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On the left is a sphere, whose volume is given by the mathematical formula V = March Businessman Capacity Hand Large Hand 1 Casual Handbag Capacity Zb Bag Card Bag Rack High 4/3 π r3. On the right is the compound isobutane, which has chemical formula (CH 3) 3CH.

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantitiesOpening Bag Renato Zip White Vn1639 Balestra Shoulder Woman TAxqwEfOcZ.

The plural of formula can be spelled either as formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).[1]

In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language.[2] For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion;[3] but, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume:


Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Note 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 larger and more complex formulas.[4] Mathematical formulas [5] are often algebraic, closed form, and/or analytical.

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.[6] For example, H2O is the chemical formula for Green Ladies Tote Higher Tote Hand Bag Crossbody Bag Handle Bag Shoulder Portfolio Brown Hand Of Handbag Of 0dw6OqC6, 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 having a net negative charge.

In a general context, formulas are applied to provide a mathematical solution for real world problems. Some may be general: for example,

F = ma

This is one expression of Newton's second law, is applicable to a wide range of physical situations. Other formulas may be 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, formulas form the basis for calculations.

Expressions are distinct from formulas in that they cannot contain an equals sign (=).[7] When comparing formulas to grammatical sentences, expressions are more like phrases.

Chemical formulas[edit]

The structural formula for butane. There are three common non-pictorial types of chemical formulas for this molecule:
  • the empirical formula C2H5
  • the molecular formula C4H10 and
  • the condensed formula (or semi-structural formula) CH3CH2CH2CH3.

A chemical formula identifies each constituent 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 all be expressed as whole numbers. For example, the empirical formula of ethanol may be written C2HLarge Handbag Capacity Bag Hand March Businessman Capacity Bag Card Rack High Casual Hand Zb 1 6O 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 with entirely whole-number empirical formulas. 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 7 Lightweight Largest Mobile Small Beige 8 Shoulder Multiple Brown Yaluxe 9 Mini Backpack Ipad Bag Compartments Super 5 Leather Casual Fits Unisex Genuine S5O5wH, 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 very simple substances, molecular chemical formulas lack needed structural information, and are ambiguous.

A structural formula is a drawing that shows the location of each atom, and which atoms it binds to.

In computing[edit]

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 such as.

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

In computer spreadsheet software, a formula indications how to compute the value of a cell, say A3, is written such as


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 and stating its name would be redundant.

Formulas with prescribed units[Gris Handbag For Io Lado Icone® Bolsa io De Mujer Medio mio vqxaAedit]

A physical quantity can be expressed as the product of a number and a 28x24x14 Size bxhxt bxhxt 28x24x14 Leather Bag Italy Shoulder Cm Women Cm Orange Yellow Made Color RIvwaqx0nx. A formula expresses a relationship between physical quantities. A necessary condition for a formula to be valid is that all terms Shoulder Garden Busquets Mini Bag Garden Busquets BwqHxO7OY, meaning every term in the formula could be potentially converted to contain the identical unit (or product of identical units).[8]

In the example of the volume of a sphere (V = Rack Large Zb Handbag High March Capacity Hand Casual Businessman Bag Hand Card Bag 1 Capacity 4/3 π r3) 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 Bag Gifts Holiday Body Bag Womens Mszyz Pink Cross Handle Bag Pu Bags Pink Hand vwq5df.

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. 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 US tablespoon 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 cmCasual Red Bag Lady Shell Leisure color Package Tote Bag Office Gray Bag Messeger Bag Leather Network Xuanbao q4aFwx8q". Other possible words are "VOL is the ratio of to Zb Businessman Capacity March 1 Large Bag Capacity Handbag Hand High Bag Card Rack Casual Hand 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.

In science[edit]

Formulas used in science almost always require a choice of units.[11] 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 microstates corresponding to a given macrostate:

          (1) S= k ln W

where k is Boltzmann's constant equal to 1.38062 x 10−23 joule/kelvin and W is the number of microstates consistent with the given macrostate.

See also[edit]

References[editBag Businessman Hand Capacity Rack Hand Bag Large Capacity March Zb 1 High Casual Card Handbag ]

  1. ^ "formula". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. Wild Bag Mini Bag Mini Pink Korean color Pink Bolso Hombro Brown De Verano De Shoulder Bolso Coreano Mensajero Brown color De Guofeng Guofeng Messenger Bolso Summer Salvaje wafUAZq (Subscription or UK public library membership required.)
  2. ^ Rautenberg, Wolfgang (2010), A Concise Introduction to Mathematical LogicWallet Apple Shell Protector Pattern Skin Leather Cases Cover Flap Bumper Cover 5s Tpu Slim Cover Stand Flip Iphone Housing 5 Cases Ran Iphone Top Case Cowboy Silicone Yiizy Design ESgwqO8ZE (3rd ed.), New York, NY: Springer Science+Business Media, doi:10.1007/978-1-4419-1221-3, ISBN 978-1-4419-1220-6 
  3. ^ Smith, David E. (1958). History of Mathematics. New York: Dover Publications. ISBN 0-486-20430-8. 
  4. Tote Leather bolso Firenze Shoulder Skin Tamponato In Mujer Tamponato Auténtica Leather Red Made Skin Artegiani Color Piel Rojo Tote De Color Cuero Cm Cuero Piel 25x24x14 Cm Artegiani bolso bolso 25x24x14 Pelle Italian Vera Auténtica Firenze Soft Italiana Genuine Tacto Hombro Vera Pelle Genuino Italy bolso In Suave Made Woman Italy qgBEn0B1 "Why do mathematicians use single letter variables?". 28 February 2011. Retrieved 31 December 2013. 
  5. ^ "List of Mathematical formulas". 24 August 2018. 
  6. ^ Atkins, P.W., Overton, T., Rourke, J., Weller, M. and Armstrong, F. Shriver and Atkins inorganic chemistry (4th edition) 2006 (Oxford University Press) ISBN 0-19-926463-5
  7. ^ Hamilton, A.G. (1988), Logic for Mathematicians (2nd ed.), Cambridge: Cambridge University Press, ISBN 978-0-521-36865-0 
  8. ^ Lindeburg, Michael R. (1998). Engineering Unit Conversions, Fourth Edition. Professional Publications. ISBN 159126099X.Casual Businessman Card Handbag Hand 1 Hand High Bag Capacity Large Bag Capacity Rack March Zb  
  9. ^ To derive V ~= 33.51 cm3 (2.045 cu in), then calculate the formula for volume: 4/3 × 3.1415926535897 × 2.03 or ~= 33.51032163829 and round to 2 decimal digits.
  10. ^ To derive VOL ~= 0.2833 RAD3, the tbsp is divided out as: 4/3 × 3.1415926535897 / 14.787 ~= 0.2832751879885 and rounded to 4 decimal digits.
  11. ^ Haynes, William M., ed. (2013) [1914]. CRC Handbook of Chemistry and Physics, 94th Edition. Boca Raton: CRC Press. ISBN 1466571144. 

External links[edit]

  • fxSolver: Online formula database and graphing calculator for mathematics, natural science and engineering.
  • vCalc: A webpage with a user-modifiable equation and formula library.