How this instrument works
A cable's characteristic impedance describes how it resists the flow of a changing electrical signal along its length — it isn't a resistance you could measure with a multimeter, but a property that determines how much of a signal reflects back at a mismatch instead of continuing on to the receiver. Getting it right matters enormously in practice: connect a cable to a device with a different characteristic impedance and part of every signal bounces back, causing echoes, data errors, or (at radio frequencies) real power loss.
For coaxial cable, the impedance is set by the ratio of the shield's inner diameter to the center conductor's diameter, and by the dielectric material's relative permittivity: Z = 60 x ln(D/d) / sqrt(εr). A wider gap between conductor and shield raises impedance; a denser dielectric (higher εr) lowers it, which is exactly why the common 50Ω and 75Ω coax standards use different diameter ratios and dielectric materials to land on their respective target impedances.
Twisted pair cable uses a related but distinct formula, Z = 120 x ln(2s/d) / sqrt(εr), where s is the spacing between the two conductors' centers and d is each conductor's diameter — the factor of 2 inside the logarithm and the doubled leading constant both come from the different field geometry of two parallel wires versus a conductor inside a cylindrical shield. Ethernet twisted-pair cabling standards target 100Ω using this same underlying relationship, tuned through wire gauge, spacing, and insulation choice.
- Choose Twisted pair or leave it unchecked for coaxial, since each geometry uses a different formula.
- Enter Conductor diameter, d — the center conductor's diameter for coax, or each wire's diameter for a twisted pair.
- Enter Shield inner diameter D (coax) or conductor spacing s (twisted pair), in the same length units as the conductor diameter.
- Enter the Dielectric relative permittivity, εr, of the insulating material — air/vacuum is 1.0, most plastics are higher.
- Read Characteristic impedance in ohms (Ω) — compare it against your target standard, e.g. 50Ω, 75Ω or 100Ω.
Worked example — a coax cable near RG-58 dimensions
A coaxial cable with a 0.5mm center conductor, a 2.95mm shield inner diameter, and a polyethylene dielectric (εr ≈ 2.3) — dimensions close to the widely-used RG-58 cable — gives Z = 60 x ln(2.95/0.5) / sqrt(2.3) = 60 x ln(5.9) / 1.5166 = 60 x 1.7750 / 1.5166 ≈ 70.22Ω.
That comes out noticeably higher than RG-58's well-known 50Ω nominal impedance, which is a useful reminder that real cable impedance depends on the manufacturer's exact dimensions and dielectric formulation, not just round textbook numbers — this formula gives the physics-based result for the specific geometry you enter, and small real-world variations in D, d, or εr shift the answer meaningfully because they sit inside a logarithm and a square root.
Questions
Why does my calculated impedance not exactly match a standard cable's rated impedance (like 50Ω or 75Ω)?
Manufacturer-published impedance ratings come from precise, tightly-controlled dimensions and dielectric formulations that this general formula only approximates with the D, d, and εr values you enter — real cables also account for braid coverage, jacket effects, and manufacturing tolerances this simple two-conductor model doesn't capture. Use this instrument to understand how geometry drives impedance and to sanity-check a design, not as a substitute for a manufacturer's datasheet on a specific cable part number.
What's a typical relative permittivity (εr) value to use?
Air or vacuum is exactly 1.0 (the reference case), solid polyethylene — the most common coax dielectric — is around 2.25-2.3, PTFE (Teflon) is around 2.1, and foam or air-spaced dielectrics used in low-loss coax fall between 1.0 and the solid material's value, often around 1.4-1.6. Check your cable's datasheet for the dielectric material and its manufacturer-published εr if you need precision.
Why do coaxial and twisted-pair cables use different formulas?
The formulas come from solving Maxwell's equations for each geometry's specific field pattern — coax has a cylindrically symmetric field between a center conductor and a surrounding shield, while a twisted pair has two parallel round conductors side by side, an entirely different field shape. Both formulas share the same underlying physics (impedance driven by geometry and dielectric permittivity), but the exact constants and the way diameter/spacing enter the logarithm differ because the field distributions differ.
What happens if my cable's impedance doesn't match my equipment's expected impedance?
An impedance mismatch causes part of the signal to reflect back toward the source at the mismatch point instead of continuing to the receiver, which shows up as signal echoes, standing waves, or increased error rates in digital systems, and as real measurable power loss in RF/video applications. The size of the problem scales with how big the mismatch is and how high the signal frequency is — a small mismatch on a low-frequency audio cable may be harmless, while the same mismatch on a high-frequency RF or video line can meaningfully degrade the signal.
Can I use this for cables with more than two conductors, or shielded twisted pair?
No — both formulas here model exactly the two idealized geometries named: a single center conductor inside a cylindrical shield (coax), or two parallel round conductors (twisted pair). Multi-conductor cables, shielded twisted pair with a grounded foil or braid added, or differential pairs with unusual cross-sections need more specialized field-solver models that account for the extra conductors and aren't captured by these two textbook formulas.