Coaxial Cable Impedance Calculator
A coaxial cable carries a signal on a centre conductor surrounded by a cylindrical shield, with a dielectric in between. Its characteristic impedance depends only on the ratio of the shield's inner diameter to the centre conductor's diameter and on the dielectric constant of the insulation. Matching this impedance to the source and load prevents reflections. This calculator uses the standard logarithmic coax formula, taking the two diameters and the dielectric constant, and returns the characteristic impedance and the diameter ratio.
Coaxial impedance formula
ratio = shield inner diameter D / inner conductor diameter d
Z0 = (138 / sqrt(er)) * log10(D / d)
Equivalently Z0 = (60 / sqrt(er)) * ln(D / d)
Impedance in air uses er = 1
Only the diameter ratio matters, so any consistent length unit is fine. The 138 constant equals 60 times the natural log conversion to base 10. Dividing by the square root of the dielectric constant accounts for the slower propagation in the insulation.
Coaxial cable facts
- RF and test cable is usually 50 ohms; video and broadcast cable is usually 75 ohms.
- Solid polyethylene has a dielectric constant of about 2.25.
- Foamed dielectrics are mostly air, lowering the dielectric constant toward 1.3 to 1.6.
- Minimum loss in air occurs near a 77 ohm impedance.
- Maximum power handling in air occurs near a 30 ohm impedance.
Coaxial impedance: frequently asked questions
How is coaxial cable impedance calculated?
The characteristic impedance of an ideal coax is Z0 = (138 / sqrt(dielectric constant)) times the base-10 logarithm of the shield inner diameter divided by the inner conductor diameter. Equivalently it is (60 / sqrt(er)) times the natural log of that diameter ratio. Both forms give the same result.
What dielectric constant should I enter?
Use the relative permittivity of the cable's insulation. Solid polyethylene is about 2.25, solid PTFE about 2.1, and foamed dielectrics range from roughly 1.3 to 1.6 because they are mostly air. The cable datasheet states the effective value. It is an editable input here.
Why are 50 ohms and 75 ohms so common?
50 ohms is a compromise between the diameter ratio that minimises loss (about 77 ohms in air) and the ratio that maximises power handling (about 30 ohms), so it suits RF and test equipment. 75 ohms minimises loss in polyethylene-filled cable and is standard for video and broadcast.
Does the diameter unit matter?
No. Only the ratio of the shield inner diameter to the inner conductor diameter appears in the formula, so any consistent length unit works. Enter both diameters in the same unit, such as millimetres, and the impedance is unaffected by the choice.
Does this account for cable loss?
No. This is the geometric characteristic impedance of a lossless line. Attenuation from conductor and dielectric loss is a separate, frequency-dependent quantity. The characteristic impedance is what matters for matching and reflection, which is the usual reason to compute it.
Official sources
- NIST: Physical Measurement Laboratory: coaxial line standards.
- IEEE: IEEE standards for radio-frequency transmission lines.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.