sphere
Sphere

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface....
 is one that requires a significant amount of integral calculus to solve.






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In mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 and in the science
Science

In its broadest sense, science refers to any systematic knowledge or practice. In its more usual restricted sense, science refers to a system of acquiring knowledge based on scientific method, as well as to the organized body of knowledge gained through such research....
s, a formula (plural: formulae, formulę or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula
Chemical formula

A chemical formula is a way of expressing information about the atoms that constitute a particular chemical compound, and how the relationship between those atoms changes in chemical reactions....
), or a general relationship between quantities. One of many famous formulae is Albert Einstein
Albert Einstein

Albert Einstein was a Germany-born theoretical physics. He is best known for his theory of relativity and specifically mass?energy equivalence, expressed by the equation E = mc2....
's E = mc² (see special relativity
Special relativity

Special relativity is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "Annus Mirabilis Papers#Special relativity"....
).

In mathematics, a formula is a key to solve an equation
Equation

An equation is a mathematics Proposition, in table of mathematical symbols, that two things are exactly the same . Equations are written with an equal sign, as in...
 with variables. For example, the problem of determining the volume
Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
 of a sphere
Sphere

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface....
 is one that requires a significant amount of integral calculus to solve. However, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
 for example). This particular formula is:



Having determined this result, and having a sphere of which we know the radius we can quickly and easily determine the volume. Note that the quantities , the volume, and 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.

In general mathematical use there is no essential difference in meaning with the term "expression
Expression (mathematics)

In mathematics, the word expression is a term for any well-formed formula combination of mathematical symbols. For example,is an expression, while...
", although the word "formula" tends to be reserved for an expression that "can stand on its own", that has a meaning outside of the immediate context in which it appears and a significance that can be grasped intuitively.

The majority of all mathematical study revolves around formulae in many different forms from quadratic equations to the equations of motion (mainly used in mechanical mathematics and physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
). In a general context, formulae are applied to provide a mathematical solution for real world problems. Some may be general formulae designed to explain a phenomenon experienced everywhere - an example is force = mass × acceleration. It is a formula which applies anywhere in the universe. 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.

In computing


In computing
Computing

Computing is usually defined as the activity of using and developing computer technology, computer hardware and computer software. It is the computer-specific part of information technology....
, a formula typically describes a calculation
Calculation

A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.The term is used in a variety of senses, from the very definite arithmetical calculation using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful rela...
, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer
Computer

A computer is a machine that manipulates Data according to a list of Code .The first devices that resemble modern computers date to the mid-20th century , although the computer concept and various machines similar to computers existed earlier....
 instruction
Instruction

Instruction may refer to:* Education, the teaching and learning of knowledge* Teaching, a form of instruction* Sebayt, a work of the ancient Egyptian didactic literature aiming to teach ethical behaviour...
 such as

Total fruit = number of Apples + number of Oranges.


Degrees Celsius = (5/9)*(Degrees Fahrenheit -32)


In computer spreadsheet
Spreadsheet

A spreadsheet is a computer application that simulates a paper worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing either alphanumeric text or numeric values....
 terminology, a formula is usually a text string containing cell references, e.g.

=A1+A2


where both A1 and A2 describe "cells" (column A, row 1 or 2) within the spreadsheet. The result appears within the cell containing the formula itself (possibly A3, at end of values in column A). The = sign precedes the right hand side of the formula indicating the cell contains a formula rather than data. The left hand side of the formula is, by convention, omitted because the result is always stored in the cell itself and would be redundant.

Formula with prescribed units


A physical quantity
Physical quantity

A physical quantity is a physical property that can be Quantitative. This means it can be measured and/or calculated and expressed in numbers. For example, "weight" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as pound or kilograms, while "beauty" is a property that is difficult to desc...
 can be expressed as the product of a number and a physical unit
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
. A formula expresses a relationship between physical quantities. A necessary condition for a formula to be valid is that all terms have the same dimension, meaning every term in the formula could be potentially converted to contain the identical unit (or product of identical units).

In the example above, for the volume of a sphere, we may wish to compute with r =2.0 cm, which yields



There is vast educational training about retaining units in computations, and converting units to a desirable form, such as in units conversion by factor-label
Units conversion by factor-label

Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m?, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb....
.

However, the vast majority of computations with measurements is done in computer programs with no facility for retaining a symbolic computation of the units. Only the numerical quantity is used in the computation. This requires that the universal formula be converted to a formula that is intended to be used only with prescribed units, meaning 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 the formula is to require that , where tbsp is the U.S. tablespoon (as seen in conversion of units
Conversion of units

Conversion of units refers to conversion factors between different units of measurement for the same quantity....
) and VOL is the name for the number used by the computer. Similarly, the formula is to require . The derivation of the formula proceeds as:



Given that , the formula with prescribed units is



The formula is not complete without words such as: "VOL is volume in tbsp and RAD is radius in cm". Other possible words are "VOL is the ratio of to tbsp and RAD is the ratio of to cm."

The formula with prescribed units could also appear with simple symbols, perhaps even the identical symbols as in the original dimensional formula:
and the accompanying words could be: "where V is volume (tbsp) and r is radius (cm)".

If the physical formula is not dimensionally homogeneous, and therefore erroneous, the falsehood becomes apparent in the impossibility to derive a formula with prescribed units. It would not be possible to derive a formula consisting only of numbers and dimensionless ratios.

See also

  • Mathematical notation
    Mathematical notation

    A mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics and the physical sciences, engineering and economics....
  • Formula (mathematical logic)
  • Spreadsheet
    Spreadsheet

    A spreadsheet is a computer application that simulates a paper worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing either alphanumeric text or numeric values....