Capacitor calculator

A parallel-plate capacitor stores charge on two conducting faces of overlapping area A separated by a gap d filled with a linear dielectric whose absolute permittivity is epsilon. The textbook identity C equals epsilon times A divided by d converts those three SI quantities into capacitance in farads, which students, sensor designers, and RF layout teams use when checking homework, sizing sense electrodes, or sanity-checking a board stack-up against a simple analytic baseline. Send absolute permittivity in farads per metre, not a unitless dielectric constant.

What parallel-plate capacitance means and how C equals epsilon A over d

An ideal parallel-plate capacitor is two conductors whose facing surfaces overlap over an area A and sit a uniform distance d apart, with a linear isotropic dielectric filling the volume between them. Introductory electrostatics shows that the electric field in the gap is sigma over epsilon when fringing is neglected, so the potential difference is that field times d, and the stored charge over that potential is C equals epsilon times A divided by d.

Epsilon here is the absolute permittivity of the filler, measured in farads per metre, not the unitless relative permittivity that many data sheets print as kappa or epsilon-r. Vacuum uses the electric constant epsilon-zero, about eight point eight five four times ten to the minus twelve farads per metre; dry air is almost the same; plastics, ceramics, and glass use larger epsilon because their relative permittivity multiplies epsilon-zero.

This calculator takes that absolute epsilon as an explicit input so a physics notebook that already computed epsilon equals epsilon-zero times kappa does not have the engine silently multiply again. Plate area is the overlapping face in square metres: a ten-by-ten centimetre pair is one hundredth of a square metre, and a plate that hangs past the other does not count the overhang. Separation is the perpendicular gap in metres; a one millimetre drawing dimension is zero point zero zero one metres.

The model assumes a gap much smaller than the plate width so edge fields can be ignored, a uniform dielectric, and electrostatic conditions with no leakage conductance.

When the parallel-plate formula is enough

Classrooms and tutoring platforms use a capacitor calculator so learners can check C equals epsilon A over d for arbitrary SI triples without dropping a power of ten on the millimetre-to-metre conversion. Sensor and PCB designers size sense electrodes and stack-up gaps against this analytic baseline before running a full field extractor, which is slower and not always available in a notebook. Lesson builders produce SI-unit capacitance checks for demos, auto-graded drills, and lab write-ups without embedding an electromagnetic solver.

Prefer this landing when you already have absolute permittivity in farads per metre and you want the ideal plate formula; if you only have a unitless dielectric constant, multiply by epsilon-zero yourself and send the product as permittivity. Fringing, multilayer stacks, and frequency-dependent dielectrics are outside the ideal formula, so treat the result as the classic textbook baseline rather than a 3D extraction. Failed validation does not consume balance.

Keep classroom centimetre plates and millimetre gaps inside ordinary SI magnitudes, pin the rounded capacitance in tests, and you get reproducible electrostatic arithmetic for homework, LMS plugins, and edge workers without standing up a field solver of your own.