Voltage Divider From Standard Resistor Values

Choosing Real Resistor Values for a Divider

Design a divider for 3.3 V from 12 V and the algebra offers you 26.364 kΩ over 10 kΩ. Nobody sells 26.364 kΩ. The question this page answers is what to do about that, and the answer is more interesting than "round it to the nearest value".

The ratio, and the freedom left over

Rearranging the divider formula for the ratio of the two resistors:

That spare degree of freedom is the impedance of the divider, and it is genuinely free as far as the voltage is concerned. 2.64 kΩ over 1 kΩ and 264 kΩ over 100 kΩ give the same output. So the search has two inputs, not one: the ratio you need, and the range of total resistance you are willing to accept.

Why a fine series does not guarantee a fine ratio

E96 has 96 values per decade, so consecutive values differ by about 2.4 %. It is tempting to conclude that any ratio can be matched to about 1.2 %. But both resistors come off the same grid, so the achievable RATIOS are also on a grid — approximately the powers of one step:

An arbitrary ratio therefore lands somewhere between two achievable ones, up to about half a step away. In practice the real tables are rounded to three significant figures rather than being exactly geometric, and that scatter happens to help: some pairs land closer than the ideal grid would allow. Searching finds those, which is exactly why searching beats calculating and rounding.

Tolerance is usually the binding constraint

Now the part that changes how you read a ranked list. Both resistors have a tolerance, and both move the output. Differentiating the divider formula gives how much:

Two consequences worth carrying. First, errors that both resistors share cancel completely, which is the argument for using two resistors of the same type from the same batch — their tolerances are correlated and their temperature coefficients nearly identical. Second, the worst case is the two sitting at opposite extremes, and the factor in front tells you how bad that is: for a 1:1 divider it is 0.5, so two 1 % resistors give a 1 % output; for a heavily attenuating divider it approaches 1, so the same parts give nearly 2 %.

Which means an exactly correct nominal ratio built from 1 % parts is still a 1-to-2 % divider. Chasing the last 0.01 % of ratio error is wasted effort unless the resistors are tighter than the ratio — and that comparison is what the table above puts side by side.

When the tolerance is not good enough

Four honest options, roughly in order of how often they are the right one:

• Do not need the accuracy. Ratiometric designs cancel the error entirely — see below.
• Buy tighter parts. 0.1 % resistors are cheap now, and going from 1 % to 0.1 % buys a factor of ten directly.
• Use a resistor network. A matched pair in one package is specified on RATIO tolerance rather than absolute, often 0.05 % or better, and its two halves track in temperature because they are the same piece of silicon.
• Measure and adjust. Fit one resistor, measure it, then choose the second to suit. A trimmer does the same thing continuously, at the cost of drift and vibration sensitivity.

Worked example

The nominal error is +0.47 %, and a brute-force sweep of every E96 pair in the window confirms nothing does better — so this is the limit of the series, not of the search. Now compare it with the tolerance: two 1 % resistors put the output anywhere within ±1.45 %, three times the ratio error. The ratio is not what is limiting this divider, and no finer series would change that.

Where the Resistance Window Comes From

The search needs a range of total resistance because without one the best ratio wins regardless of magnitude, and the answer is as likely to be 2.2 Ω over 1 Ω — which shorts the supply — as 22 kΩ over 10 kΩ. Four things set the window.

The bottom of the range: current

Total resistance sets the standing current, which flows permanently. Divide 12 V by your acceptable quiescent current and you have the minimum total resistance. At 100 µA that is 120 kΩ; at 1 mA it is 12 kΩ.

The top of the range: loading and leakage

Higher values raise the output resistance, so whatever you connect matters more, and they make the input leakage of the measuring device significant. A rough guide: keep the divider current at least a hundred times the leakage of anything attached, which for a typical ADC input means staying under a few hundred kilohms.

Noise

A high-impedance node picks up capacitively coupled noise from anything switching nearby, and the divider has little current available to hold it down. Thermal noise also rises with resistance, though for a divider feeding an ADC that is rarely the limit — coupling is.

Speed

The output resistance working into any capacitance on the node — including the input capacitance of what you connected — is a low-pass filter. A 100 kΩ output resistance into 20 pF is a 2 µs time constant, which is fine for a battery monitor and useless for a signal.

Ratiometric Design: Making the Tolerance Not Matter

The most elegant answer to divider accuracy is to arrange for the accuracy not to be needed. This is worth understanding before buying tighter resistors.

Suppose a microcontroller reads a divider from its own supply, using that same supply as the ADC reference. The ADC reports the input as a fraction of the reference, so the supply voltage cancels out of the measurement entirely — the reading depends only on the divider ratio, and a supply that sags does not move the answer. That is ratiometric measurement, and it is why sensor bridges are built this way.

The same idea applies to the resistors. If a design only ever compares two dividers made from the same parts — a bridge, a differential amplifier, a feedback network judged against a reference divider — then the absolute values and their shared drift cancel, and only the mismatch between them matters. That is what the derivation above showed: it is the DIFFERENCE of the two errors that reaches the output.

So before specifying 0.1 % parts, check whether the absolute value is actually needed. Often the answer is a firmware calibration constant rather than a component.

Getting Better Than the Series Allows

Combining two resistors

Two standard values in series or in parallel reach far more ratios than either alone: a large resistor with a much smaller one in series gives fine adjustment around the large value. It costs a part and a little board area, and it is often cheaper than a tighter tolerance.

Trimmers

A trimmer in series with the fixed resistor gives continuous adjustment, and it is the traditional answer. The costs are real: trimmers drift with temperature and age, are sensitive to vibration and moisture, need a calibration step in production, and can go open-circuit at the wiper. Use a fixed value where you can.

Resistor networks

A matched pair or a divider network in one package is specified on ratio tolerance, often 0.05 % or better, with a ratio temperature coefficient an order of magnitude below the individual one. For anything where the ratio is what matters — instrumentation amplifiers, precision dividers, feedback networks — this is the correct part rather than two discrete resistors.

Calibrating in software

Measure the divider once against a known voltage, store the correction, and the resistor tolerance stops mattering for accuracy — though its temperature drift still does. This is usually the cheapest option by a wide margin, and the reason so many products ship with a calibration constant in flash.

Reading the Ranked Table

Six columns, and the order you should read them in is not left to right.

• "In tol" first. This is the worst the output can be once both resistors are anywhere inside their tolerance, and it is normally the largest error in the row. If it is bigger than your requirement, no pair in the list will do and the answer is tighter parts.
• "Error" second. The nominal ratio error. Worth minimising, but only down to the point where it is small compared to the tolerance column.
• "Total" and "Current" together. These are your impedance and quiescent-current decision, and they are why two pairs with identical ratios both appear.
• "Zout" last, unless something is connected to the output — in which case it is first, because the loading error follows from it directly.

A pair with a slightly worse nominal error but a much more convenient total resistance is usually the better choice. The nominal error is the one number in the table you can correct in firmware.

Common mistakes

• Calculating one resistor exactly and then rounding it. Choosing both from the series together gets several times closer, because the error in one can offset the error in the other.
• Reading the nominal error and ignoring the tolerance column. An exact ratio from 5 % parts is a 5 % divider.
• Assuming a finer series always helps. Beyond the point where the tolerance dominates, E192 buys nothing over E96 except cost.
• Searching without an impedance constraint. The best ratio at the wrong magnitude is a short circuit or an antenna.
• Mixing resistor types between the two positions. Their temperature coefficients then differ, so the drift no longer cancels and the ratio moves with temperature.
• Specifying tight absolute tolerance when only the ratio matters. A matched network is both better and cheaper than two 0.1 % discrete parts.

Frequently asked questions

How do I find the closest standard resistor values for a voltage divider?

Work out the required ratio, (Vin − Vout)/Vout, then for each standard value of R2 test the standard values nearest to ratio × R2 for R1. Rank the pairs by output error and filter them by an acceptable total resistance. That is exactly what the calculator above does.

Why can’t E96 hit my divider ratio exactly?

Because both resistors come from the same geometric grid, so the achievable ratios are also on a grid — roughly the powers of 1.0242. An arbitrary ratio falls between two of them. In practice the tables are rounded to three figures, and that scatter lets some pairs land closer than the ideal grid would.

How accurate is a voltage divider made from 1 % resistors?

Between 1 % and 2 %, depending on the ratio. The output error is R1/(R1+R2) × (ΔR2/R2 − ΔR1/R1), so for a 1:1 divider the two errors half-cancel and you get about 1 %; for a heavily attenuating divider the factor approaches 1 and you get nearly 2 %.

Does using a finer resistor series improve divider accuracy?

Only up to a point. A finer series reduces the nominal ratio error, but it does nothing about tolerance. Once the tolerance-stacked error is several times the ratio error — which happens quickly — a finer series buys nothing and the answer is tighter parts or a matched network.

What total resistance should a voltage divider have?

Set the minimum from your standing-current budget: Vin divided by the current you can spare. Set the maximum from loading and leakage — keep the divider current at least a hundred times the leakage of whatever is connected. For a divider feeding an ADC, 10 kΩ to 100 kΩ total covers most cases.

Is it better to use a trimmer or a fixed resistor pair?

Fixed, wherever the accuracy allows. Trimmers drift with temperature and age, are sensitive to vibration, need a calibration step, and can fail open at the wiper. If the fixed pair is not accurate enough, a software calibration constant is usually cheaper and more stable than a trimmer.

Why do two resistors from the same batch work better together?

Because only the difference between their errors reaches the output — a drift they share cancels exactly. Resistors from one reel have correlated tolerances and nearly identical temperature coefficients, so the ratio is more stable than either value.