Capacitance of Various Geometries Calculator

C = epsilon_0 x epsilon_r x A / d, where A is the plate area, d is the separation, epsilon_0 is the permittivity of free space, and epsilon_r is the dielectric's relative permittivity. This is the simplest and most commonly used capacitance formula in introductory electronics.

C = 4 x pi x epsilon_0 x epsilon_r x (r1 x r2) / (r2 - r1), for two concentric conducting spheres of inner radius r1 and outer radius r2 with dielectric filling the gap between them. This models an idealized spherical capacitor geometry.

C = 2 x pi x epsilon_0 x epsilon_r x L / ln(r2/r1), for two concentric cylindrical conductors of length L, inner radius r1, and outer radius r2. This is the same formula used to compute the capacitance per unit length of coaxial cable.

The electric field between concentric cylinders falls off as 1/r moving outward, and integrating 1/r to find the voltage between the two radii produces a natural logarithm term, ln(r2/r1), which is why cylindrical (and coaxial) capacitance scales with the log of the radius ratio rather than the ratio itself.

As r2 approaches infinity with r1 fixed, the spherical capacitance formula approaches C = 4 x pi x epsilon_0 x epsilon_r x r1, the capacitance of a single isolated sphere relative to a conductor infinitely far away. This is a classic limiting case used to introduce the concept of self-capacitance.

Parallel-plate geometry describes most ceramic, film, and multilayer capacitors, while cylindrical (coaxial) geometry describes coaxial cables and some wound capacitor constructions. Spherical geometry is mostly a teaching tool and a model for isolated charged conductors, true spherical capacitors are uncommon in practice.

In all three geometries, capacitance scales linearly with the relative permittivity epsilon_r of the material filling the gap between conductors, a higher-permittivity dielectric always increases capacitance proportionally, regardless of which geometry it fills.

The parallel-plate formula assumes a perfectly uniform field between infinite plates, ignoring the fringing (edge) field that exists at the boundary of any real, finite-sized plate. It becomes progressively less accurate as the plate separation grows relative to the plate dimensions.

Yes, set L to 1 meter (or any unit length) in cylindrical mode and the result gives capacitance per that length, which is exactly how coaxial cable capacitance is normally specified (for example, in picofarads per meter or per foot).

Plate area is in square centimeters, lengths and separations in millimeters, and relative permittivity is dimensionless. All capacitance results are reported in picofarads.