Circuit Analysis & Fundamentals
Series/Parallel Capacitance & Inductance Calculator
Equivalent capacitance or inductance for series or parallel combinations — with the inverse-vs-resistor rules made explicit so you never mix them up.
About this calculator
Capacitors and inductors combine by rules that are easy to swap by mistake, because capacitors behave oppositely to resistors. Capacitors in PARALLEL add directly (C_eq = C1 + C2 + …) — more plate area stores more charge — while capacitors in SERIES combine reciprocally (1/C_eq = 1/C1 + 1/C2 + …), so the series equivalent is smaller than the smallest capacitor. Inductors, by contrast, follow the SAME pattern as resistors: series inductances add, and parallel inductances combine reciprocally.
This calculator applies the correct rule for the component type and topology you choose, across up to four elements, and shows the summed terms so you can see the combination rather than trust a result. Pick capacitance or inductance, pick series or parallel, enter the values in convenient units (µF/nF/pF or mH/µH/H), and read the equivalent.
The single most common error in this corner of circuits is reaching for the resistor rule when combining capacitors: adding series capacitors as if they summed, or treating parallel capacitors reciprocally. The mnemonic that helps: capacitors are 'backwards' from resistors, inductors are 'the same' as resistors. If your series-capacitor answer came out larger than the smallest capacitor, you used the wrong rule — the tool's worked steps show which formula applies so the mistake is caught before it propagates into a filter or timing calculation.
Design notes & common mistakes
- Capacitors are BACKWARDS from resistors: parallel capacitors ADD (more plate area), series capacitors combine RECIPROCALLY (smaller than the smallest).
- Inductors are the SAME as resistors: series adds, parallel is reciprocal.
- Quick check: a series-capacitor or parallel-inductor equivalent must be smaller than the smallest element. If it isn't, you used the resistor rule by mistake.
- Series capacitors share charge but split voltage inversely to their value — the smallest capacitor sees the most voltage, which matters for voltage ratings.
Assumptions
- Ideal capacitors or inductors — no equivalent series resistance, leakage, or mutual coupling between inductors.
- Values combine purely by topology; frequency does not enter the equivalent value itself.
- Elements are exact; tolerance and temperature coefficient are not applied.
When to use this calculator
Appropriate for
- Combining capacitors or inductors in a single series or parallel group
- Checking which combination rule applies before a filter or timing calculation
- Teaching why capacitors combine oppositely to resistors
Not suitable for
- Mixed series-parallel networks without stage-by-stage reduction
- Frequency-dependent impedance behavior (use the AC impedance calculator)
- Coupled inductors or real components where parasitics dominate
What this calculator does not cover
- Ideal elements only — no ESR/ESL, dielectric leakage, core saturation, or inductor mutual coupling.
- Up to four elements in a single series or parallel group; mixed networks must be reduced group by group.
- Gives the equivalent value only, not the frequency-dependent impedance (see the AC impedance tool for that).
- No voltage/current rating or tolerance analysis.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
How do capacitors combine in series and parallel?
Capacitors in parallel add directly (C_eq = C1 + C2 + …). Capacitors in series combine reciprocally (1/C_eq = 1/C1 + 1/C2 + …), making the series equivalent smaller than the smallest capacitor. This is the opposite of how resistors behave.
How do inductors combine in series and parallel?
Inductors follow the same rules as resistors: series inductances add (L_eq = L1 + L2 + …), and parallel inductances combine reciprocally (1/L_eq = 1/L1 + 1/L2 + …), assuming no mutual coupling between them.
Why are capacitors 'backwards' from resistors?
Because capacitance scales with plate area and inversely with plate spacing. Paralleling capacitors effectively adds plate area, so capacitance adds; putting them in series effectively increases the spacing, so the combined capacitance drops. Resistance depends on length and area the opposite way, giving the reversed rules.
References
- Nilsson, J. & Riedel, S., Electric Circuits, 11th ed. (series/parallel capacitors and inductors)
- Sadiku, M., Fundamentals of Electric Circuits, 6th ed. (capacitance and inductance combinations)
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