Parallel-plate capacitor capacitance

What does this quantity describe?

A capacitor stores a charge Q = C·U proportional to the applied voltage U. For an idealized parallel-plate capacitor with plate area A and spacing d, capacitance follows from C = ε0·εr·A/d, where ε0 is the electric constant of vacuum and εr is the relative permittivity of the material between the plates.

Picture the parallel-plate capacitor as a flat, elastic water reservoir: a larger area holds more water (charge) at the same pressure (voltage), while a larger gap between the plates lowers capacitance, similar to a thinner, more elastic reservoir holding less volume at the same pressure. The dielectric between the plates further raises capacitance, similar to a material that yields more easily to the electric field.

Formula and variables

C = ε0 · εr · A/d; E = ½·C·V²

• C = ε0·εr·A/d
• Q = C·U
• E = ½·C·U²

Choose the inputs correctly

Plate area A, spacing d and relative permittivity εr set the capacitance; adding a voltage U gives stored charge and energy. εr = 1 corresponds to air or vacuum; for solid dielectrics such as ceramic or plastic film, use current manufacturer data since εr is strongly material-dependent.

How to use the calculator

Select the target quantity. For capacitance, enter A, d and εr; for stored energy, additionally enter voltage U. To find the plate spacing or area needed for a target capacitance instead, choose that quantity as the target.

Worked example

A 100 cm² plate area, 1 mm spacing and air as dielectric (εr = 1) give C = 8.854·10⁻¹² · 1 · 0.01 m² / 0.001 m ≈ 88.5 pF. At 100 V this stores Q = C·U ≈ 8.85 nC of charge and E = ½·C·U² ≈ 0.443 µJ of energy.

Understand the result and units

A capacitance of 88.5 pF is typical for small discrete air or trimmer capacitors; practical filter or bypass capacitors in the nanofarad-to-microfarad range instead need either far larger areas, much smaller spacings, or — usually more economically — a high-permittivity dielectric such as ceramic.

Plate area is often given in cm², spacing in mm, and the resulting capacitance falls in the picofarad-to-nanofarad range for typical lab-scale dimensions; stored energy is usually given in µJ or mJ.

Why does a real capacitor deviate from the ideal model?

The formula C = ε0·εr·A/d assumes the electric field is uniform only in the region between the plates, as if the plates were infinitely large. At the real, finite plate edges the field bulges outward (fringing), which slightly raises actual capacitance above the bare formula. This effect grows as spacing increases relative to the plate dimensions, and is usually negligible in practice when spacing stays small compared with plate area.

Typical applications

The relationship explains how trimmer and variable capacitors work, how capacitive sensors translate a change in d or A into a capacitance change (for example proximity or pressure sensors), and supports basic sizing of PCB capacitor structures.

Assumptions, limits and common mistakes

The model assumes a uniform electric field confined to the region between infinitely extended, exactly parallel plates. Real capacitors with finite plate area show additional fringing-field effects at the edges that slightly increase actual capacitance above this model, especially when spacing is not small compared with the plate dimensions. Dissipation factor, temperature effects on εr and parasitic capacitance of neighboring traces are not included.

Common mistake: A common mistake in manual hand calculation is not converting units consistently to SI — the formula needs A in m² and d in m (the calculator handles this conversion automatically). It is also easy to overlook that εr is in reality frequency- and temperature-dependent, and catalog values usually apply only over a specific frequency range.