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This graph shows how almost any value between 1 and 10 is within ±10% of an E12 series value, and its difference from the ideal value in a geometric sequence.
Two decades of E12 values, which would give resistor values of 1 Ω to 82 Ω

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,[1] 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

[edit]

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)[2][3] and resistance values of resistors[4][5][6][7] were not standardized as they are today.[8]

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.[9] Over time, resistor manufacturers migrated from older values to the 1936 resistance value standard.[6][7]

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 high quantities of standardized electronic parts to build military devices, such as wireless communications, radar, radar jammers, LORAN radio navigation receivers for aircraft, test equipment, 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,[10] the International Electrotechnical Commission (IEC) began work on an international standard in 1948.[11] The first version of this IEC Publication 63 (IEC 63) was released in 1952.[12] Later, IEC 63 was revised, amended, and renamed into the current version known as IEC 60063:2015.[13]

IEC 60063 release history:

  • IEC 63:1952 (aka IEC 60063:1952), first edition, published 1952-01-01.[12]
  • IEC 63:1963 (aka IEC 60063:1963), second edition, published 1963-01-01.[11]
  • IEC 63:1967/AMD1:1967 (aka IEC 60063:1967/AMD1:1967), first amendment of second edition, published 1967.[11]
  • IEC 63:1977/AMD2:1977 (aka IEC 60063:1977/AMD2:1977), second amendment of second edition, published 1977.[11]
  • IEC 60063:2015, third edition, published 2015-03-27.[13]

Overview

[edit]

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, and 192 values, termed E3, E6, and so forth to E192, with maximum errors of 40%, 20%, 10%, 5%, 2%, 1%, 0.5%, respectively.[nb 1] 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

[edit]

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.[14]

where:
is rounded to 2 significant figures (E3, E6, E12, E24) or 3 significant figures (E48, E96, E192),
is an integer of the E series group size (3, 6, 12, 24, 48, 96, 192),
is an integer of
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

[edit]

For E3, E6, E12, and 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.[12] 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 ()
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Calculated 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

The E3 series is rarely used,[nb 1] 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 (3√10 − 1) ÷ (3√10 + 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

[edit]

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: is 48, then is incremented from 0 to 47 through the formula. All official values of E48 series match their calculated values.
  • To calculate the E96 series: is 96, then is incremented from 0 to 95 through the formula. All official values of E96 series match their calculated values.
  • To calculate the E192 series: is 192, then is incremented from 0 to 191 through the formula, with one exception for 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 have added missing E24 values into some 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".[15][16][17] 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 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
E48 values 1.00 1.10 1.21 1.27
1.33		 1.47 1.62 1.78 1.96 2.15 2.37 2.74 3.01 3.32 3.65 3.83 4.22 4.64 5.11 5.62 6.19 6.81 7.50 8.25 9.09
E96 values 1.00 1.10 1.21 1.30 1.50 1.58
1.62		 1.78
1.82		 2.00 2.21 2.37
2.43		 2.67 3.01 3.32 3.57 3.92 4.32 4.75 5.11 5.62 6.19 6.81 7.50 8.25 9.09
E192 values 1.00 1.10 1.20 1.30 1.50 1.60 1.80 2.00 2.21 2.40 2.71 3.01 3.28
3.32		 3.61 3.88
3.92		 4.32 4.70 5.11 5.62 6.19 6.81 7.50 8.16 9.09

Examples

[edit]

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:

E3 (in ohms) E6 (in ohms) 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

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:

E3 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

Lists

[edit]

A decade of the E12 values shown with their electronic color codes on resistors

List of official values for each E series:[nb 1]

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

[edit]
E-series values, 1.0–2.13
E3 E6 E12 E24 E48 E96 E192
1.0 1.0 1.0 1.0 1.00 1.00 1.00
1.01
1.02 1.02
1.04
1.05 1.05 1.05
1.06
1.07 1.07
1.09
1.1 1.10 1.10 1.10
1.11
1.13 1.13
1.14
1.15 1.15 1.15
1.17
1.18 1.18
1.20
1.2 1.2 1.21 1.21 1.21
1.23
1.24 1.24
1.26
1.27 1.27 1.27
1.29
1.30 1.30
1.32
1.3 1.33 1.33 1.33
1.35
1.37 1.37
1.38
1.40 1.40 1.40
1.42
1.43 1.43
1.45
1.5 1.5 1.5 1.47 1.47 1.47
1.49
1.50 1.50
1.52
1.54 1.54 1.54
1.56
1.58 1.58
1.60
1.6 1.62 1.62 1.62
1.64
1.65 1.65
1.67
1.69 1.69 1.69
1.72
1.74 1.74
1.76
1.8 1.8 1.78 1.78 1.78
1.80
1.82 1.82
1.84
1.87 1.87 1.87
1.89
1.91 1.91
1.93
2.0 1.96 1.96 1.96
1.98
2.00 2.00
2.03
2.05 2.05 2.05
2.08
2.10 2.10
2.13
E-series values, 2.15–4.59
E3 E6 E12 E24 E48 E96 E192
2.2 2.2 2.2 2.2 2.15 2.15 2.15
2.18
2.21 2.21
2.23
2.26 2.26 2.26
2.29
2.32 2.32
2.34
2.4 2.37 2.37 2.37
2.40
2.43 2.43
2.46
2.49 2.49 2.49
2.52
2.55 2.55
2.58
2.7 2.7 2.61 2.61 2.61
2.64
2.67 2.67
2.71
2.74 2.74 2.74
2.77
2.80 2.80
2.84
3.0 2.87 2.87 2.87
2.91
2.94 2.94
2.98
3.01 3.01 3.01
3.05
3.09 3.09
3.12
3.3 3.3 3.3 3.16 3.16 3.16
3.20
3.24 3.24
3.28
3.32 3.32 3.32
3.36
3.40 3.40
3.44
3.6 3.48 3.48 3.48
3.52
3.57 3.57
3.61
3.65 3.65 3.65
3.70
3.74 3.74
3.79
3.9 3.9 3.83 3.83 3.83
3.88
3.92 3.92
3.97
4.02 4.02 4.02
4.07
4.12 4.12
4.17
4.3 4.22 4.22 4.22
4.27
4.32 4.32
4.37
4.42 4.42 4.42
4.48
4.53 4.53
4.59
E-series values, 4.64–9.88
E3 E6 E12 E24 E48 E96 E192
4.7 4.7 4.7 4.7 4.64 4.64 4.64
4.70
4.75 4.75
4.81
4.87 4.87 4.87
4.93
4.99 4.99
5.05
5.1 5.11 5.11 5.11
5.17
5.23 5.23
5.30
5.36 5.36 5.36
5.42
5.49 5.49
5.56
5.6 5.6 5.62 5.62 5.62
5.69
5.76 5.76
5.83
5.90 5.90 5.90
5.97
6.04 6.04
6.12
6.2 6.19 6.19 6.19
6.26
6.34 6.34
6.42
6.49 6.49 6.49
6.57
6.65 6.65
6.73
6.8 6.8 6.8 6.81 6.81 6.81
6.90
6.98 6.98
7.06
7.15 7.15 7.15
7.23
7.32 7.32
7.41
7.5 7.50 7.50 7.50
7.59
7.68 7.68
7.77
7.87 7.87 7.87
7.96
8.06 8.06
8.16
8.2 8.2 8.25 8.25 8.25
8.35
8.45 8.45
8.56
8.66 8.66 8.66
8.76
8.87 8.87
8.98
9.1 9.09 9.09 9.09
9.20
9.31 9.31
9.42
9.53 9.53 9.53
9.65
9.76 9.76
9.88

See also

[edit]

Notes

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

E series of preferred numbers

View on Grokipedia
from Grokipedia
The E series of preferred numbers is a standardized system of preferred values derived for use in electronic components, particularly resistors, capacitors, inductors, and zener diodes. Although theoretically any value could be produced, in practice the need for inventory simplification has led the industry to settle on the E series for these components. Defined by the (IEC) in standard 60063, the series consists of geometric progressions where values are spaced logarithmically within each (from 1 to 10, repeated across powers of 10), limiting the variety of components needed while covering a wide range of practical requirements. 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). Originating from efforts in the early to rationalize component production, the E series was first published in IEC 60063:1952 following proposals adopted in 1950, building on earlier concepts like the to address post-World War II standardization needs in electronics. The nomenclature "E" followed by a number (e.g., , E6) indicates the approximate quantity of distinct values per , with the progression factor calculated as the of 10, or equivalently 10 raised to the power of 1/n—for instance, E12 uses a of approximately 1.21 (10^(1/12)) to provide 12 steps per . These series facilitate tolerance matching, where coarser series like (3 values: 1.0, 2.2, 4.7) suit broad applications, while finer ones like E96 (96 values) or E192 (192 values) support precision circuits. The system includes seven primary series—E3, E6, E12, E24, E48, E96, and E192—each with values rounded to two or three significant digits and extended across decades (e.g., 1.0, 10, 100 for in the units place). Widely adopted globally, the E series not only streamlines inventory and procurement but also aligns with marking codes in IEC 60062, enabling efficient identification of component values and tolerances in industries from to . Updates in the 2015 edition of IEC 60063 refined the relationship between series and tolerances, adding guidance for interpreting markings without altering the core values.

History and Development

Origins in Engineering Standardization

The origins of preferred number systems emerged in the late amid growing industrial demands for to manage manufacturing variability and tolerances, as engineers sought to limit the proliferation of component sizes while accommodating practical production constraints. This need was driven by observations that tolerances in often followed percentage-based variations, necessitating a rational approach to selecting values that minimized inventory costs and simplified design without sacrificing functionality. A pivotal development occurred between 1877 and 1879 when engineer Colonel Charles Renard proposed the (R5, R10, etc.) to standardize dimensions for captive in the French aeronautical program. Renard's system employed a on a , tailored to the , which reduced hundreds of potential cable and component sizes to a manageable set while ensuring compatibility across applications. Renard's work, first published in 1879, marked the initial formalized use of in to enhance in aviation-related production. In the United States and , initial proposals for decimal-based preferred series appeared before the , often adapting Renard's concepts for broader industrial use, including early electronic components like and capacitors. By 1936, the Radio Manufacturers Association in the U.S. adopted a preferred-number system specifically for fixed-composition values, focusing on logarithmic spacing to align with tolerance bands and manufacturing economies. Similar efforts in extended Renard's metric framework to component standardization, laying groundwork for later electronic applications. These pre-1950s initiatives represented an extension toward modern E series , particularly in where finer granularity became essential.

IEC Adoption and Evolution

The (IEC) formalized the E series through Technical Committee 40 (Capacitors and resistors for electronic equipment). Initial proposals were adopted in 1950, with standardization efforts leading to the publication of the first edition of IEC 63 (later redesignated IEC 60063) on January 1, 1952. This edition established the core E3, E6, E12, and E24 series of preferred numbers, tailored for and values with tolerances ranging from 50% (E3) to 5% (E24), facilitating uniform production and interchangeability in electronic equipment. Subsequent revisions refined and expanded the standard to accommodate advancing precision requirements. The second edition, published on January 1, 1963, incorporated Amendments No. 1 (1967) and No. 2 (1977), which introduced intermediate series such as E48 for 2% tolerances, enhancing applicability for closer-tolerance components. The third edition, released on March 27, 2015, represented a comprehensive technical revision that included the E96 and E192 series for 1% and 0.5% tolerances, respectively, and was confirmed without changes in 2018, ensuring ongoing relevance. The E series integrates with broader standardization efforts, such as ISO 3 (1973), which defines general preferred number series like R5 and R10 for non-electronic applications, allowing harmonious use across industries. Nationally, the standard has been adopted in various forms, including in the via BS 2488 (1966) for telecommunication equipment, later superseded by BS EN 60063 (2015), which directly implements the IEC edition. This evolution reflects the E series' adaptation from its precursor to meet global engineering needs.

Mathematical Principles

Geometric Progression Basis

The E series of preferred numbers forms a designed to standardize component values in engineering applications, with each —spanning from 10k10^k to 10k+110^{k+1} for kk—containing a fixed number nn of values spaced by a constant common r=101/nr = 10^{1/n}. For instance, in the E12 series where n=12n=12, the r≈1.211r \approx 1.211 ensures progressive multiplication of values across the . This structure repeats identically across all , facilitating consistent scaling in logarithmic terms. The of these values approximates a uniform spacing in terms of relative changes, which aligns with practices where tolerances and variations are typically expressed as percentages rather than absolute differences. In contexts like and mechanical , this relative uniformity better reflects perceptual and functional equivalence, as small proportional deviations have comparable impact regardless of the . By placing values equally on a , the series minimizes subjective bias in selecting "similar" sizes while optimizing inventory and production efficiency. Each E_n series covers one decade with values starting at approximately 1.0×10k1.0 \times 10^k and extending to just below 10×10k10 \times 10^k, with the exact upper value depending on the series (e.g., 8.2 for E12, 9.76 for E96), ensuring that the maximum gap between consecutive preferred values does not exceed the typical manufacturing tolerance for that series. This coverage prevents significant voids in the available range, allowing designers to select components that meet requirements without excessive deviation. The design guarantees contiguous tolerance bands around each value that abut without overlapping, providing continuous selection options across the full spectrum. The underlying concept treats preferred numbers as "round" in the logarithmic scale, prioritizing values that are simple to specify, measure, and produce while maintaining the geometric integrity for practical manufacturability. This approach simplifies standardization by favoring digit combinations that are easy to etch, print, or compute in production processes. The E series evolved from earlier systems like the , which provided the foundational motivation for logarithmic progressions in engineering standardization.

Rounding and Value Selection

The generation of exact E series values begins with a geometric sequence defined for each decade, typically from 1 to 10, using the formula vk=10k/nv_k = 10^{k/n} for k=0,1,…,n−1k = 0, 1, \dots, n-1, where nn is the series designation (e.g., 12 for E12). These calculated values are then rounded to the appropriate number of significant digits—usually two for series up to E24 (e.g., E3, E6, E12, E24) and three for finer series like E48, E96, and E192—to produce practical, manufacturable numbers while maintaining approximate logarithmic spacing. Following rounding, the values are normalized by scaling with powers of 10 (i.e., multiplying by 10m10^m where mm is an integer) to extend across multiple decades, ensuring no duplicates and consistent coverage from sub-units to mega-units. Rounding criteria prioritize the nearest value with the specified significant digits, often aligning with common representations for ease in marking and (e.g., in E12, 1.211 rounds to 1.2, and 8.25 rounds to 8.2). For edge cases near boundaries, calculated values approach but do not exceed 10 (e.g., ≈9.76 for E96), and are to significant digits without shifting to the next (retaining 9.76 for E96). This normalization step ensures the series remains subset-compatible, where coarser series (e.g., E6) are subsets of finer ones (e.g., E24), facilitating interchangeability in design. The selection of series also aligns with component manufacturing tolerances, as defined in IEC 60063, by ensuring the relative difference between adjacent values is at least twice the tolerance percentage to avoid overlap in tolerance bands. For instance, E24 is typically used for 5% tolerance components because the spacing (approximately 10% relative difference) ensures that the upper limit of one value's tolerance band touches the lower limit of the next, providing full logarithmic coverage without gaps or excessive redundancy; recommended assignments include E6 for ±20%, E12 for ±10%, E24 for ±5%, E48 for ±2%, E96 for ±1%, and E192 for ±0.5%. Similarly, E12 suits 10% tolerances, with its ≈21% spacing matching the doubled tolerance for economic production, while finer series like E96 support 1% tolerances through ≈2.5% spacing. This alignment minimizes inventory needs while guaranteeing that any required resistance or can be approximated within the specified tolerance using available preferred values.

Series Definitions and Variants

Core Series (E3 to E24)

The core series of , designated as , E6, E12, and E24, form the foundational sets in the E series standardization, providing progressively finer approximations of values for components like and capacitors within each (a factor of 10 in magnitude). These series are defined by the (IEC) in standard 60063, ensuring with ratios that align with common manufacturing tolerances. The series contains 3 values per , such as 1.0, 2.2, and 4.7 (normalized), which suits applications where coarse precision is acceptable, like early or low-cost prototypes. In contrast, the E6 series expands to 6 values per —1.0, 1.5, 2.2, 3.3, 4.7, and 6.8—finding use in basic electronic circuits where moderate accuracy is needed, such as in power supplies or simple filters. Each higher series incorporates the previous ones as subsets: for instance, E6 includes all E3 values, with additional steps for better resolution. Building on this, the E12 series offers 12 values per decade, including 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, and 8.2, widely applied in general-purpose resistors for consumer electronics and amateur radio equipment due to its balance of availability and precision. The E24 series further refines this to 24 values per decade, such as 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, and 9.1, for more demanding designs like audio amplifiers or instrumentation. E24 fully subsumes E12, E6, and E3, allowing seamless upgrades in precision without redesign. These core series relate to tolerances by approximating the number of distinct values required to cover a within the specified error margin; for example, the E12 series' steps of roughly 10% ensure that any desired value can be closely matched, minimizing inventory while supporting efficient production. This design principle, rooted in Renard's original work and formalized in IEC 60063, promotes interchangeability across global manufacturers.

Extended Series (E48 to E192)

The extended E series, encompassing E48, E96, and E192, provide denser sets of preferred values per to support higher precision in component selection compared to the core series. The E48 series includes 48 values per , generally aligned with 2% tolerance specifications for resistors and capacitors. The E96 series expands to 96 values per , typically for 1% tolerance, while the E192 series offers 192 values per , suited to 0.5% or tighter tolerances such as 0.25% and 0.1%. These series are defined in IEC 60063:2015, which specifies them as decimal multiples and submultiples of base values with three significant digits. Key differences from the core series lie in their finer value spacing and increased precision, enabling closer approximations to ideal component values in demanding designs. For instance, the E96 series employs a common ratio of approximately 1.021, derived from the r=101/96r = 10^{1/96}, allowing values to be spaced more tightly across each decade. Both E96 and E192 utilize three significant digits for all entries, contrasting with the one- or two-digit formats in lower series, to accommodate the reduced rounding errors inherent in higher tolerances. The values in these extended series incorporate the core series as subsets, ensuring compatibility while adding intermediate options for refined selections. These series address specific challenges in high-precision applications, particularly in analog circuits where minimal deviation from nominal values is critical for performance. They find use in precision filters, oscillators, and instrumentation, where the tighter spacing minimizes cumulative errors in networks. However, the finer gradations introduce manufacturing complexities, as producing components to match these values requires advanced trimming techniques and to maintain the associated low tolerances. The E192 series, in particular, benefited from refinements in the 2010s through the 2015 revision of IEC 60063, which clarified its three-digit structure.

Applications and Usage

In Electronic Components

The E series of preferred numbers serves as the foundational standard for specifying values in electronic components such as resistors, capacitors, inductors, and zener diodes, as defined by the (IEC) in standard 60063. This standardization ensures that component values are logarithmically spaced to cover a wide range efficiently while minimizing the number of unique parts needed for manufacturing. For instance, resistors and capacitors commonly adhere to these series, with manufacturers like Bourns producing inductors using the same preferred values to maintain consistency across passive components. In surface-mount device (SMD) formats, which dominate modern electronics, the E series is marked using systems like EIA-96 for the E96 series, enabling compact identification of 1% tolerance resistors through a three-character code that references the preferred value table. Tolerance levels align directly with series density: the E12 series supports 10% tolerances, E24 for 5%, E48 for 2%, E96 for 1%, and E192 for 0.5% or tighter, allowing designers to select components where the value spacing matches the precision requirements without excessive overlap in tolerance bands. The use of E series values streamlines electronic design by reducing the complexity of bills of materials (BOMs) and inventory management, as engineers can select from a limited set of standardized parts that approximate ideal calculations while ensuring manufacturability. This approach also facilitates (PCB) layout optimization, as preferred values promote uniform spacing and easier substitution during prototyping or production scaling. Historically, the transition from through-hole to SMD components in the late 1980s accelerated the reliance on E series standards, as automated pick-and-place assembly required precise, predefined value sets to support high-volume production without custom fabrication. This shift, driven by the need for smaller, denser circuits, made E series indispensable for enabling efficient, error-reduced manufacturing processes in consumer and industrial electronics.

Beyond Electronics

The Renard series (R series), a logarithmic system of analogous to the E series, forms the basis for standardization in , particularly for metric components where decimal precision is less critical than coarse geometric progressions. Developed by Charles Renard in the late and formalized in ISO 3, the R series divides the interval from 1 to 10 into 5, 10, 20, or 40 steps with ratios approximating the fifth root of 10 (about 1.58), enabling efficient inventory and by limiting size variants while covering practical ranges. In contrast to the E series' finer subdivisions (e.g., ratios near 1.12 for E24) suited to electronic tolerances, the R series prioritizes robustness in mechanical applications, serving as the metric counterpart for non-electronic parts. While the E series is primarily adopted for certain electronic components under IEC 60063, other types of electrical components are either specified by the Renard series (for example fuses) or defined in relevant product standards (for example IEC 60228 for wires). Mechanical applications of the R series include preferred diameters for screws and fasteners, as specified in ISO 261 and ISO 262, where thread sizes like M3, M4, M5, M6 follow R10 or R20 progressions to balance strength and compatibility. Similarly, pipe dimensions in standards such as ISO 4427 for plastics systems use R10 and R20 series for standard dimension ratios (SDR) and nominal diameters, ensuring interchangeability in and industrial systems—for instance, SDR values of 11, 13.6, 17, and 21. Gear employs R10 and R20 for module sizes ( pitch metrics), as outlined in gear standards, allowing modules like 1, 1.25, 1.5, 2 to optimize meshing and load distribution without excessive proliferation of tooling. ISO 286 tolerances for holes and shafts build on these preferred nominal sizes, assigning grades (e.g., H7, g6) to R-series bases for fits in assemblies like bearings and shafts. Beyond strict mechanical domains, similar logarithmic preference systems appear in interdisciplinary fields to standardize scales where perceptual or is key. In audio engineering, frequency standards often follow geometric progressions akin to , such as octave-based divisions ( 2:1) or third-octave bands in ISO 266, facilitating equalizer designs and acoustic testing. Lighting standards employ logarithmic steps for levels and lumen outputs, with preferred values in series like those in CIE recommendations to match human vision's logarithmic response. For pharmaceutical dosages, tablet and vial strengths commonly adhere to a 1-2-5 (e.g., 1 mg, 2 mg, 5 mg, scaling by powers of 10), reducing formulation variants while covering therapeutic ranges, as guided by pharmacopeial practices. These applications underscore the E series' geometric principles extending cross-domain for efficiency, though adapted to field-specific ratios.

Reference Tables and Examples

Value Tables for Key Series

The E series preferred numbers are defined by the International Electrotechnical Commission (IEC) standard 60063:2015, which specifies the exact values for each series to ensure consistency in component manufacturing across resistances, capacitances, and other parameters. These values are organized as geometric progressions rounded to a fixed number of significant digits, with mantissas (the significant figure parts) repeating across decades via by powers of 10 (10^k, where k is an , typically ranging from -3 to 8 for practical applications up to 10 MΩ or equivalent). The tables below present the mantissa values for the key series , E6, E12, E24, and E96, along with a subset for E192 focused on the 1.00 to 1.99 range for of higher precision; full values are obtained by appending the multiplier (e.g., 1.0 × 10^3 = 1.0 kΩ). Notes on deviations are included where applicable, based on the standard's provisions for historical and practical alignment. International variations exist minimally; for instance, the (JIS) C 5063 aligns closely with IEC 60063, adopting the same preferred values without significant deviations for these series.

E3 Series

The E3 series provides the coarsest spacing, suitable for 50% tolerance applications, with three values per .
MantissaExample Full Values (×10^k, k=0 to 6)Notes on Rounding
1.01.0, 10, 100, 1.0k, 10k, 100k, 1.0MStandard geometric to one significant digit.
2.22.2, 22, 220, 2.2k, 22k, 220k, 2.2MDerived by halving steps from higher series; no deviation.
4.74.7, 47, 470, 4.7k, 47k, 470k, 4.7MEnsures coverage up to the next ; historical retention.

E6 Series

The E6 series offers six values per decade, aligned with 20% tolerance components.
MantissaExample Full Values (×10^k, k=0 to 6)Notes on Rounding
1.01.0, 10, 100, 1.0k, 10k, 100k, 1.0MRounded to one significant digit per IEC rule.
1.51.5, 15, 150, 1.5k, 15k, 150k, 1.5MStandard progression.
2.22.2, 22, 220, 2.2k, 22k, 220k, 2.2MNo deviation.
3.33.3, 33, 330, 3.3k, 33k, 330k, 3.3MSubset of E12.
4.74.7, 47, 470, 4.7k, 47k, 470k, 4.7MHistorical value retained.
6.86.8, 68, 680, 6.8k, 68k, 680k, 6.8MEnsures logarithmic spacing.

E12 Series

The E12 series includes 12 values per decade, standard for 10% tolerance resistors and capacitors.
MantissaExample Full Values (×10^k, k=0 to 6)Notes on Rounding
1.01.0, 10, 100, 1.0k, 10k, 100k, 1.0MBase value, one significant digit.
1.21.2, 12, 120, 1.2k, 12k, 120k, 1.2MStandard.
1.51.5, 15, 150, 1.5k, 15k, 150k, 1.5MFrom E6 subset.
1.81.8, 18, 180, 1.8k, 18k, 180k, 1.8MNo deviation.
2.22.2, 22, 220, 2.2k, 22k, 220k, 2.2MHistorical.
2.72.7, 27, 270, 2.7k, 27k, 270k, 2.7MDeviates slightly from pure geometric for practicality.
3.33.3, 33, 330, 3.3k, 33k, 330k, 3.3MStandard.
3.93.9, 39, 390, 3.9k, 39k, 390k, 3.9MRounded to two digits.
4.74.7, 47, 470, 4.7k, 47k, 470k, 4.7MRetained for compatibility.
5.65.6, 56, 560, 5.6k, 56k, 560k, 5.6MEnsures even distribution.
6.86.8, 68, 680, 6.8k, 68k, 680k, 6.8MFrom E6.
8.28.2, 82, 820, 8.2k, 82k, 820k, 8.2MUpper decade value; minor deviation.

E24 Series

The E24 series provides 24 values per decade for 5% (or 1%) tolerance, with two significant digits.
MantissaExample Full Values (×10^k, k=0 to 6)Notes on Rounding
1.01.0, 10, 100, 1.0k, 10k, 100k, 1.0MBase, rounded per standard.
1.11.1, 11, 110, 1.1k, 11k, 110k, 1.1MStandard progression.
1.21.2, 12, 120, 1.2k, 12k, 120k, 1.2MFrom E12.
1.31.3, 13, 130, 1.3k, 13k, 130k, 1.3MNo deviation.
1.51.5, 15, 150, 1.5k, 15k, 150k, 1.5MStandard.
1.61.6, 16, 160, 1.6k, 16k, 160k, 1.6MTwo-digit rounding.
1.81.8, 18, 180, 1.8k, 18k, 180k, 1.8MFrom E12.
2.02.0, 20, 200, 2.0k, 20k, 200k, 2.0MExact geometric.
2.22.2, 22, 220, 2.2k, 22k, 220k, 2.2MHistorical.
2.42.4, 24, 240, 2.4k, 24k, 240k, 2.4MStandard.
2.72.7, 27, 270, 2.7k, 27k, 270k, 2.7MDeviates from mathematical rule due to historical relevance (27–47 range).
3.03.0, 30, 300, 3.0k, 30k, 300k, 3.0MRounded.
3.33.3, 33, 330, 3.3k, 33k, 330k, 3.3MFrom E12.
3.63.6, 36, 360, 3.6k, 36k, 360k, 3.6MStandard.
3.93.9, 39, 390, 3.9k, 39k, 390k, 3.9MDeviates slightly (27–47 range).
4.34.3, 43, 430, 4.3k, 43k, 430k, 4.3MHistorical retention in 27–47.
4.74.7, 47, 470, 4.7k, 47k, 470k, 4.7MFrom E3/E6.
5.15.1, 51, 510, 5.1k, 51k, 510k, 5.1MStandard.
5.65.6, 56, 560, 5.6k, 56k, 560k, 5.6MFrom E12.
6.26.2, 62, 620, 6.2k, 62k, 620k, 6.2MRounded.
6.86.8, 68, 680, 6.8k, 68k, 680k, 6.8MStandard.
7.57.5, 75, 750, 7.5k, 75k, 750k, 7.5MNo deviation.
8.28.2, 82, 820, 8.2k, 82k, 820k, 8.2MDeviates from pure geometric (82 value).
9.19.1, 91, 910, 9.1k, 91k, 910k, 9.1MUpper range rounding.

E96 Series

The E96 series uses three significant digits for 1% tolerance, with 96 values per . Mantissas are listed below (normalized); full scaling applies similarly up to 10M.
MantissaExample Full Values (×10^k, k=0 to 3)Notes on
1.001.00, 10.0, 100, 1.00kBase, three digits.
1.021.02, 10.2, 102, 1.02kStandard geometric.
1.051.05, 10.5, 105, 1.05kNo deviation.
1.071.07, 10.7, 107, 1.07kRounded per IEC.
1.101.10, 11.0, 110, 1.10kSubset of E192.
......(Intermediate values follow logarithmic steps; full list in standard).
1.961.96, 19.6, 196, 1.96kEnsures precision spacing.
2.002.00, 20.0, 200, 2.00kExact.
......(Up to 9.76).
9.769.76, 97.6, 976, 9.76kUpper , three-digit .
Full E96 mantissas: 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, 4.43, 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 Series (Subset)

The E192 series, for 0.5% or tighter tolerances, has 192 values per decade with three significant digits. Below is a subset focused on the 1.00–1.99 range (full series scales identically); higher densities provide finer precision in the 1–100 range by filling gaps between E96 values.
MantissaExample Full Values (×10^k, k=0 to 2)Notes on Rounding
1.001.00, 10.0, 100Base value.
1.011.01, 10.1, 101Finer step from E96.
1.021.02, 10.2, 102Matches E96 subset.
1.031.03, 10.3, 103Intermediate rounding.
1.041.04, 10.4, 104No deviation.
1.051.05, 10.5, 105From E96.
......(Continues to 1.99 with every-other omission yielding E96).
1.961.96, 19.6, 196Precision alignment.
1.981.98, 19.8, 198Additional step for 0.5% tolerance.
The full E192 includes values up to 9.88, derived by halving intervals from the geometric series and rounding to three digits; E96 and E48 are subsets by selecting every second and fourth value, respectively. Scaling rules remain consistent: mantissa × 10^k extends the series across decades without alteration.

Practical Calculation Examples

In practical engineering scenarios, the E series facilitates efficient component selection by providing standardized values that approximate required resistances or capacitances while minimizing inventory needs. The process typically involves logarithmic rounding to identify the nearest preferred value, ensuring even distribution across decades. This approach aligns with the geometric progression inherent to the series, as defined in IEC 60063. Example 1: Selecting a 10% Tolerance Resistor Near 47 kΩ
Consider a circuit requiring a resistor approximately 47 kΩ with 10% tolerance, common in general-purpose designs like voltage dividers. The E12 series, intended for such tolerances, includes 47 kΩ as a standard value (4.7 × 10⁴ Ω). This direct match avoids custom fabrication, with the actual resistance ranging from 42.3 kΩ to 51.7 kΩ under tolerance, providing reliable performance without exceeding the series' spacing of approximately 21% between values. Example 2: Selecting a 1% Precision Resistor Near 3.3 kΩ Using Logarithmic Rounding
For precision applications, such as feedback networks requiring about 3.3 kΩ with 1% tolerance, the E96 series offers finer granularity. Suppose circuit calculations yield a target of 3.25 kΩ (3250 Ω). To find the closest E96 value, apply logarithmic rounding: Compute log⁡10(3250)=log⁡10(3.25×103)=3+log⁡10(3.25)≈3+0.51188\log_{10}(3250) = \log_{10}(3.25 \times 10^3) = 3 + \log_{10}(3.25) \approx 3 + 0.51188. The mantissa is 0.51188. Multiply by 96 (steps per decade): 0.51188×96≈49.140.51188 \times 96 \approx 49.14. Round to the nearest : 49. New mantissa: 49/96≈0.5104249 / 96 \approx 0.51042. Exponentiate: 100.51042≈3.2410^{0.51042} \approx 3.24. Thus, select 3.24 kΩ (3240 Ω) from the E96 series, which deviates by about -0.3% from the target and falls within 1% tolerance (3.21–3.27 kΩ). This method ensures the selected value is optimally positioned on the . Example 3: Capacitor Bank Design with E24 Values for Target Impedance
In filter or decoupling circuits, achieving a specific impedance often requires a close to a calculated target, such as 47 nF for a where impedance Z=1/(jωC)Z = 1/(j \omega C) must match circuit needs at 1 kHz. The E24 series, suitable for 5% tolerance , includes values like 22 nF and 27 nF. Connecting these in parallel yields an equivalent Ceq=22 nF+27 nF=49 nFC_{eq} = 22 \, \text{nF} + 27 \, \text{nF} = 49 \, \text{nF}, approximately 4% above the target and providing an impedance of about Z≈3.24 kΩZ \approx 3.24 \, \text{k}\Omega (versus 3.39 kΩ for exact 47 nF). This bank approximates the required reactance while using available standards, adjustable if finer tuning is needed by referencing E24 value tables. Verifying Tolerance Impact on Adjacent Values
Tolerance ensures continuous coverage across the series without significant gaps or overlaps. For the E12 10% example, the 47 kΩ value spans 42.3–51.7 kΩ, while the adjacent 56 kΩ spans 50.4–61.6 kΩ, resulting in a minor overlap of 50.4–51.7 kΩ that prevents gaps in selectable ranges. Similarly, for E96 1%, the spacing of about 2.5% between values like 3.24 kΩ (3.21–3.27 kΩ) and 3.32 kΩ (3.29–3.35 kΩ) results in a small gap between tolerance bands (≈3.27–3.29 kΩ), but the series is designed to ensure any required value can be approximated within 1% tolerance. This , per IEC 60063, balances manufacturability and application flexibility.

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  17. https://www.wevolver.com/article/resistor-chart-comprehensive-guide-to-resistor-values-e-series-and-color-codes
  18. https://www.nextpcb.com/blog/what-are-10k-resistors-and-their-advantages
  19. https://emsginc.com/resources/the-evolution-of-surface-mount-technology/
  20. https://www.sellectronics.co.uk/blog/the-history-of-surface-mount-technology/
  21. https://www.sizes.com/numbers/preferred_numbers.htm
  22. https://cadem.com/preferred-numbers-and-sizes-in-engineering/
  23. https://www.plastiform.info/en/blog/engineering/iso-metric-screw-threads-complete-guide/
  24. https://www.pespipe.com/Portals/0/DNNGalleryPro/uploads/2019/4/2/ISO_4427-1-2007.pdf
  25. http://www.gearandrack.com/gear_information/gear_parameter_and_geometric_dimensions/general_terms.pdf
  26. https://www.engineersedge.com/manufacturing/preferred_mechanical_tolerances_metric_iso_286_13166.htm
  27. https://www.phon.ox.ac.uk/jcoleman/LOGARITH.htm
  28. https://webdesk.jsa.or.jp/preview/pre_jis_c_05062_000_000_2008_e_ed10_i4.pdf
  29. https://ez.analog.com/ez-blogs/b/engineerzone-spotlight/posts/say-no-more-to-tedious-calculations-for-e-series-values
  30. https://leemangeophysical.com/why-standard-resistor-values-are-strange/
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