Coaxial Transmission Line Calculator
Estimate impedance, capacitance, inductance, velocity factor, delay, wavelength, and peak electric field for a round coaxial line.
Assumes ideal, uniform coax in TEM mode (losses and connector effects not included).
What this coaxial line calculator does
A coaxial cable is one of the most common transmission line structures in RF, test equipment, broadcast systems, and high-speed electronics. This calculator helps you quickly estimate the key electrical properties of a coax geometry from its dimensions and dielectric material.
- Characteristic impedance (Z0)
- Capacitance and inductance per meter
- Wave velocity and velocity factor
- Propagation delay
- Wavelength and electrical length at a selected frequency
- Peak electric field near the center conductor
How to use it
1) Enter geometry
Input the center conductor diameter d and the inner diameter of the shield D. For physical validity, D must be greater than d.
2) Enter material properties
Add the dielectric constant (εr). Typical values are around 1.0 for air and about 2.1 to 2.3 for PTFE. Most practical coax calculations use μr = 1.
3) Add operating conditions
Cable length is used to compute total delay, total capacitance, and total inductance. Frequency is used for wavelength and electrical length. Voltage is optional and only affects the electric field estimate.
Formulas used
The calculator uses standard lossless TEM transmission-line equations:
Z0 = (1 / 2π) √(μ / ε) ln(D/d)C' = 2π ε / ln(D/d)(F/m)L' = (μ / 2π) ln(D/d)(H/m)v = 1 / √(με)andVF = v/cDelay = 1/v(s/m)Emax ≈ V / (a ln(b/a))wherea = d/2andb = D/2
Design notes for practical coax work
- For air dielectric, a ratio near D/d ≈ 3.6 gives roughly 77 Ω.
- 50 Ω is a common compromise for power handling and low loss.
- 75 Ω is often favored in video and receive chains for lower attenuation.
- As dielectric constant increases, impedance decreases for the same geometry.
- The strongest electric field appears at the surface of the inner conductor.
Limitations
This tool is intentionally simple. It does not include conductor loss, dielectric loss tangent, roughness, temperature drift, plated layers, braided shield coverage, connector discontinuities, or dispersion effects at very high frequency. For final hardware, validate with measurement or full-wave simulation.
Quick example
If you use d = 1.0 mm, D = 4.7 mm, and εr = 2.25, you should get a characteristic impedance close to 50 Ω. This is why similar geometries are common in many RF cable families.