In
industrial design
Industrial design is a process of design applied to physical Product (business), products that are to be manufactured by mass production. It is the creative act of determining and defining a product's form and features, which takes place in advan ...
, preferred numbers (also called preferred values or preferred series) are standard
guideline
A guideline is a statement by which to determine a course of action. A guideline aims to streamline particular processes according to a set routine or sound practice. Guidelines may be issued by and used by any organization (governmental or pri ...
s for choosing exact product dimensions within a given set of constraints.
Product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic
quantities
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit ...
. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the ''exact'' choice for many dimensions.
Preferred numbers serve two purposes:
# Using them increases the probability of compatibility between objects designed at different times by different people. In other words, it is one tactic among many in
standardization
Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments. Standardization ...
, whether within a company or within an industry, and it is usually desirable in industrial contexts (unless the goal is
vendor lock-in
In economics, vendor lock-in, also known as proprietary lock-in or customer lock-in, makes a customer dependent on a vendor for products, unable to use another vendor without substantial switching costs.
The use of open standards and alternative ...
or
planned obsolescence
In economics and industrial design, planned obsolescence (also called built-in obsolescence or premature obsolescence) is a policy of planning or designing a product with an artificially limited useful life or a purposely frail design, so that ...
)
# They are chosen such that when a product is manufactured in many different sizes, these will end up roughly equally spaced on a
logarithmic scale
A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
. They therefore help to minimize the number of different sizes that need to be manufactured or kept in stock.
Preferred numbers represent preferences of simple numbers (such as 1, 2, and 5) multiplied by the powers of a convenient basis, usually 10.
Renard numbers
In 1870
Charles Renard
Charles Renard (1847–1905) born in Damblain, Vosges, was a French military engineer.
Airships
After the Franco-Prussian War of 1870-1871 he started work on the design of airships at the French army aeronautical department. Together with A ...
proposed a set of preferred numbers.
His system was adopted in 1952 as international standard
ISO 3
ISO is the most common abbreviation for the International Organization for Standardization.
ISO or Iso may also refer to: Business and finance
* Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007
* Iso ...
.
Renard's system divides the interval from 1 to 10 into 5, 10, 20, or 40 steps, leading to the R5, R10, R20 and R40 scales, respectively. The factor between two consecutive numbers in a
Renard series
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in ...
is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a
geometric sequence
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ''common ratio''. For ex ...
. This way, the maximum
relative error
The approximation error in a data value is the discrepancy between an exact value and some ''approximation'' to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute er ...
is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. Example: 1.0, 1.6, 2.5, 4.0, 6.3
E series
The E series is another system of preferred numbers. It consists of the
E1,
E3,
E6,
E12,
E24,
E48,
E96 and
E192 series. Based on some of the existing manufacturing conventions, the
International Electrotechnical Commission
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
(IEC) began work on a new international standard in 1948.
The first version of this
IEC 63
The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
(renamed into
IEC 60063
The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
in 2007) was released in 1952.
It works similarly to the Renard series, except that it subdivides the interval from 1 to 10 into 3, 6, 12, 24, 48, 96 or 192 steps. These subdivisions ensure that when some arbitrary value is replaced with the nearest preferred number, the maximum relative error will be on the order of 40%, 20%, 10%, 5%, etc.
Use of the E series is mostly restricted to
electronic parts like resistors, capacitors, inductors and Zener diodes. Commonly produced dimensions for other types of electrical components are either chosen from the Renard series instead or are defined in relevant product standards (for example
wires).
1–2–5 series
In applications for which the R5 series provides a too fine graduation, the 1–2–5 series
is sometimes used as a cruder alternative. It is effectively an E3 series rounded to one significant digit:
:… 0.1 0.2 0.5 1 2 5 10 20 50 100 200 500 1000 …
This series covers a
decade
A decade () is a period of ten years. Decades may describe any ten-year period, such as those of a person's life, or refer to specific groupings of calendar years.
Usage
Any period of ten years is a "decade". For example, the statement that "du ...
(1:10 ratio) in three steps. Adjacent values differ by factors 2 or 2.5. Unlike the Renard series, the 1–2–5 series has not been formally adopted as an
international standard
international standard is a technical standard developed by one or more international standards organizations. International standards are available for consideration and use worldwide. The most prominent such organization is the International Or ...
. However, the Renard series R10 can be used to extend the 1–2–5 series to a finer graduation.
This series is used to define the scales for graphs and for instruments that display in a two-dimensional form with a graticule, such as
oscilloscopes
An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
.
The
denominations of most modern
currencies
A currency, "in circulation", from la, currens, -entis, literally meaning "running" or "traversing" is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins.
A more general def ...
, notably the
euro
The euro ( symbol: €; code: EUR) is the official currency of 19 out of the member states of the European Union (EU). This group of states is known as the eurozone or, officially, the euro area, and includes about 340 million citizens . ...
and
sterling, follow a 1–2–5 series. The United States and Canada follow the approximate 1–2–5 series 1, 5, 10, 25, 50, 100 (cents), $1, $2, $5, $10, $20, $50, $100. The ––1 series (... 0.1 0.25 0.5 1 2.5 5 10 ...) is also used by currencies derived from the former
Dutch gulden
The guilder ( nl, gulden, ) or florin was the currency of the Netherlands from the 15th century until 2002, when it was replaced by the euro.
The Dutch name ''gulden'' was a Middle Dutch adjective meaning "golden", and reflects the fact that, wh ...
(
Aruban florin
The florin (; sign: Afl.; code: AWG) or Aruban guilder is the currency of Aruba. It is subdivided into 100 cents. The florin was introduced in 1986, replacing the Netherlands Antillean guilder at par. The Aruban florin is pegged to the United Stat ...
,
Netherlands Antillean gulden
The Netherlands Antillean guilder ( nl, gulden) is the currency of Curaçao and Sint Maarten, which until 2010 formed the Netherlands Antilles along with Bonaire, Saba (island), Saba, and Sint Eustatius. It is subdivided into 100 ''cents'' (Dutch ...
,
Surinamese dollar
The Surinamese dollar (ISO 4217 code ''SRD'') has been the currency of Suriname since 2004. It is divided into 100 '' cent''. The Surinamese dollar is normally abbreviated with the dollar sign ''$'', or alternatively ''Sr$'' to distinguish it fro ...
), some Middle Eastern currencies (
Iraqi and
Jordanian dinars,
Lebanese pound
The pound or lira ( ar, ليرة لبنانية ''līra Libnāniyya''; French: ''livre libanaise''; abbreviation: LL in Latin, in Arabic, historically also £L, ISO code: LBP) is the currency of Lebanon. It was formerly divided into 100 piast ...
,
Syrian pound
The Syrian pound or lira ( ar, الليرة السورية, al-līra as-sūriyya; abbreviation: LS or SP in Latin, ل.س in Arabic, historically also £S, and £Syr; ISO code: SYP) is the currency of Syria. It is issued by the Central Bank o ...
), and the
Seychellois rupee
The rupee is the currency of the Seychelles. It is subdivided into 100 ''cents''. In the local Seychellois Creole (Seselwa) language, it is called the ''roupi'' and roupie in French. The ISO code is SCR. The abbreviation SR is sometimes used for ...
. However, newer notes introduced in Lebanon and Syria due to inflation follow the standard 1–2–5 series instead.
Convenient numbers
In the 1970s the
National Bureau of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NBS) defined a set of convenient numbers to ease
metrication in the United States
Metrication (or metrification) is the process of introducing the International System of Units, also known as SI units or the metric system, to replace a jurisdiction's traditional measuring units. U.S. customary units have been defined in t ...
. This system of metric values was described as
1–2–5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10), excluding linear dimensions above 100 mm.
Audio frequencies
ISO 266, Acoustics—Preferred frequencies, defines two different series of audio frequencies for use in acoustical measurements. Both series are referred to the standard reference frequency of 1000 Hz, and use the R10
Renard series
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in ...
from ISO 3, with one using powers of 10, and the other related to the definition of the octave as the frequency ratio 1:2.
For example, a set of nominal center frequencies for use in audio tests and audio test equipment is:
Computer engineering
When dimensioning computer components, the powers of two are frequently used as preferred numbers:
1 2 4 8 16 32 64 128 256 512 1024 ...
Where a finer grading is needed, additional preferred numbers are obtained by multiplying a power of two with a small odd integer:
1 2 4 8 16 32 64 128 256 512 1024 ...
(×3) 3 6 12 24 48 96 192 384 768 1536 3072 ...
(×5) 5 10 20 40 80 160 320 640 1280 2560 5120 ...
(×7) 7 14 28 56 112 224 448 896 1792 3584 7168 ...
In
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
, widths and heights of
raster images
upright=1, The Smiley, smiley face in the top left corner is a raster image. When enlarged, individual pixels appear as squares. Enlarging further, each pixel can be analyzed, with their colors constructed through combination of the values for ...
are preferred to be multiples of 16, as many compression algorithms (
JPEG
JPEG ( ) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable tradeoff between storage size and imag ...
,
MPEG
The Moving Picture Experts Group (MPEG) is an alliance of working groups established jointly by International Organization for Standardization, ISO and International Electrotechnical Commission, IEC that sets standards for media coding, includ ...
) divide ''color'' images into square blocks of that size. Black-and-white JPEG images are divided into 8×8 blocks. Screen resolutions often follow the same principle.
Preferred
aspect ratios have also an important influence here, e.g., 2:1, 3:2, 4:3, 5:3, 5:4, 8:5, 16:9.
Paper documents, envelopes, and drawing pens
Standard metric paper sizes use the
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
E ...
of two () as factors between neighbouring dimensions rounded to the nearest mm (
Lichtenberg
Lichtenberg () is the eleventh borough of Berlin, Germany. In Berlin's 2001 administrative reform it absorbed the former borough of Hohenschönhausen.
Overview
The district contains the Tierpark Berlin in Friedrichsfelde, the larger of Berlin's ...
series,
ISO 216
ISO 216 is an international standard for paper sizes, used around the world except in North America and parts of Latin America. The standard defines the "A", "B" and "C" series of paper sizes, including A4, the most commonly available paper size ...
). An A4 sheet for example has an aspect ratio very close to and an area very close to 1/16 square metre. An A5 is almost exactly half an A4, and has the same aspect ratio. The factor also appears between the standard pen thicknesses for technical drawings in ISO 9175-1: 0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.00, 1.40, and 2.00 mm. This way, the right pen size is available to continue a drawing that has been magnified to a different standard paper size.
Photography
In photography, aperture, exposure, and film speed generally follow powers of 2:
The aperture size controls how much light enters the camera. It is measured in
f-stop
In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill ...
s: , , , , etc. Full f-stops are a
square root of 2
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princip ...
apart. Camera lens settings are often set to gaps of successive thirds, so each f-stop is a sixth root of 2, rounded to two significant digits: 1.0, 1.1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.5, 4.0, etc. The spacing is referred to as "one-third of a stop".
The
film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system. A closely related ISO system is used to describe the relations ...
is a measure of the film's sensitivity to light. It is expressed as ISO values such as "ISO 100". An earlier standard, occasionally still in use, uses the term "ASA" rather than "ISO", referring to the (former) American Standards Association. Measured film speeds are rounded to the nearest preferred number from a modified Renard series including 100, 125, 160, 200, 250, 320, 400, 500, 640, 800... This is the same as the R10′ rounded
Renard series
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in ...
, except for the use of 6.4 instead of 6.3, and for having more aggressive rounding below ISO 16. Film marketed to amateurs, however, uses a restricted series including only powers of two multiples of ISO 100: 25, 50, 100, 200, 400, 800, 1600 and 3200. Some low-end cameras can only reliably read these values from
DX encoded film cartridges because they lack the extra electrical contacts that would be needed to read the complete series. Some digital cameras extend this binary series to values like 12800, 25600, etc. instead of the modified Renard values 12500, 25000, etc.
The
shutter speed
In photography, shutter speed or exposure time is the length of time that the film or digital sensor inside the camera is exposed to light (that is, when the camera's shutter (photography), shutter is open) when taking a photograph.
The am ...
controls how long the camera lens is open to receive light. These are expressed as fractions of a second, roughly but not exactly based on powers of 2: 1 second, , , , , , , , , , of a second.
Retail packaging
In some countries, consumer-protection laws restrict the number of different prepackaged sizes in which certain products can be sold, in order to make it easier for consumers to compare prices.
An example of such a regulation is the European Union directive on the volume of certain prepackaged liquids (75/106/EEC
). It restricts the list of allowed wine-bottle sizes to 0.1, 0.25 (), 0.375 (), 0.5 (), 0.75 (), 1, 1.5, 2, 3, and 5 litres. Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors or , in some cases even , , or some other ratio of two small integers.
See also
*
Convenient number
A convenient number is a number which in several situations can prove convenient for use by humans for counting and measuring, and is related to preferred numbers (which are standard recommendations used for choosing product dimensions).
The conv ...
*
Nominal impedance
Nominal impedance in electrical engineering and audio engineering refers to the approximate designed impedance of an electrical circuit or device. The term is applied in a number of different fields, most often being encountered in respect of:
...
*
Nominal size
The distinction between real value and nominal value occurs in many fields. From a philosophical viewpoint, nominal value represents an accepted condition, which is a goal or an approximation, as opposed to the real value, which is always present. ...
*
Preferred metric sizes
Preferred metric sizes are a set of international standards and de facto standards that are designed to make using the metric system easier and simpler, especially in engineering and construction practices. One of the methods used to arrive at thes ...
References
Further reading
*
https://web.archive.org/web/20171102005125/https://www.forgottenbooks.com/en/download/SizeStandardizationbyPreferredNumbers_10296778.pdf -->*
*
* (NB. This 1943 publication already shows a list of new "preferred values of resistance" following what was adopted by the
IEC
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
for standardization since 1948 and standardized as the
E series of preferred numbers
The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
in IEC 63:1952. For comparison, it also lists "old standard resistance values" as follows: 50, 75, 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 750, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 1 Meg, 1.5 Meg, 2.0 Meg, 3.0 Meg, 4.0 Meg, 5.0 Meg, 6.0 Meg, 7.0 Meg, 8.0 Meg, 9.0 Meg, 10.00 Meg.)
* (NB. Shows a list of "old standard resistance values" vs. new "preferred values of resistance" following the later standardized
E series of preferred numbers
The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
.)
*
* (Replaced: (1955) and )
* (Replaced: )
* (9 pages) (Replaced: Reaffirmed as USASI Z17.1-1958 in 1966 and named ANSI Z17.1-1958 since 1969.)
*
* (340 pages)
*
*
* (135 pages)
* (191 pages)
*
*
* {{cite book , author-first=Wilhelm , author-last=Strahringer , title=Zauberwelt der Normzahlen , language=de , trans-title=Magic world of preferred numbers , publisher=Verlags- und Wirtschaftsgesellschaft der Elektrizitätswerke m.b.H. (VWEW) , location=Frankfurt a. Main, Germany , date=1952 (95 pages)
Numbers
Industrial design
Logarithmic scales of measurement