Why do resistors typically have values such as 4.7kΩ or 5.1kΩ instead of round numbers like 5kΩ?

Many beginners in circuit design may find standard resistor values puzzling. Why are common values like 4.7 kΩ or 5.1 kΩ instead of round numbers such as 5 kΩ?

The reason lies in the use of an exponential distribution system for resistor values, standardized by the International Electrotechnical Commission (IEC). This system defines a series of preferred values, including the E3, E6, E12, E24, E48, E96, and E192 series.

For example:

• The E6 series uses a ratio of approximately 10^(1/6) ≈ 1.5
• The E12 series uses a ratio of approximately 10^(1/12) ≈ 1.21

In practice, resistors cannot be manufactured with perfect precision—each has a specified tolerance. For instance, a 100 Ω resistor with 1% tolerance is acceptable if its actual value falls between 99 Ω and 101 Ω. To optimize production, the American Electronics Industry Association established a standard system of preferred values.

Consider 10% tolerance resistors: if a 100 Ω resistor is already available (with a tolerance range of 90 Ω to 110 Ω), there is no need to produce a 105 Ω resistor, as it would fall within the same effective range. The next necessary value would be 120 Ω, whose tolerance range (108 Ω to 132 Ω) begins where the previous one ends. Thus, within the 100 Ω to 1000 Ω range, only specific values—such as 100 Ω, 120 Ω, 150 Ω, 180 Ω, 220 Ω, 270 Ω, and 330 Ω—are needed. This reduces the number of distinct values in production, lowering manufacturing costs.

This exponential distribution principle appears in other areas as well. For example, Chinese currency denominations include 1, 2, 5, and 10 yuan, but not 3 or 4 yuan—because 1, 2, and 5 can be combined efficiently to form any amount, minimizing the number of required denominations. Similarly, pen tip sizes often follow a sequence like 0.25, 0.35, 0.5, and 0.7 mm.

Moreover, the logarithmic spacing of resistor values ensures that, within a given tolerance, users can always find a suitable standard value. When resistor values follow an exponential progression aligned with their tolerance, the results of common mathematical operations (addition, subtraction, multiplication, division) also remain within predictable tolerance bounds.