About

Miscalculating total capacitance in a circuit leads to incorrect filtering, failed timing circuits, and damaged components. Series configurations reduce total capacitance below the smallest individual unit - a non-obvious result that catches beginners. This calculator computes total capacitance for series and parallel networks of up to 50 capacitors, normalizing all values to Farads internally before output. It also derives X_c (capacitive reactance), stored energy E, charge Q, and RC time constant τ using standard IEEE conventions. Results are snapped to the nearest E12 standard value for practical component selection.

The tool assumes ideal capacitors with zero ESR and no dielectric absorption. For electrolytic capacitors above 1000 μF, real-world tolerance can reach ±20% - factor this into your design margin. All reactance calculations assume sinusoidal AC excitation at the specified frequency.

Formulas

Total capacitance for capacitors connected in parallel (direct sum):

C_total = C₁ + C₂ + … + C_n

Total capacitance for capacitors connected in series (reciprocal sum):

1C_total = 1C₁ + 1C₂ + … + 1C_n

Capacitive reactance at frequency f:

X_c = 12πfC

Energy stored in a capacitor charged to voltage V:

E = 12CV²

Charge stored:

Q = C ⋅ V

RC time constant:

τ = R ⋅ C

Where: C = capacitance in F, V = voltage in V, f = frequency in Hz, R = resistance in Ω, X_c = reactance in Ω, E = energy in J, Q = charge in C, τ = time constant in s.

Reference Data

E12 Standard Value	Tolerance	Common Types	Typical Voltage Rating	Temperature Range
1.0 pF	±5%	C0G/NP0 Ceramic	50 V	−55 to 125 °C
10 pF	±5%	C0G/NP0 Ceramic	50 V	−55 to 125 °C
100 pF	±5%	C0G/NP0 Ceramic	100 V	−55 to 125 °C
1.0 nF	±10%	X7R Ceramic	50 V	−55 to 125 °C
10 nF	±10%	X7R Ceramic	50 V	−55 to 125 °C
100 nF	±10%	X7R / Film	50 V	−55 to 125 °C
1.0 μF	±10%	MLCC / Film	25 V	−40 to 85 °C
10 μF	±20%	MLCC / Electrolytic	25 V	−40 to 85 °C
100 μF	±20%	Electrolytic / Polymer	16 V	−40 to 105 °C
470 μF	±20%	Electrolytic	16 V	−40 to 105 °C
1000 μF	±20%	Electrolytic	25 V	−40 to 105 °C
2200 μF	±20%	Electrolytic	25 V	−40 to 105 °C
4700 μF	±20%	Electrolytic	35 V	−40 to 85 °C
10000 μF	±20%	Electrolytic	50 V	−25 to 85 °C
0.1 F	±20%	Supercapacitor (EDLC)	2.7 V	−40 to 65 °C
1.0 F	±20%	Supercapacitor (EDLC)	5.5 V	−40 to 65 °C

Frequently Asked Questions

In series, each capacitor stores the same charge Q, but the voltage divides across them. The reciprocal sum formula 1C_total = 1C₁ + 1C₂ guarantees the result is smaller than any individual term. For two equal capacitors of 100 μF in series, the result is 50 μF. This is the inverse behavior of resistors in parallel.

Ceramic C0G/NP0 types hold ±5% tolerance, while standard electrolytics reach ±20%. In a series chain of 4 electrolytics, worst-case error compounds. If each is 100 μF ±20%, actual total ranges from 16.0 to 30.0 μF instead of the nominal 25 μF. Always design with margin for tolerance stack-up in timing and filter circuits.

Reactance X_c = 12πfC drops with rising frequency. A 100 nF capacitor at 1 kHz presents 1592 Ω, but at 1 MHz only 1.59 Ω. For decoupling, choose capacitance so X_c is well below 1 Ω at the switching frequency. Above self-resonant frequency, the component behaves inductively.

The voltage across a charging capacitor follows V(t) = V_s(1 − e^−t/τ) where τ = RC. After 1τ the capacitor reaches 63.2% of supply voltage. After 5τ it reaches 99.3%. For a 1000 μF capacitor with 1 kΩ resistor, τ = 1 s, and full charge takes approximately 5 s.

Yes, the formulas apply regardless of type. However, mixing electrolytics with ceramics introduces different ESR, temperature drift, and aging characteristics. In parallel filter banks, the ceramic handles high-frequency ripple while the electrolytic handles bulk energy storage. In series, voltage distribution depends on capacitance ratios - a smaller capacitor sees a larger voltage share, which can exceed its rating. Always verify individual voltage ratings against the divided voltage.

The E12 series defines 12 preferred values per decade: 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2. Manufacturers produce capacitors in these values. If your calculation yields 37.5 nF, no such component exists - the nearest E12 value is 33 nF or 39 nF. The tool shows this so you can select a real purchasable component.