Capacitance Formula

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The capacitance formula

Capacitance is defined as C = Q / V: the charge stored per volt, measured in farads (F). For two flat parallel plates, capacitance depends only on geometry and the material between them: C = εr ε0 A / d, where A is the plate area in square metres, d the gap in metres, ε0 the permittivity of free space (8.854 × 10⁻¹² F/m) and εr the relative permittivity (dielectric constant) of the insulator. Bigger plates, a smaller gap and a higher-permittivity dielectric all increase capacitance.

Formula summary

Series and parallel

Capacitors in parallel add directly, because together they behave like one capacitor with a larger plate area. In series, the effective gap grows, so the total is less than the smallest capacitor: add the reciprocals and take the reciprocal of the sum. For two capacitors in series, C = C1C2 / (C1 + C2). This is the opposite of resistors, which add in series.

Worked examples

• Parallel plates: two 100 cm² plates 1 mm apart in air give C ≈ 1.0006 × 8.854×10⁻¹² × 0.01 ÷ 0.001 ≈ 88.6 pF.
• Combinations: 10 µF, 22 µF and 47 µF give 79 µF in parallel and about 6.00 µF in series.
• Energy: a 470 µF capacitor charged to 25 V holds Q = 11.75 mC and E = ½ × 470×10⁻⁶ × 25² ≈ 0.147 J.
• RC: 10 kΩ with 100 µF gives τ = 1 s — about 5 s to charge almost fully.
• Codes: 104 means 10 × 10⁴ pF = 100,000 pF = 100 nF = 0.1 µF.

Reading capacitor codes

The first two digits are significant figures and the third is the number of zeros, in picofarads. A letter after the code gives tolerance: J = ±5%, K = ±10%, M = ±20%. Electrolytic capacitors usually print the value and voltage directly, such as 470 µF 35 V.

Dielectric constants

Charging and discharging

When a capacitor charges through a resistor, its voltage rises quickly at first and then more slowly: after one time constant (τ = RC) it reaches about 63.2% of the supply voltage, after two about 86.5%, after three 95%, and after five about 99.3%, which is usually treated as fully charged. Discharge follows the same curve downwards. These curves are the basis of timing circuits, debounce filters and the smoothing of power supplies.

Choosing a capacitor type

Ranges are typical and vary by manufacturer. Always check the voltage rating, and note that many ceramic capacitors lose a large part of their capacitance at high DC bias.

Capacitive reactance

In AC circuits a capacitor’s opposition to current falls as frequency rises: Xc = 1 / (2πfC). A 1 µF capacitor has a reactance of about 2,653 Ω at 60 Hz but only about 159 Ω at 1 kHz. That is why capacitors pass high frequencies and block DC, and why the cut-off frequency of an RC filter is 1 / (2πRC).

Safety note

Large capacitors can store dangerous energy long after power is removed — especially in power supplies, microwave ovens and camera flashes. Discharge capacitors safely with a suitable resistor before handling, never exceed the rated voltage, and observe polarity on electrolytic capacitors.

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