# Spherical Capacitor Calculator

URL: https://speedycalculator.com/calculators/physics/spherical-capacitor/
Last updated: 2026-10-30

> The spherical capacitor calculator finds the capacitance of two concentric conducting spheres separated by a dielectric, and of an isolated sphere.

## Inputs

- Inner sphere radius a (cm, mm, m, in, ft)
- Outer sphere radius b (cm, mm, m, in, ft)
- Dielectric
- Relative permittivity ε_r

## Results

- Capacitance C
- Isolated inner sphere

## Formula

```
C = 4π·ε₀·ε_r·a·b / (b − a)  (isolated sphere: b → ∞, C = 4πε₀ε_r·a)
```

## Explanation

A spherical capacitor is the textbook example of Gauss's law in action. Van de Graaff generators are essentially isolated spheres; the Earth itself has a capacitance of about 710 µF.

### How to use the Spherical Capacitor Calculator

- **Inner sphere radius a**
- **Outer sphere radius b**
- **Dielectric**
- **Relative permittivity ε_r**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the inner and outer radii and choose the dielectric between them.

### Inputs explained

FieldWhat to enterInner sphere radius aUnits: cm, mm, m, in, ftOuter sphere radius bUnits: cm, mm, m, in, ftDielectricChoose one: Vacuum, Air, PTFE, Polyethylene …Relative permittivity ε_rA number

### What each result means

- **Capacitance C** = 4×pi×8.8541878128e-12×[er]×[Inner sphere radius a]×[Outer sphere radius b]÷([Outer sphere radius b] - [Inner sphere radius a])
- **Isolated inner sphere** = 4×pi×8.8541878128e-12×[er]×[Inner sphere radius a]

### Example values

How the main result changes when **Inner sphere radius a** changes and everything else stays at the example values above:

Inner sphere radius a (cm)Capacitance C (pF)2.53.70883.756.6759511.12656.2518.54427.533.3795

## Worked example

Inputs — Inner sphere radius a: 5 cm; Outer sphere radius b: 10 cm; Dielectric: Vacuum.

Results — **Capacitance C = 11.1265 pF**; Isolated inner sphere = 5.56325 pF.

## Key terms

- **Concentric spheres**: Spheres sharing the same centre.

## FAQ

**What is the capacitance of an isolated sphere?**
4πε₀a – about 111 pF per metre of radius.

**What is Earth's capacitance?**
About 710 µF.

**Why must b be larger than a?**
The outer sphere encloses the inner one.

**How does the dielectric change C?**
It multiplies it by ε_r.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)