Parallel Plate Capacitor

C = ε₀ × εr × A / d

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Formula

C = ε₀ × εr × A / d

Description

The capacitance of a parallel plate capacitor is directly proportional to the plate area and the dielectric constant, and inversely proportional to the plate separation. The vacuum permittivity ε₀ = 8.854 × 10⁻¹² F/m is a fundamental physical constant. The relative permittivity εr (dielectric constant) of the material between the plates multiplies the capacitance: air has εr ≈ 1, FR-4 PCB material εr ≈ 4.5, ceramic capacitor dielectrics range from 6 (C0G/NP0) to over 10,000 (Y5V). This formula also applies to parasitic capacitance in PCB traces, connectors, and IC packaging.

Variables

  • C — Capacitance (F)
  • εr — Relative permittivity of the dielectric (dimensionless)
  • A — Overlapping plate area (m²)
  • d — Distance between plates (m)

Practical Notes

MLCC (multilayer ceramic capacitors) achieve high capacitance in small packages by stacking hundreds of thin dielectric layers in parallel. A 100-layer capacitor with each layer 2µm thick and 1mm² area using X7R ceramic (εr ≈ 3000) gives about 133 nF. Parasitic capacitance between PCB traces is typically 0.5-1 pF/cm for adjacent traces on the same layer.

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