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Parallel Plate Capacitor Calculator

Calculate the capacitance of a parallel-plate capacitor from plate area, gap and dielectric (C = ε₀εᵣA/d), plus the charge, electric field, surface charge density and stored energy at a voltage.

Plate area (overlap)

Distance between the plates

Dielectric between the plates

Custom relative permittivity εᵣ

Voltage across the plates

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How it works

C = ε₀·εᵣ·A / d (ε₀ = 8.854 × 10⁻¹² F/m) · Q = C·V · E = V/d · σ = Q/A · U = ½·C·V²

Two parallel conducting plates separated by a thin insulator store charge when a voltage is applied. The capacitance grows with the overlapping plate area, shrinks as the gap widens and is multiplied by the dielectric constant εᵣ of the insulating material, which reduces the field for a given charge. The formula assumes the gap is small compared with the plate size, so fringing at the edges can be neglected. ε₀ is the CODATA 2018 vacuum permittivity; the derivation is in OpenStax University Physics Vol. 2, section 8.2.

Worked example

Two plates of 100 cm² (0.01 m²) are 1 mm apart in vacuum. C = 8.854 × 10⁻¹² × 1 × 0.01 / 0.001 = 88.54 pF. At 100 V each plate holds Q = 8.854 nC, the field is 100 / 0.001 = 100.0 kV/m, the surface charge density is 885.4 nC/m² and the stored energy is ½ × 88.54 pF × 100² = 442.7 nJ.

Sources: OpenStax University Physics Vol. 2 — Capacitors and Capacitance · NIST CODATA — vacuum electric permittivity ε₀

Frequently asked questions

How do I increase the capacitance?

Use larger plates, a thinner gap or a dielectric with a higher εᵣ. Rolling long strips of foil and film, or stacking many layers as in ceramic capacitors, packs a huge area into a small volume.

What does the dielectric do?

Its molecules polarise and partly cancel the field between the plates, so more charge can be stored at the same voltage: the capacitance is multiplied by εᵣ.

Is the formula exact?

It ignores fringing fields at the plate edges, so it is accurate when the gap is much smaller than the plate width. For wide gaps the real capacitance is slightly higher.

What limits the voltage?

The dielectric strength: air breaks down at about 3 kV/mm, PTFE around 60 kV/mm. Compare the electric field result with the material’s strength.

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This calculator is for educational purposes. Double-check important results before acting on them.