How do you solve a series-parallel capacitor network?

Reduce it from the inside out. Add the innermost parallel group, combine series groups with the reciprocal formula, and repeat until one value remains. It is the same procedure as for resistors with the two rules exchanged.

Do you calculate series or parallel capacitors first?

Whichever group is innermost — the one with nothing nested inside it. For a parallel pair in series with a third capacitor, the parallel pair is added first, then the series step is applied to the result.

Why is my mixed capacitor total smaller than the individual capacitors?

Because a series element is in the path. Series capacitance is always less than the smallest capacitor involved, and that limit applies to the equivalent value of a whole parallel bank just as much as to a single part. Three 100 nF capacitors as a parallel pair in series with the third give 66.6667 nF.

How is voltage distributed in a mixed capacitor network?

Section by section. Across a series section it divides in inverse proportion to capacitance, so the smallest part sees the most. Within a parallel bank every part sees the same voltage, and the bank is limited by its lowest-rated member.

Can a capacitor network be too complex for this method?

Yes, in the same way as resistors: only series-parallel networks reduce step by step. A bridge arrangement of capacitors has no two parts sharing both nodes and needs mesh analysis or a simulator instead.

Mixed Series-Parallel Capacitance Calculator

Mixed series-parallel capacitor networks are solved by reducing them from the inside out, adding parallel groups and combining series groups reciprocally — the two rules reversed compared with resistors.

How to Reduce a Series-Parallel Capacitor Network

A mixed capacitor network is solved exactly like a mixed resistor network, with the two rules swapped. Collapse the innermost group, then the next, until one value remains. What changes is which rule applies where — and with capacitors it is the opposite of the resistive intuition most people bring.

The two rules being applied

C_{p a r a l l e l} = C_{1} + C_{2} + \dots + C_{n}

\frac{1}{C_{s e r i e s}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \dots + \frac{1}{C_{n}}

Parallel adds, series takes reciprocals. Writing both down before starting is worth the ten seconds: applying the resistor rules to a capacitor network produces an answer that looks plausible and is wrong.

A parallel pair in series with a third capacitor

For the commonest shape — two capacitors in parallel, that bank in series with a third — the reduction is:

C_{e q} = \frac{(C_{1} + C_{2}) \times C_{3}}{C_{1} + C_{2} + C_{3}}

Add the parallel bank first, then apply product-over-sum to the series pair.

The worked example below runs this with three identical 100 nF capacitors and lands on 66.6667 nF — less than one of them. That result surprises people, and it is the series rule dominating: a series element can only reduce the total, however much capacitance is sitting in a parallel bank next to it.

Worked example

Given

C1 = 100 nF ∥ C2 = 100 nF
that bank in series with C3 = 100 nF

Working

Step 1 — the parallel pair adds:
C1 ∥ C2 = 100 nF + 100 nF = 200 nF
Step 2 — the series combination uses reciprocals:
Ceq = (200 × 100) / (200 + 100) nF = 20000 / 300 nF

Answer66.6667 nF

Three identical 100 nF capacitors, and the answer is 66.6667 nF — less than one of them. That is the series rule dominating the result.

Where Mixed Capacitor Networks Appear

Capacitive dividers and voltage sensing

A capacitive divider measures high AC voltages without the dissipation a resistive divider would have. The lower leg is often several capacitors in parallel to reach a value, and that bank is in series with the high-voltage capacitor — a mixed network by construction.

High-voltage banks

Series strings for voltage rating, paralleled for capacitance and ripple current, give the series-parallel arrays found in flash units, motor drives and pulsed supplies. The array is designed by both rules at once: series sets the voltage the bank withstands, parallel sets the energy it stores.

Crystal and oscillator load networks

A crystal specifies a load capacitance which the two loading capacitors present in series, with stray and pin capacitance in parallel with each. Getting the total right is what puts an oscillator on frequency, and it is a mixed-network calculation.

Reading the Network Correctly

The rules for identifying series and parallel are the same as for resistors, and the consequences of misreading them are larger, because the two capacitor rules move the answer in opposite directions.

In parallel: both ends of both capacitors join the same two nodes.
In series: they share one node, and nothing else connects to it.
Get it backwards on a pair of 100 nF parts and you will calculate 200 nF instead of 50 nF — a factor of four.

The schematic above is drawn from the network you enter, so it doubles as a check on your reading of the circuit. If the drawing does not match the board, the number will not either.

Voltage and Rating in a Mixed Bank

Working out the equivalent capacitance is the easy half. Deciding what each part has to withstand needs the voltage distribution as well, and the two rules differ again:

Across a series section, voltage divides in inverse proportion to capacitance — the smallest capacitor takes the most.
Within a parallel bank every capacitor sees the same voltage, so the bank is limited by its lowest-rated member.
Series electrolytics need balancing resistors, whether or not they sit inside a larger mixed network.

So a mixed bank has to be checked section by section. A part can be well inside its rating in one branch and over it in another, even in a network whose total capacitance is exactly what the design called for.

Common mistakes

Applying the resistor rules. With capacitors, parallel adds and series takes reciprocals — the reverse of resistors.
Adding the series capacitor before collapsing the parallel bank. The innermost group goes first, always.
Expecting the answer to be larger than the parts, because a parallel bank is involved. A series element in the path can pull the total below every single capacitor.
Checking only the total capacitance and not the voltage across each section.
Forgetting balancing resistors on series electrolytics inside a larger network.
Leaving stray and pin capacitance out of an oscillator load network, where a few picofarads shift the frequency.

Frequently asked questions

How do you solve a series-parallel capacitor network?: Reduce it from the inside out. Add the innermost parallel group, combine series groups with the reciprocal formula, and repeat until one value remains. It is the same procedure as for resistors with the two rules exchanged.
Do you calculate series or parallel capacitors first?: Whichever group is innermost — the one with nothing nested inside it. For a parallel pair in series with a third capacitor, the parallel pair is added first, then the series step is applied to the result.
Why is my mixed capacitor total smaller than the individual capacitors?: Because a series element is in the path. Series capacitance is always less than the smallest capacitor involved, and that limit applies to the equivalent value of a whole parallel bank just as much as to a single part. Three 100 nF capacitors as a parallel pair in series with the third give 66.6667 nF.
How is voltage distributed in a mixed capacitor network?: Section by section. Across a series section it divides in inverse proportion to capacitance, so the smallest part sees the most. Within a parallel bank every part sees the same voltage, and the bank is limited by its lowest-rated member.
Can a capacitor network be too complex for this method?: Yes, in the same way as resistors: only series-parallel networks reduce step by step. A bridge arrangement of capacitors has no two parts sharing both nodes and needs mesh analysis or a simulator instead.

Assumptions and limitations for Mixed Series-Parallel Capacitance Calculator are listed on the About page. Every worked example on this site is checked against the same solver the calculator uses.