Cable Impedance Calculator - Coaxial and Twisted Pair Z0
Use this cable impedance calculator to compute characteristic impedance Z0, capacitance, inductance, delay, and TE11 cutoff for a coaxial or twisted pair cable from its geometry and dielectric constant.
Cable Impedance Calculator
Results
What Is Cable Impedance Calculator?
A cable impedance calculator turns a cable's geometry and dielectric into the matching characteristic impedance Z0, capacitance, inductance, delay, and (for coax) the TE11 cutoff frequency.
- • RG-58 and RG-174 coax: confirm a coax sample meets its 50 Ω datasheet number before terminating it.
- • CATV and 75 Ω video: check that a foamed-PE coax falls near 75 Ω for splitters and F-connectors.
- • Ethernet twisted pair: verify a Cat 5e / Cat 6 pair lands near 100 Ω differential, the value 1000BASE-T expects.
- • RF matching and link budget: feed Z0 into a matching network, balun, or Smith-chart workflow for an antenna feed.
Every cable has a characteristic impedance that depends only on its geometry and the dielectric around the conductor, not its length. The calculator takes the four numbers on a cut sheet - d, D, s, and εr - and returns Z0, capacitance, inductance, delay, velocity factor, and cutoff without re-deriving the lossless formula by hand.
Once the cable's Z0 is known, the matching dBm and dBμV reading for a 50 Ω, 75 Ω, or 600 Ω system is one click away in the RF Unit Converter, which takes the impedance as one of its inputs.
How Cable Impedance Calculator Works
The cable impedance calculator runs the lossless transmission-line formulas for coax and twisted pair against four geometric and dielectric inputs.
- d: Inner conductor diameter (coax) or single-wire diameter (twisted pair), in mm
- D: Inner diameter of the coax outer shield, in mm (coax only)
- s: Centre-to-centre spacing between the two twisted-pair conductors, in mm (twisted pair only)
- εr: Relative permittivity of the dielectric around the conductor (1.0 air, 2.25 PE, 2.1 PTFE, 4.2 FR4)
The coax branch uses 60 Ω because Z0 of an air-dielectric coaxial geometry equals sqrt(μ0 / (ε0 · π)) ≈ 60 Ω; the twisted-pair branch uses 120 Ω because the same derivation on parallel conductors in free space gives twice that base. After Z0, the calculator derives per-unit-length capacitance and inductance, propagation delay as sqrt(εr) / c, and for coax the TE11 cutoff from the mean shield diameter.
RG-58 coax with solid PE dielectric (d = 0.9 mm, D = 2.95 mm, εr = 2.25)
cableType = coaxial, d = 0.9 mm, D = 2.95 mm, εr = 2.25
Z0 = (60 × ln(2.95 / 0.9)) / sqrt(2.25) = (60 × 1.188) / 1.5 = 47.5 Ω, with C ≈ 105.4 pF/m, L ≈ 237.5 nH/m, delay ≈ 5.00 ns/m, v/c ≈ 0.667, TE11 cutoff ≈ 49.6 GHz
Z0 ≈ 47.5 Ω, within 5 % of the RG-58 50 Ω datasheet number
The cutoff sits well above any practical HF/VHF/UHF use, which is why RG-58 is rated to a few GHz.
According to Wikipedia Characteristic Impedance, the lossless coax formula is Z0 = (60 × ln(D/d)) / sqrt(εr) and the lossless twisted-pair formula is Z0 = (120 × ln(2s/d)) / sqrt(εr).
According to Wikipedia Speed of Light, the speed of light in vacuum is exactly 299 792 458 m/s, which sets the per-metre propagation delay of a lossless dielectric-filled line.
For the dB side of the same cable analysis, the cable loss in dB/m that goes alongside Z0 in a link budget, the Decibel Calculator covers the 20·log10 and 10·log10 arithmetic without re-deriving the constants.
Key Concepts Explained
Four ideas explain every number in the result panel: what characteristic impedance means, the geometric origin of the ln(D/d) and ln(2s/d) terms, the role of the dielectric constant, and the difference between lossless Z0 and DC resistance.
Characteristic impedance is geometry-driven
Z0 of a lossless coax depends only on D/d and εr, and Z0 of a lossless twisted pair depends only on 2s/d and εr. Cable length does not enter the formula, which is why a 1 m and a 100 m sample of the same coax read the same impedance on a TDR.
The 60 Ω and 120 Ω constants come from free space
An air-dielectric coax gives Z0 = 60 · ln(D/d) and an air-dielectric twisted pair gives Z0 = 120 · ln(2s/d) because the underlying derivation of an axial E/H field in those geometries starts from sqrt(μ0/(ε0 · π)) ≈ 60 Ω and twice that for the pair. A real dielectric divides both results by sqrt(εr).
Dielectric constant slows the wave
εr scales the per-metre capacitance by εr, scales the delay by sqrt(εr), and scales the velocity factor v/c by 1 / sqrt(εr). PE (εr ≈ 2.25) gives v/c ≈ 0.667; PTFE (εr ≈ 2.1) gives v/c ≈ 0.69; air (εr = 1) gives v/c = 1.
Z0 is not the same as DC resistance
Characteristic impedance is an AC property that describes how voltage and current waves share energy between inductance and capacitance per unit length. DC resistance is a separate, lossy term. A cable can read Z0 = 50 Ω while its DC loop resistance is several ohms per kilometre.
When the per-metre capacitance from this calculator needs to be read in pF, nF, or μF for a passive-component design step, the Capacitance Conversion Calculator converts the same C value to the unit the rest of the schematic uses.
How to Use This Calculator
Pick the cable type, type the geometric and dielectric numbers from the datasheet, and read Z0, capacitance, delay, and cutoff in a single result panel.
- 1 Pick coax or twisted pair: Use the Cable Type selector first. The form shows D for coax or s for twisted pair so the right geometry is asked for.
- 2 Enter the conductor diameter d: Inner conductor diameter (coax) or single-wire diameter (twisted pair) in mm. Pull from the datasheet or measure with a caliper.
- 3 Enter D for coax or s for twisted pair: For coax, the inner diameter of the outer shield. For twisted pair, the centre-to-centre spacing of the two wires.
- 4 Enter the dielectric constant εr: PE ≈ 2.25, PTFE ≈ 2.1, foamed PE ≈ 1.5, FR4 ≈ 4.2, air = 1.0.
- 5 Read Z0, C, L, delay, and cutoff: Match Z0 to the system impedance of the radio, analyzer, or Ethernet PHY that will drive the cable.
- 6 Cross-check against the datasheet: If Z0 is more than 10 % off, re-check εr and the geometry - one of them is wrong before the cable is.
To verify a 50 Ω RG-58 coax before a transmitter test, pick Coaxial cable, type d = 0.9 mm, D = 2.95 mm, εr = 2.25, and read Z0 ≈ 47.5 Ω, C ≈ 105.4 pF/m, delay ≈ 5.0 ns/m.
After the Z0 check passes, the matching cable length and maximum baud rate for the link is the same one-click step in the Baud Rate Calculator, which uses the propagation delay from this calculator as its timing budget.
Benefits of Using This Calculator
This cable impedance calculator replaces four hand calculations and a Smith-chart sketch with one result panel that updates as the inputs change.
- • Removes the 60 ln(D/d) re-derivation: Stops you from re-typing Z0 = 60 × ln(D/d) / sqrt(εr) every time the dielectric changes - the form takes the inputs, the result panel takes the arithmetic.
- • Covers coax and twisted pair: Pulls both branches of the lossless transmission-line formula into the same result panel, so the same UI works for an RG-58 coax check and a Cat 6 twisted-pair check.
- • Returns C, L, delay, and cutoff alongside Z0: Reports per-unit-length capacitance and inductance, propagation delay in ns/m, and (for coax) TE11 cutoff - the values that turn Z0 into a usable cable spec.
- • Pairs with the tools RF cluster: Outputs the Z0 you can read straight into the impedance input of an RF unit converter or a 50 Ω / 75 Ω system check.
- • Surfaces geometry errors before RF power goes in: Refuses to compute when D ≤ d (coax) or s ≤ d (twisted pair), so a mis-typed value cannot silently produce a Z0 that looks reasonable but is wrong by an order of magnitude.
For the structured-cabling checklist that ends with a known Z0 on every Cat 5e / Cat 6 run, the IP Address Converter covers the addressing half of the same checklist without re-deriving either step.
Factors That Affect Your Results
Three things decide the number in the result panel: the geometry you typed, the dielectric constant you typed, and the cable-type branch the formula uses.
Geometry (d, D, s)
Z0 is driven by the natural log of the geometric ratio. Doubling D/d on a coax adds 60 × ln(2) / sqrt(εr) ≈ 41.6 / sqrt(εr) Ω to the reading. The same idea applies to 2s/d on a twisted pair, with the constant 120.
Dielectric constant εr
Doubling εr cuts Z0 by sqrt(2) ≈ 1.414, doubles the per-metre capacitance, and lengthens the propagation delay by the same sqrt(2). PE → air on the same cable therefore raises Z0 and shortens the delay.
Cable-type branch (coax vs twisted pair)
The coax branch uses 60 × ln(D/d); the twisted-pair branch uses 120 × ln(2s/d). Switching the selector is what moves the form between the two formula sets, so picking the wrong branch gives a Z0 that is off by a constant factor of 2.
Frequency-dependent loss (beyond the model)
The lossless formula returns a single real Z0 for any frequency, but real cables pick up skin-effect conductor loss and dielectric loss as the signal goes up in frequency. Z0 moves little; the loss term is what moves.
- • The impedance formula assumes a lossless line. It does not include skin-effect conductor loss, dielectric loss, or the small frequency dependence a VNA would measure on a lossy coax.
- • The TE11 cutoff is reported for coax only. Twisted-pair cables do not support a clean waveguide mode, so the cutoff row is 0 GHz for the twisted-pair branch.
According to Microwaves101 Why Fifty Ohms, the characteristic impedance of a coax for a given outer diameter and dielectric is solely a function of the inner conductor diameter and the dielectric constant.
When the loss term beyond the lossless Z0 needs to be read as RMS power into a matched load, the RMS to Watts Calculator turns the same V and Z into the matching watt and dBm reading without leaving the page.
Frequently Asked Questions
Q: What does this cable impedance calculator compute?
A: It takes the cable type plus the inner conductor diameter d, the coax outer shield inner diameter D (or the twisted-pair centre spacing s), and the substrate relative permittivity εr, and returns the lossless characteristic impedance Z0 in ohms, plus per-unit-length capacitance in pF/m, inductance in nH/m, propagation delay in ns/m, velocity factor v/c, and the coax TE11 cutoff frequency in GHz.
Q: How is the impedance of a coaxial cable calculated?
A: Z0 = (60 × ln(D/d)) / sqrt(εr), where D is the inner diameter of the outer shield, d is the diameter of the inner conductor, and εr is the substrate dielectric constant. RG-58 with D = 2.95 mm, d = 0.9 mm, and εr = 2.25 reads about 47.5 Ω before rounding, which matches its 50 Ω datasheet number.
Q: How is the impedance of a twisted pair cable calculated?
A: Z0 = (120 × ln(2s/d)) / sqrt(εr), where s is the centre-to-centre spacing of the two wires and d is the diameter of a single conductor. A Cat 5e pair with s ≈ 0.9 mm, d ≈ 0.5 mm, and εr ≈ 2.0 reads close to 100 Ω differential, which matches the Ethernet 1000BASE-T link target.
Q: What is the cutoff frequency of a coaxial cable?
A: The TE11 waveguide-mode cutoff is c / (π × mean diameter), where the mean diameter is (D + d) / 2 in metres and c is the speed of light in vacuum. RG-58 with D = 2.95 mm and d = 0.9 mm reads a TE11 cutoff near 49 GHz, which is why the cable is only rated for use up to a few GHz.
Q: What dielectric constant should I use for common cable insulators?
A: Air is exactly 1.0, polyethylene (PE) is about 2.25, solid PTFE is about 2.1, foamed PE used in CATV coax is about 1.5, and FR4 used in PCB traces is about 4.2. These values come from cable manufacturer datasheets and standard reference tables for polymer dielectrics.
Q: Does the impedance formula change with frequency?
A: For a lossless line it does not - Z0 is real and frequency-independent. For a real cable the geometry and εr still drive Z0 across the audio to microwave range, but the cable picks up conductor loss and dielectric loss as frequency rises, which a network analyzer can measure as a small imaginary part to Z0.