Why 4.7 kΩ Exists and 5 kΩ Doesn't

What Are E-Series Values?

Pick up almost any resistor and its printed value comes from a short, fixed list: 4.7 kΩ, 10 kΩ, 22 kΩ, 47 kΩ — never 5 kΩ, 20 kΩ, or 50 kΩ. That list is not arbitrary. It is the E-series, a set of “preferred numbers” defined by IEC 60063 and used by every major resistor manufacturer so that a designer in one country and a fab in another agree on the same catalog of stock values. E6, E12, E24, E48, E96, and E192 are the common series — the number tells you how many values each one packs into a single decade (a ×10 span, e.g. 1 to 10).

The reason the values look strange at first glance — 1.0, 1.5, 2.2, 3.3, 4.7, 6.8 for E6 — is that they are not spaced by equal amounts. They are spaced by an equalratio. Understanding why that choice was made explains almost everything odd about standard resistor values, including why a plain 5 kΩ resistor simply does not exist.

Why Logarithmic Spacing, Not Arithmetic

Imagine spacing resistor values evenly instead: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Ω. Near the bottom of that list, the step from 1 Ω to 2 Ω is a 100% jump — hopelessly coarse for any circuit that needs a resistor tolerance tighter than ±50%. Near the top, the step from 9 Ω to 10 Ω is only about 11% — far finer than most designs would ever need. An arithmetic scale wastes resolution exactly where it is not needed and starves it exactly where it is.

Resistor tolerance is always specified as a percentage of the nominal value (±5%, ±1%, ±0.1%), not as a fixed number of ohms. So the value list that actually matches how tolerance works is one where every step represents roughly the same percentage change, not the same absolute change. That is a geometric progression: each value is the previous one multiplied by a constant ratio. For a series with N values per decade, that ratio is close to 10 raised to the power of 1⁄N — written 10^(1/N) — because multiplying by that ratio N times in a row gets you exactly from 1 to 10.

The E6 Series: A Concrete Walkthrough

E6 is the loosest common series, built for ±20% tolerance parts, with 6 values per decade. Its ratio is 10^(1/6), which works out to about 1.4678 — call it roughly 1.5. Starting from 1.0 and repeatedly multiplying by that ratio gives the theoretical sequence 1.0, 1.47, 2.15, 3.16, 4.64, 6.81, which IEC 60063 then rounds to two significant figures for a value list that is actually practical to print on a resistor body:

1.0 — 1.5 — 2.2 — 3.3 — 4.7 — 6.8

Check the ratio between any two neighbors and you get roughly the same number every time: 1.5 ÷ 1.0 = 1.5, 2.2 ÷ 1.5 ≈ 1.47, 3.3 ÷ 2.2 = 1.5, 4.7 ÷ 3.3 ≈ 1.42, 6.8 ÷ 4.7 ≈ 1.45, and wrapping around, 10 ÷ 6.8 ≈ 1.47. None of that is a coincidence — it is the rounded version of the same 10^(1/6) ≈ 1.47 ratio applied six times over, which is exactly what takes you from 1.0 back up to 10 at the top of the decade.

Why 5 kΩ and 500 Ω Don't Exist — the Bracket Math

This is where the logarithmic spacing directly explains the missing round numbers. Take the E24 series (±5% tolerance, 24 values per decade), which sits right next door to where a 5 kΩ resistor would go: it defines 4.7 kΩ and 5.1 kΩ, but nothing at 5.0 kΩ. Work out what each of those two real parts actually guarantees at ±5%:

• 4.7 kΩ ±5% covers 4.465 kΩ to 4.935 kΩ
• 5.1 kΩ ±5% covers 4.845 kΩ to 5.355 kΩ

Those two ranges overlap between 4.845 kΩ and 4.935 kΩ, and together they span the entire 4.465–5.355 kΩ neighborhood without a single gap. Now compare that to what a hypothetical dedicated 5.0 kΩ ±5% part would guarantee: 4.75–5.25 kΩ. That entire range already sits inside the coverage the two real parts jointly provide. A resistor manufactured at exactly 5000 Ω would pass inspection as a 5.1 kΩ ±5% part (5000 Ω is comfortably inside its 4.845–5.355 kΩ band) with no additional part number required. Defining a separate 5.0 kΩ value would add a redundant SKU that manufactures, stocks, and tests a resistance the existing two values already have covered — which is exactly what a preferred-number system is built to avoid.

The same argument applies at every decade, because E-series values repeat their digit pattern and just shift the decimal point (more on that below). 500 Ω is missing for identical reasons that 5 kΩ is: 470 Ω and 510 Ω already bracket it. So is 50 Ω, bracketed by 47 Ω and 51 Ω. Every “obviously round” number you would expect to find on a resistor — 500, 5 k, 50 k — is absent because the two real E24 neighbors either side of it already guarantee coverage of that exact resistance within tolerance.

Matching Series Density to Tolerance

The bracket argument above only works because the step ratio and the tolerance band are matched to each other. Loosen the tolerance and you need fewer values to keep coverage gap-free; tighten it and you need more. That is exactly why there are six standard series instead of one:

• E6 — 6 values/decade, ±20% tolerance, ratio ≈ 1.47
• E12 — 12 values/decade, ±10% tolerance, ratio ≈ 1.21
• E24 — 24 values/decade, ±5% tolerance, ratio ≈ 1.10
• E48 — 48 values/decade, ±2% tolerance, ratio ≈ 1.05
• E96 — 96 values/decade, ±1% tolerance, ratio ≈ 1.024
• E192 — 192 values/decade, ±0.5% tolerance (also used for the tighter ±0.25% and ±0.1% precision grades), ratio ≈ 1.012

Notice the pattern: each step ratio sits close to (1 + tolerance) ÷ (1 − tolerance) — the ratio at which one part's upper bound just meets the next part's lower bound. For E24 that works out to 1.05 ÷ 0.95 ≈ 1.105, almost exactly the series' real 10^(1/24) ≈ 1.10 ratio. A looser series like E12 can get away with a much bigger 1.21 step precisely because its ±10% band is wide enough that a single value's own tolerance already reaches into its neighbor's territory — recall that 4.7 kΩ at ±10% alone covers up to 5.17 kΩ, already swallowing the 5 kΩ neighborhood without any help. Drop to ±5% and that same 4.7 kΩ part only reaches 4.935 kΩ, so E24 has to insert 5.1 kΩ to close the gap. Precision series like E96 and E192 exist for the same reason taken further: a ±1% or ±0.5% part has such a narrow band that it takes far more values, packed far more tightly, to avoid leaving stretches of the decade with no standard value close enough to certify.

The Same Digits, Every Decade

E-series values are decade-relative, not fixed to a particular magnitude. The E6 digit sequence 1.0, 1.5, 2.2, 3.3, 4.7, 6.8 is the entire series — multiplying it by 1, 10, 100, 1,000, and so on generates every E6 resistor Resistora or anyone else stocks: 1.0 Ω, 10 Ω, 100 Ω, 1.0 kΩ, 10 kΩ, 100 kΩ, 1.0 MΩ, and 1.5 Ω, 15 Ω, 150 Ω, 1.5 kΩ, 15 kΩ, and on through every decade the same way. That is why the missing-round-number pattern repeats identically at every magnitude: 5 Ω, 50 Ω, 500 Ω, 5 kΩ, 50 kΩ, and 500 kΩ are all absent for the same reason, because none of them is the rounded 10^(k/N) value the series actually lands on at that position in the decade.

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Frequently Asked Questions

Why is there no 5 kΩ resistor?

There is no need for one. In the E24 series (±5% tolerance), 4.7 kΩ covers 4.465–4.935 kΩ and 5.1 kΩ covers 4.845–5.355 kΩ. Together those two bands already span 4.465–5.355 kΩ with overlap in the middle, so a resistor manufactured near 5 kΩ is already guaranteed to pass as one of them. A distinct 5.0 kΩ part, with its own ±5% band of 4.75–5.25 kΩ, would sit entirely inside that combined coverage — a redundant value the standard doesn't bother defining.

What does the "E" in E6, E12, and E24 mean?

E-series are the IEC 60063 preferred number series for resistors, capacitors, and other passive components. The number after the E is how many values it defines per decade (per ×10 span): E6 has 6 values from 1 to 10, E12 has 12, and so on up through E48, E96, and E192.

Why are E-series values spaced logarithmically instead of evenly?

Evenly spaced values (1, 2, 3, 4...) would waste resolution at the low end — the gap from 1 to 2 is a 100% jump — while barely differing near 10. E-series values instead use a constant ratio between neighbors, close to 10^(1/N) for an N-value series, so every step represents roughly the same percentage change. That matches how resistor tolerance works: tolerance is a percentage of the nominal value, not a fixed number of ohms, so a percentage-spaced value list is what actually lines up with it.

Why does a 1% tolerance resistor need E96 instead of E24?

A tighter tolerance shrinks each value's coverage band, so the same E24 spacing would leave gaps between adjacent values that no standard part could legitimately claim. E96 packs 96 values per decade instead of 24, at roughly a 2.4% step instead of 10%, so 1% (and 2%) parts stay gap-free. Denser series exist precisely to keep pace with tighter guaranteed tolerance.

Are E-series values exact, or rounded?

Rounded. The underlying formula is a pure geometric progression, 10^(k/N), which produces irrational-looking numbers like 1.4678 or 2.1544. IEC 60063 rounds each one to 2–3 significant figures — E6's third value is 2.2, not the theoretical 2.1544 — so the values are practical to print on a part and remember, at the cost of the step ratio being only approximately constant.

What's the fastest way to find the closest E-series value to a target resistance?

Use the E-Series Resistor Finder — enter your target resistance and pick a series (E6 through E192), and it returns the closest standard catalog value instead of making you scan a printed table.