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 logarithmic value "steps" per decade. Although it is theoretically possible to produce components of any value, in practice the need for inventory simplification has led the industry to settle on the Eseries for resistors, capacitors, inductors, and zener diodes. Other types of electrical components, such as fuses, are either specified by the Renard series or are defined in relevant product standards, such as IEC 60228 for wires.

History

During the Golden Age of Radio (1920s to 1950s), numerous companies manufactured vacuum-tube–based AM radio receivers for consumer use. In the early years, many components were not standardized between AM radio manufacturers. The capacitance values of capacitors (previously called condensers) and resistance values of resistors were not standardized as they are today.

In 1924, the Radio Manufacturers Association (RMA) was formed in Chicago, Illinois by 50 AM radio manufacturers to license and share patents. This group created some of the earliest standards for electronics components. In 1936, the RMA adopted a preferred-number system for the resistance values of fixed-composition resistors. Over time, resistor manufacturers migrated to the 1936 resistance value standard.

During World War II (1940s), American and British military production was a major influence for establishing numerous standards across many industries, especially in electronics, where it was essential to produce high quantities of standardized electronic components to build military devices, such as wireless communications, radar, jammers, LORAN (radio navigation homing receivers for aircraft), ASDIC (sonar for submarine navigation and detection), test equipment, and more.

During the 1950s, the mid-20th century baby boom and the invention of the transistor kicked off demand for consumer electronics goods. In the late 1950s, portable AM transistor radio manufacturing migrated from United States towards Japan, thus it was critical for the electronic industry to have international standards.

After worked on by the RMA, the International Electrotechnical Commission (IEC) began work on an international standard for preferred values in 1948. The first version of this IEC Publication 63 (IEC63) was released in 1952. Later, IEC63 was revised, amended, and renamed into the current version known as IEC60063:2015.

IEC60063 release history:

• IEC63:1952 (aka IEC60063:1952), first edition, published 1952-01-01.
• IEC63:1963 (aka IEC60063:1963), second edition, published 1963-01-01.
• IEC63:1967/AMD1:1967 (aka IEC60063:1967/AMD1:1967), first amendment of second edition, published 1967.
• IEC63:1977/AMD2:1977 (aka IEC60063:1977/AMD2:1977), second amendment of second edition, published 1977.
• IEC60063:2015, third edition, published 2015-03-27.

Overview

The Eseries of preferred numbers was chosen such that when a component is manufactured it will end up in a range of roughly equally spaced values (geometric progression) on a logarithmic scale. Each Eseries subdivides each decade magnitude into steps of 3, 6, 12, 24, 48, 96, and 192 values, termed E3, E6, and so forth to E192, with maximum errors of 40%, 20%, 10%, 5%, 2%, 1%, and 0.5%, respectively. The E192 series is also used for 0.25% and 0.1% tolerance resistors.

Historically, the Eseries is split into two major groupings:

• E3, E6, E12, E24 are subsets of E24. Values in this group are rounded to 2 significant figures.
• E48, E96, E192 are subsets of E192. Values in this group are rounded to 3 significant figures.

Formula

The formula for each value is determined by the m-th root, but the calculated values do not match the official values of all E series values.

V n = r o u n d ( 10 n m ) {\displaystyle V_{n}=\mathrm {round} ({\sqrt[{m}]{10^{n}}})}

where: V n {\displaystyle V_{n}} is rounded to 2 (E3, E6, E12, E24) or 3 (E48, E96, E192) significant figures, m {\displaystyle m} is an integer of { 3 , 6 , 12 , 24 , 48 , 96 , 192 } , {\displaystyle \{3,6,12,24,48,96,192\},} n {\displaystyle n} is an integer of { 0 , 1 , . . . , m − 1 } . {\displaystyle \{0,1,...,m-1\}.}

exceptions: The official values for E48 and E96 series match their calculated values, but all other series (E3, E6, E12, E24, E192) have one or more official values that do not match their calculated values (see subsets sections below).

E24 subsets

For E3, E6, E12, and E24, the values from the formula are rounded to 2 significant figures, but eight official values (shown in bold and green) are different from the calculated values (shown in red). During the early half of the 20th century, electronic components had different sets of component values than today. In the late 1940s, standards organizations started working towards codifying a standard set of official component values, and they decided that changing some of the former established historical values was not practical. The first standard was accepted in Paris in 1950, then published as IEC63 in 1952. The official values of the E3, E6, and E12 series are subsets of the following official E24 values.

Comparison of rounded log-scaled values and official values of E24 series (m = 24 {\displaystyle m=24}) n = { 0 , . . . , 23 } {\displaystyle n=\{0,...,23\}}01234567891011121314151617181920212223 Calculated V n {\displaystyle V_{n}} values1.01.11.21.31.51.61.82.02.22.42.62.93.23.53.84.24.65.15.66.26.87.58.39.1 Official E24 values1.01.11.21.31.51.61.82.02.22.42.73.03.33.63.94.34.75.15.66.26.87.58.29.1

The E3 series is rarely used, except for some components with high variations like electrolytic capacitors, where the given tolerance is often unbalanced between negative and positive such as +50% −30% or +80% −20%. The calculated constant tangential tolerance for this series gives 10 3 − 1 10 3 + 1 = 36.597 % {\displaystyle \textstyle {\frac {{\sqrt[{3}]{10}}-1}{{\sqrt[{3}]{10}}+1}}=36.597\%}. While the standard only specifies a tolerance greater than 20%, other sources indicate 40% or 50%. Currently, most electrolytic capacitors are manufactured with values in the E6 or E12 series, so the E3 series is mostly obsolete except as the foundation for the other Eseries numbers.

E192 subsets

For E48, E96, and E192, the values from the formula are rounded to 3 significant figures, but one value (shown in bold) is different from the calculated values.

• To calculate the E48 series: m {\displaystyle m} is 48, then n {\displaystyle n} is incremented from 0 to 47 through the formula. All official values of E48 series match their calculated values.
• To calculate the E96 series: m {\displaystyle m} is 96, then n {\displaystyle n} is incremented from 0 to 95 through the formula. All official values of E96 series match their calculated values.
• To calculate the E192 series: m {\displaystyle m} is 192, then n {\displaystyle n} is incremented from 0 to 191 through the formula, with one exception for n = 185 {\displaystyle n=185} where 9.20 is the official value instead of the calculated 9.19 value.

Since some values of the E24 series do not exist in the E48, E96, or E192 series, some resistor manufacturers produce E24-valued resistors in 1%, 0.5%, 0.25%, and 0.1% tolerance. This allows easier purchasing migration between various tolerances. This Eseries merging is noted on resistor datasheets and webpages as "E96+E24" or "E192+E24". In the following table, the red cells denote E24 values that don't exist in the E48, E96, or E192 series, and indicate the closest value or values that do instead.

E24 values that exist in E48, E96, and E192 series E24 values1.01.11.21.31.51.61.82.02.22.42.73.03.33.63.94.34.75.15.66.26.87.58.29.1 E48 values1.001.101.211.27 1.331.471.621.781.962.152.372.743.013.323.653.834.224.645.115.626.196.817.508.259.09 E96 values1.001.101.211.301.501.58 1.621.78 1.822.002.212.37 2.432.673.013.323.573.924.324.755.115.626.196.817.508.259.09 E192 values1.001.101.201.301.501.601.802.002.212.402.713.013.28 3.323.613.88 3.924.324.705.115.626.196.817.508.169.09

Examples

If a manufacturer sold resistors with all values in a range of 1Ω to 1megaohms (MΩ), the available resistance values for E3 through E12 would be:

E3 (in ohms) E6 (in ohms) E12 (in ohms) 1.0, 2.2, 4.7, 10, 22, 47, 100, 220, 470, 1k, 2.2k, 4.7k, 10k, 22k, 47k, 100k, 220k, 470k, 1M, 2.2M, 4.7M, 10M 1.0, 1.5, 2.2, 3.3, 4.7, 6.8, 10, 15, 22, 33, 47, 68, 100, 150, 220, 330, 470, 680, 1k, 1.5k, 2.2k, 3.3k, 4.7k, 6.8k, 10k, 15k, 22k, 33k, 47k, 68k, 100k, 150k, 220k, 330k, 470k, 680k, 1M, 1.5M, 2.2M, 3.3M, 4.7M, 6.8M, 10M 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2, 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820, 1k, 1.2k, 1.5k, 1.8k, 2.2k, 2.7k, 3.3k, 3.9k, 4.7k, 5.6k, 6.8k, 8.2k, 10k, 12k, 15k, 18k, 22k, 27k, 33k, 39k, 47k, 56k, 68k, 82k, 100k, 120k, 150k, 180k, 220k, 270k, 330k, 390k, 470k, 560k, 680k, 820k, 1M, 1.2M, 1.5M, 1.8M, 2.2M, 2.7M, 3.3M, 3.9M, 4.7M, 5.6M, 6.8M, 8.2M, 10M

If a manufacturer sold capacitors with all values in a range of 1pF to 10,000μF, the available capacitance values for E3 and E6 would be:

E3 E6 1.0pF, 2.2pF, 4.7pF, 10pF, 22pF, 47pF, 100pF, 220pF, 470pF, 1nF, 2.2nF, 4.7nF, 10nF, 22nF, 47nF, 100nF, 220nF, 470nF, 1μF, 2.2μF, 4.7μF, 10μF, 22μF, 47μF, 100μF, 220μF, 470μF, 1000μF, 2200μF, 4700μF, 10000μF 1.0pF, 1.5pF, 2.2pF, 3.3pF, 4.7pF, 6.8pF, 10pF, 15pF, 22pF, 33pF, 47pF, 68pF, 100pF, 150pF, 220pF, 330pF, 470pF, 680pF, 1nF, 1.5nF, 2.2nF, 3.3nF, 4.7nF, 6.8nF, 10nF, 15nF, 22nF, 33nF, 47nF, 68nF, 100nF, 150nF, 220nF, 330nF, 470nF, 680nF, 1μF, 1.5μF, 2.2μF, 3.3μF, 4.7μF, 6.8μF, 10μF, 15μF, 22μF, 33μF, 47μF, 68μF, 100μF, 150μF, 220μF, 330μF, 470μF, 680μF, 1000μF, 1500μF, 2200μF, 3300μF, 4700μF, 6800μF, 10000μF

Lists

List of official values for each Eseries:

E3 values

(40% tolerance)

1.0, 2.2, 4.7

E6 values

(20% tolerance)

1.0, 1.5, 2.2, 3.3, 4.7, 6.8

E12 values

(10% tolerance)

1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2

E24 values

(5% tolerance)

1.0, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1

E48 values

(2% tolerance)

1.00, 1.05, 1.10, 1.15, 1.21, 1.27, 1.33, 1.40, 1.47, 1.54, 1.62, 1.69, 1.78, 1.87, 1.96, 2.05, 2.15, 2.26, 2.37, 2.49, 2.61, 2.74, 2.87, 3.01, 3.16, 3.32, 3.48, 3.65, 3.83, 4.02, 4.22, 4.42, 4.64, 4.87, 5.11, 5.36, 5.62, 5.90, 6.19, 6.49, 6.81, 7.15, 7.50, 7.87, 8.25, 8.66, 9.09, 9.53

E96 values

(1% tolerance)

1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76

E192 values

(0.5% and lower tolerance)

1.00, 1.01, 1.02, 1.04, 1.05, 1.06, 1.07, 1.09, 1.10, 1.11, 1.13, 1.14, 1.15, 1.17, 1.18, 1.20, 1.21, 1.23, 1.24, 1.26, 1.27, 1.29, 1.30, 1.32, 1.33, 1.35, 1.37, 1.38, 1.40, 1.42, 1.43, 1.45, 1.47, 1.49, 1.50, 1.52, 1.54, 1.56, 1.58, 1.60, 1.62, 1.64, 1.65, 1.67, 1.69, 1.72, 1.74, 1.76, 1.78, 1.80, 1.82, 1.84, 1.87, 1.89, 1.91, 1.93, 1.96, 1.98, 2.00, 2.03, 2.05, 2.08, 2.10, 2.13, 2.15, 2.18, 2.21, 2.23, 2.26, 2.29, 2.32, 2.34, 2.37, 2.40, 2.43, 2.46, 2.49, 2.52, 2.55, 2.58, 2.61, 2.64, 2.67, 2.71, 2.74, 2.77, 2.80, 2.84, 2.87, 2.91, 2.94, 2.98, 3.01, 3.05, 3.09, 3.12, 3.16, 3.20, 3.24, 3.28, 3.32, 3.36, 3.40, 3.44, 3.48, 3.52, 3.57, 3.61, 3.65, 3.70, 3.74, 3.79, 3.83, 3.88, 3.92, 3.97, 4.02, 4.07, 4.12, 4.17, 4.22, 4.27, 4.32, 4.37, 4.42, 4.48, 4.53, 4.59, 4.64, 4.70, 4.75, 4.81, 4.87, 4.93, 4.99, 5.05, 5.11, 5.17, 5.23, 5.30, 5.36, 5.42, 5.49, 5.56, 5.62, 5.69, 5.76, 5.83, 5.90, 5.97, 6.04, 6.12, 6.19, 6.26, 6.34, 6.42, 6.49, 6.57, 6.65, 6.73, 6.81, 6.90, 6.98, 7.06, 7.15, 7.23, 7.32, 7.41, 7.50, 7.59, 7.68, 7.77, 7.87, 7.96, 8.06, 8.16, 8.25, 8.35, 8.45, 8.56, 8.66, 8.76, 8.87, 8.98, 9.09, 9.20, 9.31, 9.42, 9.53, 9.65, 9.76, 9.88

Table

See also

• Electronic color code–color-code used to indicate the values of axial electronic components, such as resistors, capacitors, inductors, diodes (also see IEC 60062)
• Geometric progression
• Preferred number
• Renard series–used for current rating of electric fuses
• Three-character marking code for resistors–for (E48/)E96 values (see EIA-96 and IEC60062:2016)
• Two-character marking code for capacitors–for (E3/E6/E12/)E24 values (see ANSI/EIA-198-D:1991, ANSI/EIA-198-1-E:1998, ANSI/EIA-198-1-F:2002 and IEC60062:2016/AMD1:2019)
• Reference designator– Location identifier for a circuit component

Notes

External links

• OEIS
• OEIS

Printable Eseries tables

• – Servenger
• – Vishay