Capacitors In Series Calculator

What the capacitors in series calculator does

When capacitors are wired in series, their combined capacitance is less than any one of them, following a reciprocal rule. This calculator finds the equivalent capacitance of up to ten capacitors connected in series.

Below is what series capacitors do, the equation behind it, why the total shrinks, and a worked example.

How to use it

1. Enter the value of the first capacitor, choosing its unit.
2. Add more capacitors as needed, up to ten.
3. Press Calculate for the equivalent capacitance, or Reset to clear it.

What capacitors in series do

Capacitors are in series when they are connected end to end, one after another, so that the same charge passes through each in turn. This is the second of the two basic ways to connect capacitors, and it behaves oppositely to the parallel connection. Where parallel capacitors add up to a larger total, series capacitors combine to a smaller one, ending up with less capacitance than even the smallest capacitor in the chain.

This might seem backward at first, since stacking things usually adds up, but it makes sense once you see what series connection does to the geometry. Putting capacitors in series is like increasing the distance between the plates of a single capacitor, and a wider gap means less capacitance, not more. So the chain stores less charge at a given voltage than any one capacitor would. What series connection gains instead is the ability to withstand a higher voltage, since the voltage is shared among the capacitors. This calculator computes the reduced combined capacitance for any series chain.

The equation it uses

For capacitors in series, the reciprocals of the capacitances add, and the reciprocal of that sum is the total:

1 ÷ C_total = 1 ÷ C₁ + 1 ÷ C₂ + …

So you add up one over each capacitance, then take one over the result. This is the same reciprocal form that governs resistors in parallel, which is the mirror-image symmetry between the two components. For just two capacitors, it works out to the product over the sum, but the calculator uses the general reciprocal rule so it can combine any number of capacitors in series at once and give the single equivalent value.

Why the total is always smaller

Just as resistors in parallel always combine to less than the smallest, capacitors in series always combine to less than the smallest capacitor in the chain. Adding another capacitor in series, however large, lowers the total capacitance further. You cannot build up capacitance by stacking capacitors in series; doing so only reduces it.

The reason is the widening effective gap. Each capacitor in the series chain adds to the effective separation between the outermost plates, and since capacitance falls as the gap grows, more capacitors in series means less capacitance. Put two equal capacitors in series and you get exactly half of one; put three in series and you get a third. This is the opposite of the parallel case, where equal capacitors would double or triple the total. Because of this, series connection is rarely used just to set a capacitance value, but it is valuable when a higher voltage rating is needed, and the calculator shows exactly how much the combined capacitance drops.

Sharing the voltage

If series connection lowers the capacitance, why use it at all? The answer is voltage rating. Every capacitor can withstand only so much voltage before it breaks down, and when capacitors are placed in series, the applied voltage is divided among them rather than falling entirely across one. This means a series chain can safely handle a higher total voltage than any single capacitor in it could on its own.

This is the main practical reason to wire capacitors in series: to build a combination rated for a higher voltage. The trade-off is the reduced capacitance, which is the price paid for the higher voltage tolerance. The voltage does not necessarily split evenly, depending on the capacitor values, which is something designers watch carefully, but the basic benefit is real. So while this calculator focuses on the resulting capacitance, it is worth remembering that the series arrangement is usually chosen for its voltage-handling advantage, with the lower capacitance accepted as part of the bargain.

Units and precision

The calculator takes each capacitance in farads or its smaller multiples, from millifarads down to picofarads, and handles up to ten capacitors at once. It applies the reciprocal rule exactly and presents the equivalent capacitance in a sensible unit. Because series combinations always reduce the capacitance, the total will sit below your smallest capacitor, which is a useful check on the result.

A worked example

Suppose you connect a 10-microfarad capacitor and a 22-microfarad capacitor in series.

The total is 1 ÷ C_total = 1/10 + 1/22, which gives C_total ≈ 6.875 microfarads, less than either capacitor, as expected for a series combination. Two equal 10-microfarad capacitors in series would instead give exactly 5 microfarads, half of one. The gain, in return for this lower capacitance, is a combination that can withstand a higher voltage.

Questions people ask

How do you calculate capacitors in series?

Add the reciprocals of the capacitances and take the reciprocal of the sum: 1 ÷ C_total = 1/C₁ + 1/C₂ + ….

Why is the series total smaller than each capacitor?

Because series connection widens the effective gap between the outer plates, and capacitance falls as the gap grows. The total is always less than the smallest capacitor.

Why connect capacitors in series?

Mainly for a higher voltage rating. The voltage divides among the capacitors, so the chain withstands more total voltage than any one, at the cost of lower capacitance.

What about just two capacitors?

For two, the total is the product divided by the sum: C₁C₂ ÷ (C₁ + C₂). Two equal capacitors in series give exactly half their value.

References

A quick note on where the physics comes from. Capacitors in series and the reciprocal rule are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 8.2, Capacitors in Series and in Parallel. https://openstax.org/books/university-physics-volume-2/pages/8-2-capacitors-in-series-and-in-parallel
2. HyperPhysics, Capacitor Combinations. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capac.html
3. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811