Open any resistor kit and you will find 4.7 kΩ, 5.6 kΩ and 6.8 kΩ, but no 5 kΩ or 6 kΩ. Those strange numbers come from the E-series of preferred values, defined in the IEC 60063 standard, and the logic behind them is simple once you see it. Knowing it also makes it easier to spot a misread color code and to pick the closest part when a calculation gives an awkward answer.
Equal ratios, not equal steps
Suppose resistors were sold in 1 kΩ steps: 1k, 2k, 3k and so on up to 10k. The jump from 1k to 2k is 100%, while the jump from 9k to 10k is only 11%. That is useless, because a circuit's sensitivity to a resistor is almost always proportional. Being 10% off matters as much at 1 kΩ as at 9 kΩ.
So the values are spaced geometrically. Each one is the previous value multiplied by a constant ratio, r = 10^(1/n), where n is the number of values per decade. For the E12 series, r = 10^(1/12) ≈ 1.212, which produces 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. Every decade repeats the same pattern, so the E12 value 4.7 gives you 4.7 Ω, 47 Ω, 470 Ω, 4.7 kΩ, 47 kΩ, 470 kΩ and 4.7 MΩ.
The series and their tolerances
| Series | Values per decade | Step ratio | Usual tolerance | Values from 1 to 10 |
|---|---|---|---|---|
| E3 | 3 | 2.15 | wider than ±20% | 1.0, 2.2, 4.7 |
| E6 | 6 | 1.47 | ±20% | 1.0, 1.5, 2.2, 3.3, 4.7, 6.8 |
| E12 | 12 | 1.21 | ±10% | E6 plus 1.2, 1.8, 2.7, 3.9, 5.6, 8.2 |
| E24 | 24 | 1.10 | ±5% | E12 plus 12 more (table below) |
| E48 | 48 | 1.049 | ±2% | three significant figures |
| E96 | 96 | 1.024 | ±1% | 100, 102, 105, 107, 110… |
| E192 | 192 | 1.012 | ±0.5% and tighter | 100, 101, 102, 104, 105… |
The pairing of series and tolerance is deliberate. Take two neighboring E12 values: 4.7 kΩ ±10% covers 4.23 to 5.17 kΩ, and 5.6 kΩ ±10% covers 5.04 to 6.16 kΩ. The windows just overlap, so every resistor a factory produces falls inside the tolerance of some E12 value, and none of the spread is wasted. The E24 ratio of 1.10 does the same job for ±5% parts. Today E24 values are routinely made at ±1%, so the pairing is a guide rather than a rule, but it explains why the series have the sizes they do.
Each lower series sits inside the next one up: E6 is every second E12 value and E12 is every second E24 value. E48 is likewise every second E96 value. The jump from E24 to E48 is where the pattern breaks, as the next section explains.
The E24 values that break the formula
Series up to E24 are rounded to two significant figures and E48 and above to three. If you calculate 10^(k/24) and round, most E24 values match. Eight do not:
| Step k | 10^(k/24) | Rounded | Actual E24 value |
|---|---|---|---|
| 10 | 2.610 | 2.6 | 2.7 |
| 11 | 2.873 | 2.9 | 3.0 |
| 12 | 3.162 | 3.2 | 3.3 |
| 13 | 3.481 | 3.5 | 3.6 |
| 14 | 3.831 | 3.8 | 3.9 |
| 15 | 4.217 | 4.2 | 4.3 |
| 16 | 4.642 | 4.6 | 4.7 |
| 22 | 8.254 | 8.3 | 8.2 |
Values such as 2.7, 3.3, 3.9, 4.7 and 8.2 were already in wide use before the series were standardized, and the standard kept them. The in-between E24 values 3.0, 3.6 and 4.3 were then nudged so they still sit between their E12 neighbors. The practical consequence is that E24 is not a subset of E96. There is no 220, 330 or 470 in E96; the nearest values are 221, 332, and 464 or 475. If a design calls for a 4.7 kΩ ±1% resistor, you are buying an E24 value made to 1% tolerance, not an E96 part.
E192 has its own oddity. Step 185 calculates to 919, but the published series lists 920. It is the only E192 value that departs from the formula, and it is a good test case if you ever write code that generates the series.
E12 and E24 values
The E24 series is the E12 series with one extra value slotted between each pair. The left column alone is E12; both columns together are E24.
| E12 value | Extra E24 value | Example parts |
|---|---|---|
| 1.0 | 1.1 | 10 Ω, 1 kΩ, 1.1 kΩ |
| 1.2 | 1.3 | 120 Ω, 1.2 kΩ, 13 kΩ |
| 1.5 | 1.6 | 150 Ω, 1.5 kΩ, 16 kΩ |
| 1.8 | 2.0 | 180 Ω, 2 kΩ, 20 kΩ |
| 2.2 | 2.4 | 22 Ω, 2.2 kΩ, 24 kΩ |
| 2.7 | 3.0 | 270 Ω, 3 kΩ, 27 kΩ |
| 3.3 | 3.6 | 330 Ω, 3.3 kΩ, 36 kΩ |
| 3.9 | 4.3 | 390 Ω, 4.3 kΩ, 39 kΩ |
| 4.7 | 5.1 | 47 Ω, 4.7 kΩ, 5.1 kΩ |
| 5.6 | 6.2 | 560 Ω, 5.6 kΩ, 62 kΩ |
| 6.8 | 7.5 | 68 Ω, 6.8 kΩ, 75 kΩ |
| 8.2 | 9.1 | 820 Ω, 8.2 kΩ, 91 kΩ |
Knowing these values is also a reliable way to catch color-code mistakes. If you decode a band sequence as 5.7 kΩ or 2.5 kΩ, neither exists in E24, so recheck the colors with the color code reading guide.
Picking the nearest value
When a calculation lands between two values, the right direction depends on the job. For an LED or any current-limiting resistor, round up so the current ends up slightly lower. For a pull-up or a bias resistor, the nearest value either way is usually fine. For a voltage divider, the ratio of the two resistors matters more than either value.
Suppose you need 5.0 kΩ. The E12 neighbors are 4.7 kΩ (6% low) and 5.6 kΩ (12% high). E24 offers 5.1 kΩ, 2% high. E96 offers 4.99 kΩ, only 0.2% low:
Because the spacing is geometric, the true midpoint between two neighbors is their geometric mean, not the arithmetic average. Between 4.7 and 5.6 it is √(4.7 × 5.6) ≈ 5.13, so anything below 5.13 kΩ is closer, in percentage terms, to 4.7 kΩ.
For a divider, look for a convenient pair. Dropping 5 V to about 3.3 V needs a ratio near 0.66: 1 kΩ on top and 2 kΩ below gives 5 × 2 / 3 = 3.33 V using E24 values, while the E12 pair 1.8 kΩ and 3.3 kΩ gives 3.24 V. The voltage divider calculator lets you try pairs quickly.
Making odd values from two resistors
When no single value is close enough, combine two. In series the values add; in parallel the result is R1 × R2 / (R1 + R2), and two equal resistors in parallel give exactly half.
- 5 kΩ: two 10 kΩ in parallel.
- 6 kΩ: two 12 kΩ in parallel, or two 3 kΩ in series.
- 5.0 kΩ another way: 4.7 kΩ plus 300 Ω in series. A large value plus a small trim value is the most flexible method.
- 4.49 kΩ: 4.7 kΩ in parallel with 100 kΩ. A large resistor in parallel nudges a value down by a few percent.
Combining parts does not make tolerance worse. Two ±5% resistors in series or parallel give a result that is still within ±5% in the worst case, and their random errors often partly cancel. The combination also shares the heat, which helps with power-hungry spots. The series and parallel resistor calculator works out combinations, and the standard resistor values page lists every member of each series. For most hobby work, an E12 kit covers nearly everything, an E24 kit fills the gaps, and E96 parts are worth buying only for specific precision values.