Wire Impedance Calculator

When transmitting a signal over a cable or wire, calculating the impedance is crucial. With this calculator, you can calculate the impedance of coaxial cables or twisted pairs. Apart from cable impedance, this tool calculates cable capacitance, delay, inductance, and cutoff frequency.

Impedance is to alternating current (AC), the same that resistance is to direct current (DC). Impedance is, in essence, opposition to AC and results from the combined effect of resistance and reactance.

For transmission lines, like cables, the type of impedance we use is the characteristic impedance. The characteristic impedance of an AC cable is analog to the wire resistance in a DC cable.

The first thing to know when calculating the impedance of a wire is whether it's a coaxial or twisted pair cable. For each case, we use a different cable impedance formula:

• To calculate the impedance of a coaxial cable, we use the following formula:

  $\text{Impedance} = \frac{60 \times \ln(D_2/D_1)}{\sqrt{\varepsilon_r}}$

  , where:

  • $D_1$ — Inner conductor diameter;
  • $D_2$ — Inner diameter of the outer shielding; and
  • $\varepsilon_r$ — Relative permittivity of the inner dielectric insulator.

• To calculate the impedance of a twisted pair, we use the following formula:

  $\text{Impedance} = \frac{120 \times \ln(2S/D)}{\sqrt{\varepsilon_r}}$
  , where:

  • $S$ — Separation between the wires;
  • $D$ — Diameter of the wires; and
  • $\varepsilon_r$ — Relative permittivity of the insulating dielectric material between the wires.

Some important points about the units and variables of the previous equations:

• In both equations, the result of the wire impedance calculation is in ohms (Ω) units.

• The Relative permittivity ($\varepsilon_r$), also known as the dielectric constant, is the absolute permittivity ($\varepsilon$) of the dielectric material divided by the permittivity of vacuum ($\varepsilon_0$):

  $\varepsilon_r = \varepsilon/\varepsilon_0$

  Absolute permittivity units are farads per meter (F/m), while relative permittivity is unitless. Vacuum permittivity equals 8.8541878128 × 10⁻¹² F/m.

• For the coaxial cable, we can choose whenever units we want for the diameters, as long as both units are the same. We can do this as the units cancel each other.

• When calculating twisted pair impedance, we can also choose the units we want for $D$ and $S$, as long as both units are the same.