Capacitor Size Calculator

The capacitor size calculator gives you the capacitance required to handle a given voltage in an electric motor, considering a specific start-up energy.

Capacitance3.099 nFε₀ × 3.5 × 100 cm² ÷ 0.1 mm

Charge stored at 50 V154.9483 nC9.671e+11 electrons

Energy stored3.8737 µJ

Electric field in the gap500 kV/m0.5 MV/m — dry air breaks down around 3 MV/m, and this is why thin gaps need good dielectrics

Energy density in the field3.874 J/m³½ε₀ε_r E²

Without the dielectric885.4188 pF3.5× smaller — the dielectric is doing exactly that much of the work

At half the gap6.1979 nFdouble the capacitance, but also double the field, so the voltage rating halves

Magnetic energy density at 1 T3.979e+5 J/m³B² ÷ 2µ₀

Magnetic against electric density1.027e+5×a 1 T field stores far more energy per cubic metre than any practical electric field, which is why energy storage rings are magnetic

The formula

C = ε₀ε_r A ÷ d; Q = CV; E = ½CV²; u = ½ε₀E²

Thin gaps, and why they limit voltage

A parallel-plate capacitance is proportional to plate area and inversely proportional to the gap. Halving the gap doubles the capacitance — but it also doubles the electric field for the same voltage, so the voltage rating halves. That trade is the central constraint in capacitor design, and it is why a high-capacitance part is usually a low-voltage one.

The dielectric does real work. Its molecules polarise and partly cancel the applied field, letting more charge sit at the same voltage. Relative permittivity measures that, running from 1 for vacuum through about 3.5 for paper to several thousand for some ceramics — though the high-value ceramics are strongly voltage and temperature dependent, which is why they are unsuitable for precision work.

Dry air breaks down at roughly 3 MV/m, so a 0.1 mm air gap arcs at about 300 V. Solid dielectrics withstand ten to a hundred times more, which is the other reason they are used.

Comparing energy densities is illuminating: a 1 tesla magnetic field stores far more energy per cubic metre than any electric field that will not arc. That asymmetry is why large-scale energy storage uses magnetic fields and inertia rather than capacitors.