Capacitors in Series: formula & calculator

- in some instances capacitors may appear in series and it is necessary to be able to calculate the value.

Capacitance Tutorial Includes:
Capacitance     Capacitor formulas     Capacitive reactance     Parallel capacitors     Series capacitors     Dielectric constant & relative permittivity     Dissipation factor, loss tangent, ESR     Capacitor conversion chart    

There are several instances where capacitors may be required to be placed in series. In some circuits, this occurs naturally, for example in some oscillators there may be a capacitor AC voltage divider. In other instances capacitors may be placed in series for a variety of reasons and some examples are given below.

Although the most common combination is to see two capacitors in series, it is possible to place three or more in series.

Series capacitors formula

If capacitors are placed in parallel this is a bit akin to increasing the size of the capacitor plates and hence the values of capacitors in parallel can simply be added together. If the capacitors are in series, they cannot simply be added.

Capacitors connected in series.
Capacitors connected in series

In theory there is no limit to the number of capacitors that can be added in series. Obviously there can be practical limits dependent upon the application, space and other physical limitations.

When capacitors are connected in series, the total capacitance can be determined by taking the reciprocal of the capacitance of each capacitor, and adding these together to give the reciprocal of the total capacitance.

1 C Total = 1 C 1 + 1 C 2 + 1 C 3   .   .   .   .   .

Two capacitors in series

When calculating the general case for the total capacitance value for a series of capacitors in series, the computation can be a little long winded if done manually. As most networks, only two capacitors are placed in series and it is possible to considerably simplify the formula. This makes manual computation very much easier.

Two capacitors connected in series.
Two capacitors connected in series

C Total = C 1   C 2 C 1 + C 2

Capacitors in series calculator

The calculator below provides the total capacitance for two capacitors in series. The capacitance can be entered as Farads, µfarads, nanofarads, or picofarads, provided that the same units are used for both capacitors. The answer is provided in the same units as those entered.

Series Capacitor Calculator

Enter Capacitance Values:

C1:   Farads, F;
C2:   Farads, F;


Ctotal:   Farads, F

Precautions for using capacitors in series

Although capacitors do appear in series in a number of circuit configurations like oscillators and the like, capacitors may be used in series to increase the working voltage.

When two capacitors are used in series, then the issue is often that the two capacitors do not share the voltage equally. Differences in leakage current occur between capacitors, especially for capacitors like electrolytic versions and this means that the voltages across the two capacitors can differ greatly, and as a result one may be subject to an over-voltage conditions which could result in the destruction of one or both capacitors. This can occur if the two capacitors have been placed in series to provide an increase in working voltage.

A difference in leakage current can easily result from minor differences in the manufacture, or even differences n the rate at which the two capacitors age – the leakage current in electrolytic capacitors increases with time, especially if they are not used.

Two capacitors connected in series with resistor voltage divider to even voltages.
Two capacitors connected in series with resistor voltage divider

To assist in sharing the voltage equally across the two capacitors, high value resistors are placed around the capacitors as a potential divider. Values may be of the order 100kΩ or possibly even a little higher, but enough so that the voltages can reliably be divider across both capacitors.

In essence the values of the two resistors should be such that the current flowing through them is at least ten times higher than that of the leakage current. In this way, the voltage will be shared more equally across the capacitors in series. Even when this approach is applied it is good to leave a good margin in the working voltage, especially when electrolytic capacitors are used.

Connecting capacitors in series occurs in many circuits. Knowing how to calculate the overall value, even if it is a rough calculation in your head is very useful. If a more accurate value is needed then the online series capacitor calculator can be very useful.

More Basic Concepts:
Voltage     Current     Resistance     Capacitance     Power     Transformers     RF noise     Decibel, dB     Q, quality factor    
    Return to Basic Concepts menu . . .