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 E series for resistors, capacitors, inductors, and zener diodes. Other types of electrical components are either specified by the Renard series (for example fuses) or are defined in relevant product standards (for example 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 numerous 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 radio manufacturers to license and share patents. Over time, 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 from older values to the 1936 resistance value standard.

During World War II (1940s), American and British military production was a major influence for establishing common standards across many industries, especially in electronics, where it was essential to produce large quantities of standardized electronic parts for military devices, such as wireless communications, radars, radar jammers, LORAN navigation, and more.

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

After being worked on by the RMA, the International Electrotechnical Commission (IEC) began work on an international standard in 1948. The first version of this IEC Publication 63 (IEC 63) was released in 1952. Later, IEC 63 was revised, amended, and renamed into the current version known as IEC 60063:2015.

IEC 60063 release history:
 * IEC 63:1952 (aka IEC 60063:1952), first edition, published 1952-01-01.
 * IEC 63:1963 (aka IEC 60063:1963), second edition, published 1963-01-01.
 * IEC 63:1967/AMD1:1967 (aka IEC 60063:1967/AMD1:1967), first amendment of second edition, published 1967.
 * IEC 63:1977/AMD2:1977 (aka IEC 60063:1977/AMD2:1977), second amendment of second edition, published 1977.
 * IEC 60063:2015, third edition, published 2015-03-27.

Overview
The E series 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 E series subdivides each decade magnitude into steps of 3, 6, 12, 24, 48, 96, 192 values. Subdivisions of E3 to E192 ensure the maximum error will be divided in the order of 40%, 20%, 10%, 5%, 2%, 1%, 0.5%. Also, the E192 series is used for 0.25% and 0.1% tolerance resistors.

Historically, the E series 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 unfortunately the calculated values don't match the official values of all E series.

$$V_n = \mathrm{round} (\sqrt[m]{10^n})$$


 * where:
 * $$V_n$$ is rounded to 2 significant figures (E3, E6, E12, E24) or 3 significant figures (E48, E96, E192),
 * $$m$$ is an integer of the E series group size (3, 6, 12, 24, 48, 96, 192),
 * $$n$$ is an integer of $$\{0, 1, ..., m-1\} .$$


 * 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 don't match their calculated values (see subsets sections below).

E24 subsets
For E3 / E6 / E12 / E24, the values from the formula are rounded to 2 significant figures, but eight official values (shown in bold & 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 it wasn't practical to change some of the former established historical values. The first standard was accepted in Paris in 1950, then published as IEC 63 in 1952. The official values of the E3 / E6 / E12 series are subsets of the following official E24 values.


 * {| class="wikitable" style="text-align: center;"

! $$n = \{0, ..., 23\}$$ || 0 || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || 17 || 18 || 19 || 20 || 21 || 22 || 23
 * +Comparison of rounded log-scaled values and official values of E24 series ($$m = 24$$)
 * Calculated $$V_n$$ values || 1.0 || 1.1 || 1.2 || 1.3 || 1.5 || 1.6 || 1.8 || 2.0 || 2.2 || 2.4 || 2.6 || 2.9 || 3.2 || 3.5 || 3.8 || 4.2 || 4.6 || 5.1 || 5.6 || 6.2 || 6.8 || 7.5 || 8.3 || 9.1
 * Official E24 values || 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
 * }
 * Official E24 values || 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
 * }

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 $+80% −20%$, or for components with uncritical values such as pull-up resistors. The calculated constant tangential tolerance for this series gives ($\sqrt{10|3}$ − 1) ÷ ($\sqrt{10|3}$ + 1) = 36.60%, approximately. 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, thus E3 series is mostly obsolete.

E192 subsets
For E48 / E96 / 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: $$m$$ is 48, then $$n$$ is incremented from 0 to 47 through the formula. All official values of E48 series match their calculated values.
 * To calculate the E96 series: $$m$$ is 96, then $$n$$ is incremented from 0 to 95 through the formula. All official values of E96 series match their calculated values.
 * To calculate the E192 series: $$m$$ is 192, then $$n$$ is incremented from 0 to 191 through the formula, with one exception for $$n=185$$ 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 / E192 series, some resistor manufacturers have added missing E24 values into of their 1%, 0.5%, 0.25%, 0.1% tolerance resistor families. This allows easier purchasing migration between various tolerances. This E series merging is noted on resistor datasheets and webpages as "E96 + E24" or "E192 + E24". In the following table, the dashed E24 values don't exist in E48 / E96 / E192 series:


 * {| class="wikitable" style="text-align: center;"

! E24 values || 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
 * +E24 values that exist in E48 / E96 / E192 series
 * E48 values || 1.00 || 1.10 || – || – || – || – || – || – || – || – || – || – || – || – || – || – || – || – || – || – || – || 7.50 || – || –
 * E96 values || 1.00 || 1.10 || – || 1.30 || 1.50 || – || – || 2.00 || – || – || – || – || – || – || – || – || – || – || – || – || – || 7.50 || – || –
 * E192 values || 1.00 || 1.10 || 1.20 || 1.30 || 1.50 || 1.60 || 1.80 || 2.00 || – || 2.40 || – || – || – || – || – || – || 4.70 || – || – || – || – || 7.50 || – || –
 * }
 * E192 values || 1.00 || 1.10 || 1.20 || 1.30 || 1.50 || 1.60 || 1.80 || 2.00 || – || 2.40 || – || – || – || – || – || – || 4.70 || – || – || – || – || 7.50 || – || –
 * }
 * }

Examples
If a manufacturer sold resistors with all values in a range of 1 ohm to 10 megaohms, the available resistance values for E3 through E12 would be:
 * {| class="wikitable"

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

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

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

Lists
List of official values for each E series:


 * 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