Adding Capacitors in Series
A capacitor is an electronic component that stores electric charge (electrical energy). Capacitors can be arranged in a circuit both in series and in parallel, depending on the application. This calculator helps you find the equivalent capacitance of up to 10 capacitors connected in series.
The Series Capacitance Formula
When capacitors are connected in series, the reciprocal of the total capacitance equals the sum of the reciprocals of each individual capacitance:
1/Ceq = 1/C1 + 1/C2 + … + 1/Cn
Or equivalently:
Ceq = 1 / (1/C1 + 1/C2 + … + 1/Cn)
A key consequence: the total capacitance is always smaller than the smallest individual capacitor in the chain.
Why Do Capacitors in Series Share the Same Charge?
Imagine a series circuit without any voltage source — each capacitor starts uncharged. When voltage is applied, electrons flow from the source. The outer plate of C1 gains charge +Q. Because the absolute charge on both plates of any capacitor must be equal but opposite, the inner plate carries −Q. This charge is induced from the adjacent capacitor, which therefore also holds charge +Q on its plate. This cascade continues through every capacitor in the chain, so every capacitor in series carries the same charge Q.
The total voltage, however, is distributed across the capacitors:
Vtotal = V1 + V2 + … + Vn
Since V = Q/C for each element, substituting gives the series formula above.
How to Use This Calculator
- Select the number of capacitors in the series circuit (2 to 10).
- Enter the capacitance value for each capacitor. Each field has its own unit selector (pF, nF, µF, mF, F) — you can mix units freely.
- Optionally, enter the total supply voltage to calculate the charge on the capacitors and the voltage drop across each one.
- Click Calculate. The result shows the equivalent capacitance in all standard units plus a step-by-step derivation.
Capacitance Units — Metric and American Systems
Capacitance is measured in farads (F) — the SI unit used worldwide in both metric and American engineering. Because the farad is very large for practical components, sub-multiples are almost always used:
| Symbol | Name | Value | Typical use |
|---|---|---|---|
| F | Farad | 1 F | Supercapacitors / ultracapacitors |
| mF | Millifarad | 10⁻³ F | Large electrolytic capacitors |
| µF | Microfarad | 10⁻⁶ F | Electrolytic and film capacitors |
| nF | Nanofarad | 10⁻⁹ F | Ceramic and film capacitors |
| pF | Picofarad | 10⁻¹² F | Small ceramic and RF capacitors |
Worked Example
Find the total capacitance of four capacitors in series: C1 = 2 mF, C2 = 5 µF, C3 = 6 µF, C4 = 200 nF.
Convert everything to farads:
- C1 = 2 × 10⁻³ F = 0.002 F
- C2 = 5 × 10⁻⁶ F
- C3 = 6 × 10⁻⁶ F
- C4 = 200 × 10⁻⁹ F = 2 × 10⁻⁷ F
Apply the formula:
1/Ceq = 1/0.002 + 1/0.000005 + 1/0.000006 + 1/0.0000002
1/Ceq = 500 + 200 000 + 166 666.7 + 5 000 000
1/Ceq ≈ 5 367 166.7 F⁻¹
Ceq ≈ 186.3 nF
Capacitors in Series vs. Parallel
The behavior of capacitors in series is analogous to resistors in parallel, and vice versa: capacitors in parallel behave like resistors in series. Key differences:
| Property | Series | Parallel |
|---|---|---|
| Charge (Q) | Same on all capacitors | Different (Qi = Ci·V) |
| Voltage | Splits across capacitors | Same across all capacitors |
| Ceq | Smaller than smallest C | Larger than largest C |
| Formula | 1/Ceq = Σ(1/Ci) | Ceq = ΣCi |
Practical Applications
- Voltage division — a series string divides the supply voltage across each capacitor, useful for withstanding high voltages when individual ratings are exceeded.
- Energy storage reduction — the equivalent capacitance is always smaller, limiting stored energy.
- 555 timer circuits — the 555 IC in astable mode uses capacitors in series to define timing intervals.
- Filter and tuning circuits — series capacitors set cutoff frequencies in RC and LC filters.
- RF and impedance matching — picofarad-range capacitors in series fine-tune impedance in antenna and RF circuits.