E-series finder

The value you want is usually between two you can buy. This finds the closest single part, the closest pair, and the divider that lands on a target voltage — with what each one misses by, and what it costs.

Fig 1 — How far each option misses 12.3 kΩ. Scale is ±0.63 %.

Find

Series

Target (Ω)

Smallest allowed (Ω)

Largest allowed (kΩ)

Nearest single: 12.4 kΩ · +0.446 %
Best series pair: 1.05 kΩ + 11.3 kΩ = 12.4 kΩ · +0.041 %
Best parallel pair: 12.7 kΩ ∥ 442 kΩ = 12.3 kΩ · +0.002 %
Improvement: a pair gets 195× closer than the single

The single value is already within 0.45 %, which is inside the tolerance E96 is sold at. A second resistor buys precision the parts do not have — unless the two are in one package and track.

How this is calculated

Standard: IEC 60063 — preferred number series for resistors and capacitors

$R_{series} = R_1 + R_2, \qquad R_{parallel} = \frac{R_1 R_2}{R_1 + R_2}$: For each stocked first value the ideal partner is solved exactly and then snapped to the stocked values either side of it, so the search is exhaustive without being quadratic. The unit tests check it against a brute-force sweep of every ordered pair.
$\frac{V_{out}}{V_{in}} = \frac{R_{bottom}}{R_{top} + R_{bottom}}$: The divider ratio, unloaded. Loading it changes the answer, which is what the voltage divider calculator is for.
$R_{source} = \frac{R_{top} R_{bottom}}{R_{top} + R_{bottom}}, \qquad I = \frac{V_{in}}{R_{top} + R_{bottom}}$: The two numbers that usually decide the values. Source impedance is what the next stage has to tolerate; the current runs continuously, including while the product is asleep.
$t = \frac{10^{1/N} - 1}{10^{1/N} + 1}$: Why each series comes with the tolerance it does: the value at which neighbouring tolerance bands just meet. It gives 4.79 % for E24 against a sold ±5 %, and 1.20 % for E96 against ±1 %.

Assumptions

The series values are tabulated, not derived. They are close to a geometric progression but are not that progression rounded — 10^(n/24) to two figures gives 29 where E24 has 30, and 10^(n/96) to three gives 136 where E96 has 137 — so the tables come from the ones the resistor decoder already ships, and a unit test asserts the deviation rather than letting a formula quietly replace them.
E12 is every other E24 value and E48 every other E96 value. Those relations are tested rather than stored as separate tables.
The tolerance of the parts is not modelled. A pair that lands within 0.05 % of a target out of ±1 % resistors is still a ±1 % combination; what this removes is the grid error, not the part error.
Divider results are unloaded. The source impedance is reported so the loading can be judged, but the voltage divider calculator is the tool that works it through.
Ratios repeat every decade, so widening the range changes the impedance and the current rather than the reachable ratios. When a ratio is out of reach in E96, the answer is a finer series.

What the E-series grid can and cannot hit

Resistors come in a grid. IEC 60063 fixes that grid — twelve values a decade at ±10 %, twenty-four at ±5 %, ninety-six at ±1 % — and the value you actually want is usually between two of them. This finds the closest single part, the closest series pair and the closest parallel pair, and shows what each one misses by, so the second resistor is fitted for a reason rather than out of habit.

The divider mode is the same search against a ratio, and it reports two things the ratio alone does not: the source impedance the next stage sees, and the current the divider draws forever. Those are usually what decides the values, not the third decimal place of the ratio.

E-series resistor value chart

The standard significands per decade, as the calculator above holds them. Multiply by any power of ten for the actual part: the E12 entry 4.7 is 4.7 Ω, 47 Ω, 470 Ω, 4.7 kΩ and so on. Each series is built on a constant ratio between neighbours, so the gaps are equal in percentage terms, not in ohms.

Series	Values per decade	Step	Significands
E12	12	21.2 %	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	24	10.1 %	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	48	4.9 %	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	96	2.4 %	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

E24 contains E12, but E96 does not contain E24: the 1 % grid was rounded from the pure ratio separately, which is why 4.7 kΩ is not an E96 value and 4.75 kΩ is. A design that mixes 1 % and 5 % parts has two grids to reconcile, and the finder searches whichever one is selected.

Worked example: reaching 12.345 kΩ from E24

12.345 kΩ from the E24 grid — a value nothing in the series is close to.

nearest single    12 k                 -2.795 %
best series pair  1.3 k + 11 k         -0.365 %
best parallel     13 k || 240 k        -0.105 %   -> 12.332 k

The parallel pair is twenty-seven times closer than the single value. Whether that is worth a second resistor is the interesting question, and the answer is usually no: E24 parts are sold at ±5 %, so a 2.8 % grid error sits inside the tolerance of the part you would be correcting. The exception is aratio — two resistors in the same package, at the same temperature, drift together, and their ratio holds far better than either value does.

Note what the parallel pair does: a 240 kΩ resistor trimming a 13 kΩ one down by 5 %. That is the usual shape of a parallel trim, and it is also why it is fragile — the trimming resistor is twenty times the value being trimmed, so its own tolerance is divided by twenty on the way in, but so is any error in reading it.

Where chasing an exact value stops being worth it

Precision you cannot buy is not precision. Getting within 0.05 % of a target with two ±1 % resistors gives a combination whose real tolerance is still about 1 %. The grid error and the part tolerance are different things, and only the first is what this tool removes. Use it when the grid is the binding constraint — matched networks, a ratio that has to land on a reference voltage, a feedback divider trimmed by selection.

A finer series is usually the better answer than a second part.Two resistors are two footprints, two solder joints and two things to get wrong in the BOM. Moving from E24 to E96 costs nothing in board area.

Ratios repeat every decade, so widening the range rarely helps a divider. The set of achievable ratios is fixed by the significands; scaling both resistors by ten changes the impedance and the current, not the ratio. When a divider cannot reach a ratio in E96, the answer is E192 or a trim, not a bigger search.

Tolerance, not value, is what the series is really selling.Adjacent values differ by a factor 10^1/N, and the tolerance each series is sold at is very nearly the value that makes neighbouring tolerance bands meet — 4.79 % derived against ±5 % for E24, 1.20 % against ±1 % for E96. Buying a tighter tolerance from a coarser grid wastes most of it.

Common E-series mistakes

Assuming 4.7 kΩ is available in E96. It is not: E96 carries 4.64 kΩ and 4.75 kΩ. A "1 % 4k7" is an E24 value sold to a tighter tolerance, which is a perfectly ordinary thing to buy — but it is not on the E96 grid, and a search restricted to E96 will not offer it.
Sizing a divider on the ratio and discovering the source impedance afterwards. A 1 MΩ / 2 MΩ divider has a 667 kΩ source impedance, which any amplifier's bias current and the board's own leakage will walk around.
Putting a precision divider on a rail that has to sleep. The standing current runs whether the product is doing anything or not.
Correcting a grid error with a second resistor and leaving both at ±5 %. The combination is no more accurate than its parts.