How this calculator works
Concentric conductors create a radial electric field. Integrating that field across the gap gives voltage, and charge divided by voltage gives capacitance. Narrower gaps and larger permittivity increase capacitance. The dielectric must fill the gap uniformly; mixed layers require a different integration. As the outer radius grows without bound, the result approaches the capacitance of an isolated conducting sphere.
Formula
C = 4 pi epsilon0 er a b/(b-a), with 0 < a < b; a = Cb/(C+4 pi epsilon0 er b); b = Ca/(C-4 pi epsilon0 er a).
Worked example
Vacuum-separated spheres with radii 0.1 and 0.2 m have capacitance about 22.2530 pF. A uniform dielectric with relative permittivity 2 doubles it to about 44.5060 pF.
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Frequently asked questions
Which outer radius should I measure?
Use the inner surface of the outer conducting shell, because that bounds the dielectric gap.
Can I choose a dielectric by name?
Enter its measured or specified relative permittivity. Values can vary with frequency, moisture and temperature.
Why can an outer-radius inverse fail?
For fixed inner radius, the finite-shell capacitance must exceed the isolated-sphere limit.