Capacitance of a Cylindrical Capacitor

The Capacitance of a Cylindrical Capacitor calculator computes the capacitance of a capacitor that has two coaxial cylindrical shells.  

INSTRUCTIONS: Choose units and enter the following:

• (L) - Length of the cylinders
• (a) - Radius of the smaller cylinder
• (b) - Radius of the larger cylinder
• (ε_r) - Dielectric Constant of materials between cylinders

Capacitance (C): The capacitance is returned in picoFarads.  However, this can be automatically converted to other capacitance units via the pull-down menu.

General Information

The calculator uses the formula:

C = `2pi * epsilon_r * epsilon_0 * L/(ln "b/a")`

where:

• (L) is the length of the cylinders
• (a) is the radius of the smaller cylinder
• (b) is the radius of the larger cylinder
• (ε_r) is the Dielectric Constant of materials between cylinders. For more information on the Dielectric Constant,  a.k.a. Relative Permittivity, of the material between the shells. For more info, click here.  To see common dielectric constants, CLICK HERE.
• (ε₀) Is the constant for the Permittivity of a Vacuum (8.85418782E-12 F/m)

Related Calculators:

• Capacitance of Two Concentric Spherical Shells
• Capacitance of an Isolated Spherical Shell
• Capacitance of a Cylindrical Capacitor

We're working under the assumption that the cylinders are much longer than they are wide.  This equation can be derived from Gauss's Law and the relation q = CV ¹.  

1. ^ Walker, Jearl, David Halliday, and Robert Resnick. "Capacitance." Fundamentals of Physics. 8E ed. Hoboken, NJ: Wiley, 2008. 660. Print.