Enter the inner diameter, outer diameter, and relative permittivity of a coaxial cable to calculate its impedance, inductance, capacitance, and cutoff frequency.

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## Coax Cable Formula

The following formula is used to calculate the impedance of a coaxial cable.

Z = 138 * log (D/d) / Sqrt(pr)

- Where Z is the impedance
- D is the outer diameter of the cable
- d is the inner diameter of the cable
- pr is the relative permittivity of the material the cable is made from

Some additional formulas for the cable, which the calculator solves for, are as follows:

Capacitance = 7.354*pr / log(D/d)

- Units = pF (pico farads)

Inductance = 140.4*log(D/d)

- Units = nH (nano henries)

Cutoff Frequency = 11.8 / [ SQRT(pr)*pi*((D+d)/2) ]

- Units = GHz (giga hertz)

## Example Problem

**How to calculate a coax cable impedance? **

First, determine the outer diameter of the cable. The units of this dimension must be the same as the inner diameter or the formulas will not hold. For this example, the outer diameter is 1.25 inches.

Next, determine the inner diameter of the cable. Using the same units as above, the inner diameter is found to be .75 inches.

Next, determine the relative permittivity of the medium, in this case, the material of the cable. For this problem, we will use a relative permittivity of 3.

Finally, calculate the impedance using the formula above:

Z = 138 * log (D/d) / Sqrt(p_{r})

= 138 * log (1.25/.75) / Sqrt(3)

= 17.675 ohms

Enter the information from above into the calculator to determine the capacitance, inductance, and cutoff frequency.