Coax Impedance from Dimensions
Z₀ of a coaxial line from shield ID, center-conductor OD, and the dielectric.
Your recent runs (stored only in your browser)
No calculations yet — results land here so you can compare runs.
The engineering
Coax impedance is pure geometry divided by dielectric: only the ratio D/d matters, scaled down by √εr. Solid-PE 50 Ω wants D/d ≈ 3.5; air-line 50 Ω wants 2.3. The same formula run backward explains why connectors keep 50 Ω through their guts by stepping both diameters together wherever the dielectric changes.
The famous compromises drop out of this equation: for air dielectric, minimum loss lands near 77 Ω, maximum power handling near 30 Ω, and peak voltage rating near 60 Ω — 50 Ω splits the difference, while 75 Ω video/CATV cable sits at the low-loss optimum where signals are weak and watts are few.
Where this math comes from
Oliver Heaviside patented the concentric line in 1880 as a cure for telegraph crosstalk, decades early as usual. Espenschied and Affel's 1929 Bell system patent made coax a broadband medium, and 1930s Bell Labs work on air-dielectric lines produced the loss-vs-power trade study that made 50 Ω the standard split — a compromise later canonized by wartime radar and the postwar connector industry.
Cable TV picked 75 Ω from the same chart's low-loss point (and because a 75 Ω line matches a folded-dipole-era antenna world), permanently bifurcating the coax aisle at the electronics store.
- 1880Oliver HeavisideCoaxial line patented.
- 1929Espenschied & Affel (Bell)Broadband coaxial transmission system.
- 1940Bell Labs / radar industry50 Ω standardized as the loss-power compromise, circa.
See the full timeline of the math behind every calculator →
Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.