Whether you are designing a power-supply bypass network, tuning a resonant LC filter, or simply replacing a capacitor bank, knowing the equivalent capacitance of a group of components is a fundamental step. This calculator applies the exact textbook formulas for both parallel and series configurations, shows the full working, and converts the answer into every common capacitance unit.
How it works
Capacitance is measured in farads (F). In practice, most discrete capacitors are in the picofarad (pF, 10⁻¹² F), nanofarad (nF, 10⁻⁹ F), or microfarad (µF, 10⁻⁶ F) range, so the calculator accepts any of those plus millifarads (mF) and farads.
Capacitors in parallel
When capacitors are connected in parallel — positive terminals tied together, negative terminals tied together — each one sees exactly the same voltage V. The charge stored by each is Q_i = C_i × V, and the total charge is the sum of all individual charges. Dividing through by V:
C_total = C1 + C2 + … + Cn
This is a direct addition: the more capacitors you add in parallel, the larger the equivalent capacitance. Parallel banks are the standard technique for achieving large capacitance values (e.g., many electrolytic capacitors in a power-supply bulk stage) or for reducing ESR (equivalent series resistance) by sharing current.
Capacitors in series
When capacitors are connected in series — end to end — the same charge Q is deposited on every capacitor (conservation of charge on the floating inner plates). Each capacitor develops a voltage V_i = Q / C_i, and the total voltage is the sum of all individual voltages. Dividing through by Q:
1/C_total = 1/C1 + 1/C2 + … + 1/Cn
Rearranging: C_total = 1 ÷ (1/C1 + 1/C2 + … + 1/Cn). This is identical in form to the parallel-resistance formula. The series equivalent is always smaller than the smallest capacitor — two equal capacitors in series give exactly half the capacitance of one. Series strings are used where a higher working voltage is needed (voltage distributes across each cap) or to synthesize very small capacitance values.
Worked example
Suppose you have three capacitors: 100 µF, 47 µF, and 10 µF.
Parallel:
C_total = 100 + 47 + 10 = 157 µF
The parallel combination stores more charge than any individual capacitor.
Series:
1/C_total = 1/100 + 1/47 + 1/10 = 0.01 + 0.021277 + 0.1 = 0.131277 µF⁻¹
C_total = 1 / 0.131277 ≈ 7.62 µF
The series combination is smaller than the smallest individual capacitor (10 µF).
| Configuration | 100 µF + 47 µF | 100 µF + 47 µF + 10 µF |
|---|---|---|
| Parallel | 147 µF | 157 µF |
| Series | ≈ 31.97 µF | ≈ 7.62 µF |
Formula note
These formulas are derived from two fundamental capacitor equations: Q = CV (charge equals capacitance times voltage) and Kirchhoff’s voltage law. They are exact for ideal capacitors. Real capacitors also have parasitic equivalent series resistance (ESR), equivalent series inductance (ESL), and dielectric absorption — factors this calculator does not model but which matter at high frequencies or in precision timing circuits.
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