How to Calculate Capacitance
What Capacitance Means
Capacitance is the ability of a component to store electric charge per unit of voltage, measured in farads (F). The defining relationship is C = Q / V, where Q is the stored charge in coulombs and V is the voltage across the capacitor in volts. One farad is an enormous amount of capacitance; practical capacitors range from picofarads (pF, 10⁻¹²) to millifarads (mF, 10⁻³). A 100 µF capacitor charged to 5 V stores 500 µC of charge.
Reading Capacitor Markings
Ceramic and film capacitors use a 3-digit code where the first two digits are significant figures and the third is the power-of-ten multiplier in picofarads. A marking of "104" means 10 × 10⁴ pF = 100,000 pF = 100 nF = 0.1 µF. Electrolytic capacitors print the value directly (e.g., "100 µF 25 V"). Always note the voltage rating — exceeding it will destroy the capacitor and can cause it to vent or rupture.
Capacitors in Parallel
When capacitors are connected in parallel, their capacitances add directly: C_total = C1 + C2 + C3 + .... This is because parallel connection increases the effective plate area. Two 10 µF capacitors in parallel give 20 µF. Parallel combinations are used when a larger capacitance is needed than a single component can provide, or to combine a large bulk capacitor with a small high-frequency bypass capacitor.
Capacitors in Series
Capacitors in series combine like resistors in parallel: 1/C_total = 1/C1 + 1/C2 + 1/C3. For two capacitors, the shortcut is C_total = (C1 × C2) / (C1 + C2). Two equal 10 µF capacitors in series yield 5 µF, but the working voltage doubles. Series configurations are used to achieve higher voltage ratings from lower-rated components, though the capacitance is reduced.
Capacitance and RC Timing
One of the most important uses of capacitance is in RC timing circuits. The time constant τ (tau) = R × C determines how quickly a capacitor charges or discharges through a resistor. After one time constant, the capacitor reaches about 63.2% of its final voltage; after five time constants (5τ), it is considered fully charged (99.3%). A 10 kΩ resistor with a 100 µF capacitor gives τ = 10,000 × 0.0001 = 1 second.
Capacitive Reactance in AC Circuits
In AC circuits, capacitors present an impedance called capacitive reactance: Xc = 1 / (2π × f × C), where f is frequency in hertz and C is capacitance in farads. At higher frequencies, Xc decreases, meaning capacitors pass high-frequency signals more easily. At 1 kHz, a 1 µF capacitor has Xc = 1 / (2π × 1000 × 0.000001) ≈ 159 Ω. This frequency-dependent behavior is the basis of capacitive filters and coupling circuits.
Energy Stored in a Capacitor
The energy stored in a capacitor is given by E = ½CV², where E is in joules, C is in farads, and V is the voltage. A 1000 µF capacitor charged to 50 V stores E = 0.5 × 0.001 × 2500 = 1.25 joules — enough to deliver a painful shock. This energy storage property is exploited in camera flash circuits, power supply bulk filtering, and supercapacitor energy storage systems.