Spherical Capacitor Calculator

The Spherical Capacitor Calculator evaluates the capacitance of two concentric spheres with a dielectric between them, or of a single isolated sphere relative to infinity.

How to Use Spherical Capacitor Calculator

Choose the geometry — concentric shells or isolated sphere.
Enter the radii — inner radius a and outer inner radius b for shells, or radius R for an isolated sphere.
Enter εr — relative permittivity of the medium between the conductors.
Read C — automatically scaled to pF, nF or μF.

Formula & Theory — Spherical Capacitor Calculator

C_shell = 4π · ε₀ · εr · a · b / (b − a)
C_isolated = 4π · ε₀ · εr · R
ε₀ = 8.854187817 × 10⁻¹²  F/m

Use Cases for Spherical Capacitor Calculator

Physics teaching — illustrate Gauss’s law applied to spherical symmetry.
High-voltage hardware — estimate capacitance of spherical electrodes and Van de Graaff terminals.
EMC studies — model conductors approximated as spheres.
Sensor design — analyse capacitive sensors with spherical electrodes.

Frequently asked questions about Spherical Capacitor Calculator

Why does capacitance grow as b → a?

As the gap shrinks, the field per unit charge stays high while the volume of dielectric drops — the structure stores more charge for the same voltage.

What is an isolated sphere capacitance?

It is the capacitance of a sphere measured against a hypothetical electrode at infinity — the limit of the spherical capacitor as b → ∞.

Does dielectric loss matter?

For DC analysis no. For AC use the complex permittivity εr·(1 − j·tan δ).

Is my data stored?

No. All calculations run locally in your browser; nothing is sent to any server.