Voltage divider calculator for real E-series resistors

One problem with resistive dividers is to find a couple of resistors that will give a required potential division ratio. This problem comes from the fact that resistors only exist in discrete sets of standard values depending on their tolerance. Those sets are called 'E series', and denoted as E followed by the number of resistors in one decade. Well, you probably know all this already if you arrived on this page... Anyway, with only discrete values available it is not trivial to find the pairs of resistors that yield a ratio close to the one you want. Hence this nifty tool :-) Usage is pretty simple: just type in the I/O voltages or the desired division ratio, select the E series you are working with and you will get a list of the best 12 matches. The tolerance of the voltage divider is also calculated 1, which is a unique feature of this tool. Several options are provided. You can also set min/max values for Rtot, which will adjust the resistor pairs to the proper range/decade. If you have entered an input or output voltage then the current flowing in the divider and the resulting dissipated power will be shown, and their boundaries can be set. Finally the circuit load can be specified, which can have a big impact on which optimal resistor pair is selected. Note that scientific notation can be used (e.g. 123.45e-6) but only values within [1e-15, 1e+15] are accepted throughout (in particular, no negative or zero). The smallest value that can be entered is 1e-15. There is (primitive) input validation to help you there. Please spread the word by linking/sharing this page and do get in touch if you found a bug or have a suggestion. :-) Last updated on June 3rd, 2023

Notes:

1. The tolerance in the dividing ratio, which is not identical to the one of the resistors, is shown in the 'Tolerance' column. Using resistive dividers with small ratios (e.g. 0.01) will result in an uncertainty on the ratio that is larger than the tolerances of the individual resistors. You may want to rethink your design or add a trimmer to calibrate your divider if you really need a very small ratio (also watch out for thermal effects and other ways ppms can escape!). Another solution is to use a tighter tolerance for the smaller resistor. For example, trying to get a ratio of 0.012 with 5% resistors (E24) will result in an uncertainty in the resulting ratio of around 7%. On the other hand, ratios close to 1.0 will result in a much smaller tolerance. For example, a ratio of .98 has a low tolerance of 0.14% when using 5% resistors. In other words: small ratios are bad for tolerance, large ratios are good. The tipping point is around 1-sqrt(0.5)=0.293 where resistors and ratio tolerances are equal.
2. The requested ratio should obviously be between zero and one. Do not put something under 0. Weird things may happen. Like the destruction of the universe. Or worse. Math is powerful, be careful. Values over 1 are considered as "division factors" and will be automatically inverted. The ratio input is ignored and recalculated from V_in and V_out if the latter two inputs are provided.
3. E24 values can be found in higher precisions than just 5%. If this option is selected then values of E24 not present in the selected series will also be used. This is obviously only valid for E series > 24. For example: 270 ohm is part of E24 but not of E96; ticking this option with the E96 series will add 270 ohm (among others) to the E96 list of possible resistor values.
4. Ratio tolerances are not calculated when only custom values are used. When combined with an E series, custom values are supposed to have the same tolerance as the E series. Custom values that are part of the selected E series will still be highlighted (in light blue) like other custom values. This can be used to highlight specific / preferred values without actually adding new custom values. When custom values are used, the best 5 resistor pairs not in the top 12 and which include at least one of your custom values will also be shown. This can help assess how good resistor pairs that use your custom values are compared to the overall best pairs.
5. You can get the current estimation if you supply (a) both voltages, and thus no ratio or (b) a division ratio and one of V_in or V_out. If you supply both voltages and the division ratio then the latter is ignored and the calculation falls back to the (a) case.
6. In some circuits V_out is fixed, for example when the voltage divider is used in the feedback loop of a DC/DC converter. In such case the DC/DC control IC will set its output (the top of the divider) to whatever is needed to keep V_out (the middle of the divider, connected to the IC feedback input) equal to a fixed internal reference, typically around 1.2V. The V_in column shows what the input of the divider will be when such external circuit 'fixes' V_out to the exact value you have entered. This is simply the inverse calculation: V_in = V_out / ratio = V_out (R_H+R_L)/R_L. Note that the best resistor pair, and thus the ordering of the table, remains the same irrespective of whether you look at the V_out or V_in column.

Random thoughts:

• What is usually asked to students in school is "Calculate the voltage at the output of this circuit given R_L=100k and R_H=150k", but in real life a designer faces the inverse problem: "Given this ratio I want, which resistors am I going to choose?". This makes this problem - and thus this tool - particularly interesting because it solves the real life equivalent of the trivial question everyone had to answer at school. And the real life problem is a bit more complex :-)
• Speaking about beginners: the values for R_L and R_H returned by this tool can of course be both multiplied by a constant and the ratio of the divider will not change. This scaling will let you change the impedance of the divider to match your current needs, for example.
• I did this small program for a problem with an analog/digital converter (ADC). It was a 10bit ADC fed by the output of a resistive divider (factor 1/10). Maximum input for the ADC was 10V. 10 bits means 1023 steps, so the LSB of the results was close (but not equal!) to 10mv (10V/1023 ~ 10mV). To have it equal to 10mv I wanted to add the 1000/1023 factor in the upstream divider. So instead of a 1/10 divider I was now looking for 1/10.23 = 0.097752. Which, as it turns out, can be obtained almost exactly by using two simple 3K9 and 36K resistors.
• Numberphile time: you can reach the ratio of pi/10 with 6 decimals accuracy by using 284 and 620 ohm resistors (E192 with extra E24 values). Similarly, 1/pi can be estimated with 4 significant digits using 390 and 835 ohm resistors. It should be noted that these seemingly very accurate results will not be seen in real life due to the tolerance of the resistors which result in a ~0.7% tolerance in the ratio of the divider (E192, 0.5%). See Note 1 above. Still, this could be a way to get the value of pi in an analog computer. Or impress your friends in a youtube video.

TODO list:

• Use the tolerance to only keep the meaningful decimals of values like the ratio, V_out, current and power
• Capacitor divider anyone? Or generalize to any impedance?

Special thanks:

• Uwe Schueler for spotting that the range of proposed values was incorrectly limited.
• Michael Bendzick for spotting a few bugs and providing many interesting suggestions.
• Synco Reynders for spotting an error in the tolerance calculation. Top tip: the python package 'uncertainties' is an excellent tool for those who want to play with tolerances.
• Alex Whittermore for suggesting the R_tot and current columns.
• Marc André Duverney for suggesting the R_tot min/max inputs.
• Piotr Wyderski for suggesting the current boundaries inputs.
• Jeff Gough for spotting a nasty value formatting bug (yet another one!) and suggesting the V_out and V_in columns.