Electric Field Between Parallel Plates Calculator

The electric field between two parallel plates carrying opposite charge and separated by a uniform gap is E = V/d, where V is the voltage across the plates and d is the separation distance. This uniform field approximation holds well when the plate area is large compared to the gap.

C = epsilon_0 x epsilon_r x A / d, where epsilon_0 is the permittivity of free space, epsilon_r is the dielectric's relative permittivity, A is the plate area, and d is the separation. Capacitance increases with larger plate area or smaller separation, and with a higher-permittivity dielectric.

The charge stored on each plate is Q = CV, directly proportional to both the capacitance and the applied voltage. This is the same fundamental relationship that defines capacitance for any capacitor geometry, not just parallel plates.

The energy stored in a charged capacitor is U = 0.5 x C x V^2 (equivalently 0.5 x Q x V or 0.5 x Q^2/C). This represents the work done to charge the capacitor against the growing electric field between its plates.

Energy density u = 0.5 x epsilon_0 x epsilon_r x E^2 is the energy stored per unit volume of the field region, it depends only on the field strength and the dielectric, making it a useful measure for comparing energy storage efficiency independent of the specific plate dimensions.

Since E = V/d, for a fixed voltage the field is inversely proportional to the separation distance, halving the gap concentrates the same potential difference over half the distance, doubling the field strength. This is why capacitors with very thin dielectrics can achieve very high fields at modest voltages.

Relative permittivity epsilon_r describes how much more a material can be polarized by an electric field compared to vacuum (epsilon_r = 1). Common dielectrics used in real capacitors, ceramics, polymers, tantalum oxide, have epsilon_r values ranging from around 2 up to several thousand for high-permittivity ceramics.

Every dielectric material has a maximum electric field, its dielectric strength, beyond which it breaks down electrically (arcing or permanent damage). Air breaks down at roughly 3 MV/m at standard conditions, solid dielectrics used in real capacitors typically sustain far higher fields, which is part of why they allow much higher capacitance and voltage ratings in a compact size.

This calculator uses the idealized infinite-parallel-plate approximation, which depends only on total plate area, not shape, for real finite plates the field near the edges (fringing field) differs from the uniform interior field, becoming more significant when the separation is not small compared to the plate dimensions.

Voltage is in volts, plate separation in millimeters, and plate area in square centimeters. Results are reported in MV/m (electric field), picofarads (capacitance), nanocoulombs (charge), nanojoules or microjoules (energy), and joules per cubic meter (energy density).