What is the formula for a parallel-plate capacitor?

C = ε₀·εᵣ·A / d, where ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space, εᵣ is the relative permittivity (dielectric constant) of the material between the plates, A is the plate area in square metres, and d is the separation in metres. Doubling the area doubles C; doubling the gap halves C.

How much energy does a capacitor store?

Energy W = ½·C·V², or equivalently ½·Q·V or Q²/(2C). All three formulas give the same result — choose the one matching the variables you already know. A 470 µF capacitor charged to 12 V stores ½ × 470×10⁻⁶ × 144 ≈ 33.8 mJ.

What is the RC time constant?

τ = R·C in seconds. It is the time for a capacitor to charge to about 63.2% of the supply voltage through a series resistor, or to discharge to about 36.8% of its initial voltage. A 10 kΩ resistor with a 100 µF capacitor gives τ = 1 s; after 5τ (5 s) the capacitor is considered fully charged (99.3%).

Do capacitors in parallel add directly?

Yes. For capacitors in parallel, C_total = C₁ + C₂ + … + Cₙ. Parallel connection increases total capacitance because the effective plate area increases while separation stays the same. In contrast, capacitors in series follow 1/C_total = 1/C₁ + 1/C₂ + …, giving a smaller result than the smallest individual capacitor.

What units are used for capacitance?

The SI unit is the farad (F), named after Michael Faraday. In practice, most capacitors are far smaller: 1 µF = 10⁻⁶ F, 1 nF = 10⁻⁹ F, 1 pF = 10⁻¹² F. The calculator automatically picks the most readable unit for the answer.

What dielectric constant should I use for my material?

Typical relative permittivity (εᵣ) values: vacuum = 1 exactly, air ≈ 1.0006, polyethylene ≈ 2.3, paper ≈ 3.5, epoxy (PCB) ≈ 4.4, glass ≈ 7, barium titanate ceramics 1 000–10 000, pure water ≈ 80. Higher εᵣ gives higher capacitance for the same geometry.

Capacitance Calculator

Capacitance governs how much charge a component stores for a given voltage, and it appears in everything from the smoothing caps in a phone charger to the gate dielectrics in modern CMOS transistors. This calculator covers the five most common capacitance problems in a single tool, with full step-by-step working and automatic unit conversion from picofarads through to farads.

How it works

The calculator is split into five tabs, each targeting a different formula or use-case.

Parallel-plate uses the classic geometry formula C = ε₀·εᵣ·A / d. Enter the relative permittivity of the dielectric, the plate area in square metres, and the separation in metres — the tool multiplies by the permittivity of free space (ε₀ = 8.854×10⁻¹² F/m) and expresses the result in the most convenient sub-unit.

Q = C·V is the fundamental capacitor equation linking charge (coulombs), capacitance (farads) and voltage (volts). Select which variable to solve for and fill in the other two.

Energy offers all three equivalent stored-energy formulas: W = ½·C·V², W = ½·Q·V, and W = Q²/(2C). They are algebraically identical; pick whichever pair of inputs you already have.

RC Time Constant computes τ = R·C (or rearranges for R or C). The working panel also shows the time to reach 63.2% charge (one τ) and the conventional “fully charged” time of five τ.

Series/Parallel accepts up to four capacitor values and combines them correctly: parallel uses direct addition, series uses the reciprocal-sum rule.

Worked example — RC filter design

Suppose you need a low-pass RC filter with a cut-off frequency of 1 kHz. The time constant you need is τ = 1/(2π·f) ≈ 159 µs. If you have a 10 kΩ resistor available, what capacitor do you need?

Open the RC Time Constant tab, select “Capacitance C (given τ, R)”, enter τ = 0.000159 s and R = 10 000 Ω.

C = τ / R = 1.59×10⁻⁴ / 10 000 = 15.9 nF

The nearest standard E12 value is 15 nF; the nearest E24 value is 15 nF or 18 nF. Plug that back in to confirm the actual cut-off frequency.

Formula reference

Formula	Variables	Use
`C = ε₀·εᵣ·A / d`	permittivity, area, gap	Parallel-plate geometry
`Q = C·V`	charge, capacitance, voltage	Fundamental charge relation
`W = ½·C·V²`	energy, capacitance, voltage	Stored energy
`τ = R·C`	time constant, resistance, capacitance	RC charging/discharging
`C_p = C₁ + C₂ + …`	parallel capacitances	Parallel combination
`1/C_s = 1/C₁ + 1/C₂ + …`	series capacitances	Series combination

Physical constants used: ε₀ = 8.854 187 817 × 10⁻¹² F/m.

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