Capacitors combine the opposite way to resistors. Enter your capacitor values in microfarads to get the equivalent capacitance for series and parallel connections.
Enter capacitance values in µF.
Read the parallel and series totals.
Parallel: Cp = C₁ + C₂ + …
Series: 1/Cs = 1/C₁ + 1/C₂ + …
Capacitors store electric charge, and like resistors they can be combined to make a different effective value. The rules, however, are the reverse of the resistor rules. Capacitors in parallel simply add, while capacitors in series combine through reciprocals and give a total smaller than any one of them. This calculator takes a list of capacitances in microfarads and returns both the parallel and the series equivalent, formatting very small results in nanofarads or picofarads.
The topic is part of the Class 12 electrostatics chapter and a practical need in electronics, where you may want a value your parts box lacks, or a higher voltage rating than a single capacitor offers.
1. Convert every value to microfarads: 1 nF = 0.001 µF and 1 pF = 0.000001 µF.
2. Parallel: add them, Cp = C₁ + C₂ + C₃ + ….
3. Series: add the reciprocals, 1/Cs = 1/C₁ + 1/C₂ + 1/C₃ + ….
4. Take the reciprocal of that sum to get Cs.
5. For two in series: Cs = C₁C₂ ÷ (C₁ + C₂).
6. For series strings, work out the voltage on each capacitor, Vᵢ = Q ÷ Cᵢ, and check it against its voltage rating.
A capacitor holds charge Q = CV. Connected in parallel, all capacitors share the same voltage V, so each stores C₁V, C₂V and so on. The total charge is (C₁ + C₂ + …)V, which is what a single capacitor of value C₁ + C₂ + … would hold. Physically, connecting plates side by side is like making one capacitor with a larger plate area, and capacitance is proportional to area. That is why parallel capacitances add directly, the same way series resistances do.
In a series chain, the charge that leaves one plate must arrive on the next, so every capacitor carries the same charge Q. The voltages Q/C₁, Q/C₂ and so on add up to the total V. So V = Q(1/C₁ + 1/C₂ + …), which gives 1/Cs = 1/C₁ + 1/C₂ + …. Series is like increasing the gap between plates, and capacitance falls as the gap grows. The smallest capacitor takes the largest share of the voltage, which is critical when voltage ratings are close to the limit.
Electrolytic capacitors, common for values above about 1 µF, are polarised: reversing them can make them fail, sometimes violently. Their tolerance is often wide, ±20% being common, so the calculated total is only approximate. When capacitors are put in series to handle a higher voltage, their unequal leakage can upset the voltage sharing, so designers often add equal balancing resistors across each one. The energy stored, ½CV², is also worth checking: a large capacitor bank can hold a dangerous charge after power is removed.
Vikram is repairing a speaker crossover and has capacitors of 4.7 µF, 10 µF and 2.2 µF on hand. He wants to know the values he could make by joining all three in parallel or all three in series.
Parallel: add them: 4.7 + 10 + 2.2 = 16.9 µF
Series: add reciprocals: 1/Cs = 1/4.7 + 1/10 + 1/2.2 = 0.76731141 Cs = 1.303252 µF
Answer: Parallel 16.9 µF; Series 1.3033 µF
Using the resistor rules the wrong way round, adding capacitors directly when they are in series.
Mixing nF and µF values in one list without converting.
Assuming a series string can handle the sum of the individual voltage ratings without checking how the voltage actually divides.
Connecting polarised electrolytic capacitors the wrong way round.
Expecting precise results from capacitors with ±20% tolerance.
Making up a non-standard capacitance from parts on hand.
Class 12 physics problems on combinations of capacitors.
Building capacitor banks for power supplies and motor-start circuits.
Designing timing and filter circuits that need specific values.
Getting a higher working voltage by connecting capacitors in series with balancing resistors.
Why connect capacitors in series?
To handle a higher voltage than a single capacitor's rating, at the cost of lower capacitance.
Can I mix units?
Convert everything to µF first; 1 nF = 0.001 µF.