Capacitors in Series Calculator
Calculate the equivalent capacitance of up to 4 capacitors wired in series. Input values in nanofarads (nF). Also shows the parallel equivalent.
How to use this tool
- Enter capacitor c₁, capacitor c₂, capacitor c₃ (optional) and capacitor c₄ (optional) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your series capacitance and the full breakdown beneath it.
For capacitors in series: 1/C = 1/C₁ + 1/C₂ + …. Series combination reduces capacitance (opposite to resistors). For capacitors in parallel: C = C₁ + C₂ + …
Formula
1/Cs = 1/C1 + 1/C2 + 1/C3 + 1/C4
Series equivalent: Cs = 1 ÷ (1/C1 + 1/C2 + …). Parallel reference: Cp = C1 + C2 + …
How it works
Capacitors in series share the same charge on each plate, so the reciprocal of the total capacitance equals the sum of reciprocals of individual capacitances — the opposite behaviour to resistors. The calculator sums 1/C for every non-zero input and inverts to get the series equivalent. A parallel sum is provided for reference.
All values are entered and returned in nanofarads (nF), rounded to 5 decimal places. The formula assumes ideal capacitors; real capacitors have tolerances, equivalent series resistance (ESR), and leakage currents not captured here.
Worked example
Worked example
- Given: C₁ = 10 nF, C₂ = 10 nF.
- Sum of reciprocals: 1/10 + 1/10 = 0.1 + 0.1 = 0.2.
- Series capacitance: Cₛ = 1 / 0.2 = 5.0 nF.
- Parallel capacitance (reference): Cₚ = 10 + 10 = 20 nF.
Series capacitance = 5 nF; Parallel capacitance = 20 nF.
Key terms
- Capacitance
- The ability of a component to store electric charge per unit voltage, measured in farads (F). 1 nF = 10⁻⁹ F.
- Series capacitors
- Capacitors connected end-to-end so the same charge accumulates on each plate pair; the total capacitance is always less than the smallest individual value.
- Parallel capacitors
- Capacitors sharing the same voltage across their terminals; total capacitance is the sum of individual capacitances.
- Nanofarad (nF)
- A unit of capacitance equal to 10⁻⁹ F, commonly used for small capacitors in electronics.
- Equivalent series resistance (ESR)
- A real-world parasitic resistance in a capacitor that causes energy loss, not modelled by the ideal series formula.
Frequently asked questions
- Why does series wiring reduce capacitance?
- Each capacitor in series adds to the effective gap between plates, reducing the ability to store charge. It is the mirror image of parallel resistors.
- When would I wire capacitors in series?
- To increase the voltage rating of a capacitor bank, or to achieve a smaller capacitance than any available single component.