About

Capacitors in series produce a total capacitance C_total that is always less than the smallest individual capacitor in the chain. This is the inverse behavior of resistors in series. Miscalculating series capacitance leads to incorrect RC time constants, filter cutoff frequencies shifted by octaves, and coupling capacitors that attenuate signal below specification. This calculator computes C_total using the reciprocal-sum method across 2 to 20 capacitors with automatic unit normalization from pF through F.

The tool assumes ideal capacitors with zero equivalent series resistance (ESR) and no parasitic inductance. In practice, ESR and board-level parasitics become significant above 100 MHz. For electrolytic capacitors, derate the nominal value by 20% due to aging and temperature drift. Ceramic capacitors (Class II/III) lose up to 80% of rated capacitance under DC bias. Always verify with a capacitance meter on the assembled board.

Formulas

For n capacitors connected in series, the total equivalent capacitance C_total is computed by summing the reciprocals of each individual capacitance and then inverting the result:

1C_total = 1C₁ + 1C₂ + … + 1C_n

Which can be expressed compactly using summation notation:

C_total = 1n∑i=1 1C_i

For the special case of exactly two capacitors in series, the formula simplifies to:

C_total = C₁ × C₂C₁ + C₂

For n identical capacitors each of value C, the total reduces to:

C_total = Cn

The voltage across each capacitor C_k in a series chain with applied voltage V is inversely proportional to its capacitance:

V_k = V × C_totalC_k

Where: C_total = total equivalent capacitance in F. C_i = capacitance of the i-th capacitor. n = number of capacitors. V = total applied voltage in V. V_k = voltage across capacitor k.

Reference Data

Capacitor Type	Typical Range	Tolerance	ESR	Temp. Stability	Common Series Use
Ceramic (C0G/NP0)	0.5 pF - 100 nF	±1%	< 0.05 Ω	±30 ppm/°C	RF filters, timing
Ceramic (X7R)	1 nF - 10 μF	±10%	< 0.1 Ω	±15% over range	Decoupling, coupling
Ceramic (Y5V)	10 nF - 100 μF	+22/−82%	< 0.5 Ω	Poor	Bypass only
Film (Polyester)	1 nF - 10 μF	±5%	< 0.5 Ω	±5%	Audio coupling, timing
Film (Polypropylene)	100 pF - 1 μF	±1%	< 0.02 Ω	±2.5%	Snubbers, resonant circuits
Electrolytic (Aluminum)	0.1 μF - 1 F	±20%	0.1 - 5 Ω	Poor	Power supply filtering
Electrolytic (Tantalum)	0.1 μF - 1 mF	±10%	0.05 - 3 Ω	Moderate	Voltage division, timing
Mica (Silver)	1 pF - 10 nF	±1%	< 0.01 Ω	±50 ppm/°C	RF resonant tanks
Supercapacitor (EDLC)	0.1 F - 3000 F	±20%	0.3 - 50 Ω	Poor	Energy storage balancing
Glass	10 pF - 1 nF	±1%	< 0.01 Ω	±25 ppm/°C	Precision RF
Vacuum	1 pF - 5 nF	±5%	Negligible	Excellent	High-voltage RF transmitters
Paper	1 nF - 10 μF	±10%	1 - 10 Ω	Poor	Legacy motor-start circuits

Frequently Asked Questions

The reciprocal-sum formula guarantees this mathematically. Each term 1C_i adds a positive value to the denominator sum. Since C_total is the reciprocal of this growing sum, it must be smaller than any single C_i. Physically, series connection increases the effective dielectric thickness and electrode separation, reducing stored charge per volt.

Worst-case analysis: if each capacitor has ±10% tolerance, the series total can deviate more than ±10% because the reciprocal function is nonlinear. For a pair of 100 nF ±10% capacitors in series, C_total ranges from 40.5 nF to 60.5 nF (nominal 50 nF). Always perform Monte Carlo or RSS tolerance stacking for precision circuits.

Three primary use cases: (1) Voltage rating multiplication - two 25 V capacitors in series withstand 50 V (with balancing resistors). (2) Reducing effective capacitance below available discrete values - placing two 10 pF caps in series yields 5 pF. (3) DC blocking in signal chains where a single cap's self-resonance is insufficient and two smaller values extend bandwidth.

Yes, for electrolytic and film capacitors in DC applications. Leakage current varies between units, causing unequal voltage distribution. Without balancing resistors (typically 100 kΩ to 1 MΩ per cap), one capacitor may exceed its rated voltage and fail. Ceramic capacitors in RF/AC circuits generally do not require balancing due to negligible DC leakage.

ESR values add directly in series: ESR_total = ESR₁ + ESR₂ + … This increases total impedance and power dissipation. For power supply filtering where low ESR is critical, series capacitor configurations are generally avoided. Each additional series element adds its ESR plus PCB trace resistance.

Yes. Each capacitor row has an independent unit selector supporting pF, nF, μF, mF, and F. All values are internally normalized to Farads before applying the reciprocal-sum formula. The result is then displayed in the most readable unit automatically (e.g., a result of 4.7 × 10⁻⁹ F displays as 4.7 nF).