Cable Impedance Calculator
This cable impedance calculator works out the characteristic impedance of a coaxial cable from its physical dimensions and the dielectric between the conductors. Characteristic impedance is the single most important number for any RF or video cable, because a signal only travels cleanly when the source, the cable and the load all share the same impedance. A mismatch sends part of the signal bouncing back as a reflection, which shows up as loss, ghosting or standing waves. For a coaxial cable the impedance depends on just three things: the diameter of the inner conductor, the inner diameter of the outer conductor or shield, and the dielectric constant of the insulation between them. The calculator applies the standard transmission-line formula, impedance equals 138 divided by the square root of the dielectric constant, times the log of the diameter ratio, and it also reports the cable's capacitance and inductance per metre, which set the impedance and the signal delay. Enter the two conductor diameters in millimetres and the dielectric constant of the insulation, around 2.25 for solid polyethylene or lower for foam, and read off the impedance. Use it to check whether a cable is close to the 50 or 75 ohm standards, to design a custom line, or to understand why a homemade cable misbehaves. The result assumes an ideal, lossless cable with a non-magnetic dielectric.
With a conductor ratio D/d of 3.60 and a dielectric constant of 2.25, this coaxial cable has a characteristic impedance of about 51.2 Ω.
Assumes an ideal lossless coax with a non-magnetic dielectric. Only the diameter ratio and dielectric set the impedance, not the absolute size. Standard coax is made to 50 Ω or 75 Ω.
How it works
The characteristic impedance of a coaxial cable is 138 divided by the square root of the dielectric constant, times the base-10 log of D over d, where D is the inner diameter of the shield and d is the diameter of the inner conductor. Notice that only the ratio D/d matters, so scaling both conductors keeps the same impedance. Capacitance per metre is 55.63 times the dielectric constant, divided by the natural log of D/d, in picofarads. Inductance per metre is 200 times the natural log of D/d, in nanohenries. The impedance also equals the square root of inductance divided by capacitance, which is a handy cross-check.
Worked example
Take an inner conductor of 1 mm, a shield inner diameter of 3.6 mm, and solid polyethylene insulation with a dielectric constant of 2.25. The ratio D/d is 3.6, so the impedance is 138 divided by the square root of 2.25, times the log of 3.6, which is 92 times 0.556, or about 51.2 ohms, close to the 50 ohm standard. The capacitance works out to 97.7 picofarads per metre and the inductance to 256 nanohenries per metre, and the square root of 256 over 97.7 confirms the same 51.2 ohms.
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