Capacitors in Series & Parallel: details, equations & calculator

Understand how capacitors can be connected in series or parallel and why, how to calculate the overall capacitance and some practical circuit considerations.

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

In a variety of areas of electrical and electronic circuit design, installation and use, it can be necessary to place capacitors in series with each other, or in other instances in parallel.

In these instances it is necessary to be able to calculate the total capacitance of the series and parallel capacitor combinations.

There are some easy calculations to use, and also we have included a calculator for calculating the value of two capacitors in series with each other.

Parallel capacitors formula

It is very easy to calculate the total capacitance of a set of capacitors in parallel. The total value is simply the sum of the capacitance values of the individual capacitors.

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

The overall value of a number of capacitors placed in parallel is simple the sum of the values. This can be expressed on the formula given below:

C_{Total} = C_{1} + C_{2} + C_{3} . . . . . .

Reasons for using capacitors in parallel

There are several reasons why it may be beneficial to place capacitors in parallel:

To obtain non-preferred capacitance value: Like many components, capacitors come in preferred values. For some applications, specific values may be required that may not coincide with the preferred values, or with those that might be available. Almost any value can be made from combining two or more preferred values, although be aware that some capacitors wide tolerance levels so the final value will be subject to these figures.
Increase value of capacitor: The most obvious reason for having two or more capacitors in parallel is to increase the value of capacitance available. It may be convenient to use two or more capacitors of a smaller value than a single larger one. Again availability may be an issue and require the use of two capacitors in parallel.
Utilise different capacitors for decoupling different frequencies: A single capacitor is not always able to remove all the frequencies that may be present on a voltage supply line etc. To fully achieve this, it is often the practice to use tow capacitors in parallel: one such as an electrolytic with a larger value to remove the low frequency components (the electrolytic capacitor is not good at passing high frequency signals); and one such as a ceramic capacitor with a smaller value for removing the high frequency components (the smaller ceramic capacitor will not have a low enough reactance to pass the low frequency components).

When using this approach it is necessary to be aware of the effects of spurious series inductance because it is possible for the stray inductance from one capacitor to resonate with the capacitance of the second. These effects do not normally cause a problem, but running two capacitors in parallel can give rise to these combined effects.
Distributed decoupling: On many logic boards where there are many logic ICs it is common practice to distribute the decoupling around the board, typically having a capacitor on each IC, or possibly every other IC, and larger decoupling capacitors placed strategically around the circuit. It is necessary in circumstances like these to be able to calculate the overall capacitance level. Although each capacitor may not be large, the sum of all the capacitors on the board can add up. It is always wise to calculate the total value of all the capacitors in parallel.

Placing capacitors in parallel can provide the advantages detailed above. Using capacitors in parallel provides additional flexibility in their use.

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.

\frac{1}{C_{Total}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} . . . . .

Two capacitors in series

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.

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} = \frac{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

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.