# Wire Impedance Calculator

Created by Luis Hoyos
Last updated: Sep 14, 2022

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.

🙋 After calculating your wire impedance, you can use our impedance matching calculator to maximize power transfer by matching the source and load impedances to the cable impedance.

## What's the impedance of a cable?

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.

## Cable impedance formula

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.

🙋 If you're struggling with diameter units, you can use our length converter.

Luis Hoyos
Cable Type
Coaxial
Inner conductor diameter (D1)
mil
Inner diameter of surface shield (D2)
mil
Insulator dielectric constant (εᵣ)
Results
Impedance
Ω
Capacitance
pF / inch
Delay
ns / inch
Inductance
nH / inch
Cutoff frequency
GHz
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