Resistors and capacitors in series and parallel

Two components of the same kind side by side make a third value, and the arithmetic depends on which kind they are. Resistors in series add; capacitors in series do not. That single asymmetry is behind most of the wrong answers in this corner of electronics, so this page works out the arrangement you asked for and prints the other one next to it, with as many parts on the list as you care to type.

How it is calculated

Series R = R₁ + … + Rₙ · Parallel R = 1 ÷ (1/R₁ + … + 1/Rₙ) · capacitors take the other one

A resistor resists, so putting two in a row resists more and the values add. A capacitor stores, and its plates are what store — putting two side by side is a bigger plate, so it is capacitors in parallel that add. Wire capacitors in a row instead and you are stacking the gaps between the plates, which does the same thing to capacitance as parallel does to resistance: the reciprocals add.

Source: Texas Instruments — Analog Engineer's Pocket Reference, fifth edition (SLYW038D, April 2025): Series resistors, equation (17): RT = R1 + R2 + ⋯ + RN, and parallel capacitors, equation (28): Ct = C1 + C2 + … + CN

Questions people ask

Why do capacitors add the opposite way round to resistors?

Because capacitance grows with plate area and shrinks with the distance between the plates. Two capacitors in parallel share their terminals, which is one wider plate, so the values add. In series the gaps stack instead, and the total falls below the smallest part — exactly what parallel does to resistors. The formulas are not arbitrary; they follow from which physical quantity is being added.

Can the total ever be bigger than the largest part?

Only in the arrangement that adds directly. Resistors in parallel and capacitors in series always come out below the smallest value on the list, no matter how many parts there are — a useful sanity check on any answer you get from anywhere, including here.

How do I write 4.7 kΩ?

As 4.7 with the unit set to kΩ, not as 4,700. Commas separate parts on the list, so a comma inside a number splits it into two components. Everything on the list is read in the unit you pick, so keep the whole list in one unit and let the answer come back in whichever prefix suits it.

Does this account for tolerance?

No, and neither does the arithmetic. Combining ten 1 % resistors does not give a 1 % result in any simple way, though parallel combinations of equal parts do average their errors out. If the value matters to better than the tolerance of the parts, measure the ones in front of you.

What about the voltage and current ratings?

They do not combine the way the values do, and this page does not touch them. Resistors in series each take a share of the voltage but the same current; in parallel it is the other way round. Capacitors in series share voltage in inverse proportion to their capacitance while they charge, which is why stacked electrolytics are given balancing resistors.

Sources

The documents this page reads its numbers out of, linked so you can check them yourself.

1. Texas Instruments — Analog Engineer's Pocket Reference, fifth edition (SLYW038D, April 2025): Series resistors, equation (17): RT = R1 + R2 + ⋯ + RN, and parallel capacitors, equation (28): Ct = C1 + C2 + … + CN
2. NIST SP 811 (2008), Table 5, SI prefixes — mega denotes the factor 10^6

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