The cable impedance calculator above computes the characteristic impedance of a transmission line from its cross-section. That number decides whether a signal arrives cleanly or arrives with a reflection stacked on top of it, and it is set entirely by the geometry of the conductors and the material between them — not by the length of the cable, not by the load at the far end, and not, in the lossless limit, by frequency.
Arb Digital builds free physics and electronics calculators that own one job properly. This page is about lines, not networks. If you want the impedance of a resistor, inductor and capacitor connected together at a particular frequency, that is a different quantity and the RLC impedance calculator is the tool for it. The boundary matters, so the next section states it plainly.
Characteristic Impedance Is Not the Impedance of a Circuit
Two different quantities share the word impedance and they behave nothing alike. The impedance of an RLC network is what a source sees looking into a collection of components at one frequency. It changes with frequency, it has a phase angle, and it goes to a resonance. The characteristic impedance of a transmission line is the ratio of the voltage to the current in a wave propagating along the line, and for a well-behaved line it is a real number, roughly constant over a wide band, and completely independent of how long the cable is or what is attached to its end.
The way to keep them apart is to ask what varies. Double the frequency into an RLC network and the impedance changes substantially. Double the frequency into a coaxial cable and the characteristic impedance barely moves. Double the length of the cable and it does not move at all, though the delay and the loss both double. Use the RLC impedance calculator for the network case and the reactance calculator for a single component; this page is for the cable.
What This Cable Impedance Calculator Does
The calculator covers the three transverse electromagnetic geometries that account for almost all practical cable: coaxial, a two-wire line such as a twisted or parallel pair, and a single wire above a ground plane. For each it computes the characteristic impedance from the conductor dimensions and the dielectric constant, then reports the velocity factor, the propagation delay per metre, the shunt capacitance per metre and the series inductance per metre.
Those last four are not decoration. The velocity factor is what turns a physical length into an electrical length, and it is the number you need for cable-length measurements and for cutting a stub or a delay line. The capacitance per metre is what a driver has to charge, and it is the figure that dominates in short low-frequency runs where the line never behaves like a line at all. The inductance per metre completes the pair, and the impedance is simply the square root of their ratio.
Length is included as an input but deliberately does nothing to the impedance. It is used only to report the total delay and total capacitance of the run, because those are the numbers people actually go looking for once they have the impedance.
How to Use It
- Pick the geometry first. The formula changes completely between a coaxial line and a two-wire line, and the second dimension means something different in each case.
- Measure the right diameter. For coax, the second input is the inside diameter of the shield, which is the outside diameter of the dielectric — not the outside diameter of the jacket. This is the single most common error and it inflates the answer badly.
- Use the dielectric constant of the actual insulation. Solid polyethylene is about 2.25, PTFE about 2.1, and foamed dielectrics are lower because they are mostly gas. Getting this wrong scales the impedance by the square root of the error.
- Read the velocity factor as a sanity check. It is one over the square root of the dielectric constant, so it should land near 0.66 for solid polyethylene and near 0.8 for foam. A value outside 0.5 to 1.0 means the dielectric constant is wrong.
- Compare against the datasheet. If you have a manufactured cable, its published impedance is a measured figure for that construction and beats anything computed from nominal dimensions.
The Formula: How Characteristic Impedance Is Calculated
For any lossless transverse electromagnetic line, Z0 = √(L′ / C′), where L′ and C′ are the inductance and capacitance per unit length. Each geometry has a closed form.
Coaxial: Z0 = (59.96 ÷ √εr) × ln(D / d), where the constant is the impedance of free space divided by 2π, D is the shield inner diameter and d the centre conductor diameter. Two-wire line: Z0 = (119.92 ÷ √εr) × arcosh(s / d), where s is the centre-to-centre spacing. Wire above a ground plane: Z0 = (59.96 ÷ √εr) × arcosh(2h / d), where h is the height of the wire centre above the plane.
The velocity factor is 1 ÷ √εr and the propagation velocity is the speed of light times that factor, so the delay per metre is √εr ÷ c. From the impedance and the velocity, C′ = 1 ÷ (Z0vp) and L′ = Z0 ÷ vp. The coaxial capacitance expression this rests on is derived in OpenStax University Physics Volume 2, section 8.1 on capacitors and capacitance, and the guided-wave treatment that produces the impedance itself is covered in MIT OpenCourseWare 6.013, Electromagnetics and Applications.
Work the defaults by hand. A coaxial line with a 0.9 mm centre conductor, a 3.0 mm shield inner diameter and a polyethylene dielectric at εr = 2.25 gives ln(3.0 ÷ 0.9) = ln(3.3333) = 1.20397, and √2.25 = 1.5. So Z0 = (59.96 ÷ 1.5) × 1.20397 = 39.972 × 1.20397 = 48.12 Ω. The velocity factor is 1 ÷ 1.5 = 0.6667, the propagation velocity is 1.9986 × 10⁸ m/s and the delay is 5.003 ns per metre. The capacitance per metre is 1 ÷ (48.12 × 1.9986 × 10⁸) = 104.0 pF/m, and the inductance per metre is 48.12 ÷ 1.9986 × 10⁸ = 240.8 nH/m. Checking, √(240.8 nH ÷ 104.0 pF) = √2,315 = 48.1 Ω, which closes the loop.
Why the Datasheet Beats the Calculation
These formulas are exact for an idealised cross-section: perfectly round conductors, perfectly concentric, a uniform homogeneous dielectric, and no losses. Manufactured cable is none of those things, and the differences are not always small.
A stranded centre conductor does not have a single well-defined diameter, and its effective electrical diameter sits somewhere between the circumscribed circle and the copper cross-section. A braided shield is not a solid cylinder, so the effective inner radius is not exactly the braid radius. Foamed dielectrics have a density gradient, so the effective dielectric constant is a weighted figure rather than the value for the base polymer. In a twisted pair the field is partly in the insulation and partly in the air between the conductors, so no single dielectric constant is strictly correct and the practical figure is an effective one derived from measurement.
The result is that a calculated impedance is a good design estimate and a poor specification. If you are choosing a cable, take the manufacturer’s published impedance, which is measured on the real construction, over anything this page computes from nominal dimensions. Where the calculation earns its keep is the other way round: designing a cross-section, understanding why a change in geometry moves the impedance, checking whether a homemade line or a fixture is anywhere near the value you assumed, and seeing the sensitivity of the answer to each dimension.
Why 50 and 75 Ohms, and Not Some Other Number
Both standard values fall out of optimising a coaxial cross-section for something specific, and they optimise for different things. For an air-dielectric coax, the ratio of diameters that minimises conductor loss for a given outer size lands near 77 Ω, and the ratio that maximises power handling before the dielectric breaks down lands near 30 Ω. Fifty ohms is close to the geometric compromise between those two, which is why it became the general-purpose radio-frequency standard. Seventy-five ohms sits at the low-loss end and became the video and broadcast standard, where signal levels are small and attenuation matters more than power.
Twisted-pair values are set differently. Around 100 Ω is what a practical pair of insulated conductors twisted together naturally produces, and structured cabling standardised on it rather than the other way round. The physical layer specifications that depend on it are published in IEEE 802.3-2018, the IEEE Standard for Ethernet, which sets out the balanced-pair, coaxial and fibre media it permits.
The practical point is that these are conventions with reasons behind them, not natural constants. If you are designing a line for a purpose of your own, the calculator will tell you what geometry gives any impedance you like — but connecting it to standard equipment means matching the standard value, because every mismatch reflects.
What Happens When the Impedance Does Not Match
When a wave travelling along a line meets a load of a different impedance, part of it reflects. The reflection coefficient is (ZL − Z0) ÷ (ZL + Z0), so a 75-ohm load on a 50-ohm line reflects 20 per cent of the voltage. In a digital system that reflection returns to the driver, bounces again and shows up on the waveform as ringing or as a step partway up an edge. In a radio system it produces standing waves and returns power to the transmitter.
Whether it matters depends on the delay relative to the signal’s rise time. A line is electrically short — and mismatch can be ignored — when the round-trip delay is a small fraction of the edge rate. That is why the delay-per-metre figure in the grid matters as much as the impedance itself, and why the propagation delay calculator is a useful companion. At mains frequencies a hundred-metre cable is electrically short; with a one-nanosecond edge, thirty centimetres is not.
The other consequence of length is loss, which unlike impedance does grow with distance and with frequency. The attenuation calculator handles that side, and the two together are what decide whether a run is usable.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the jacket diameter for coax — the formula wants the shield inner diameter, which is the dielectric outer diameter. Using the jacket inflates the ratio and the impedance with it.
- Assuming impedance depends on length — it does not. Length changes delay and loss, never the characteristic impedance.
- Using the base polymer’s dielectric constant for a foamed cable — foam is mostly gas, so the effective value is far lower and the velocity factor far higher.
- Applying a single dielectric constant to a twisted pair — the field is shared between the insulation and the air, so the useful figure is an effective one derived from measurement.
- Confusing it with the impedance of an RLC network — that quantity varies strongly with frequency and has a phase angle; the characteristic impedance of a good line is a nearly constant real number.
Related Free Tools From Arb Digital
For the impedance of components wired together at a frequency rather than a line, use the RLC impedance calculator, or the reactance calculator for a single inductor or capacitor. The propagation delay calculator covers the timing side of a run, and the attenuation calculator covers the loss. The capacitance calculator computes coaxial and parallel-plate capacitance directly from geometry, which is the quantity underneath the per-metre figure reported here, and the inductance converter and LC resonant frequency calculator handle the inductive half. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
No. Characteristic impedance is fixed by the cross-section and the dielectric, so a 50-ohm cable measures 50 ohms whether it is one metre or one hundred. Length changes the propagation delay and the loss, both of which grow in proportion, but never the impedance.
Characteristic impedance is the ratio of voltage to current in a wave travelling along a line, and for a good line it is a nearly constant real number. The impedance of an RLC network is what a source sees at one frequency, changes strongly with frequency and carries a phase angle. They share a name and a unit and nothing else.
The inside diameter of the shield, which is the same as the outside diameter of the dielectric. Using the outside diameter of the jacket is the most common error on this calculation and makes the answer too high, because the ratio inside the logarithm is inflated.
No. The formulas assume perfectly round concentric conductors and a uniform dielectric, while real cable has stranded centres, braided shields and foamed or mixed dielectrics. Take the manufacturer's published impedance for a manufactured cable; use the calculation for design, sensitivity and sanity checking.
For an air-dielectric coax the diameter ratio that minimises loss lands near 77 ohms and the ratio that maximises power handling lands near 30 ohms. Fifty ohms is close to the compromise between them and became the general radio-frequency standard, while 75 ohms sits at the low-loss end and became the video and broadcast standard.
The ratio of the propagation speed along the cable to the speed of light in a vacuum, equal to one over the square root of the dielectric constant. Solid polyethylene gives about 0.66 and foamed dielectrics about 0.8. It is what converts a physical length into an electrical length.
Part of the wave reflects, with a voltage reflection coefficient of the load minus the line impedance over their sum. The reflection shows up as ringing on a digital edge or as standing waves in a radio system. Whether it matters depends on how the round-trip delay compares with the signal's rise time.
Slightly. At low frequencies, where conductor resistance is comparable to the series reactance, the impedance rises and becomes complex. Above that region it settles to the near-constant real value these formulas give, which is why cable is specified with a single figure over its working band.
This tool is provided for educational and design-estimate use. It applies published closed-form relations to idealised geometry and does not account for stranding, braid construction, dielectric gradients or losses, so treat the output as an estimate rather than a specification. Use the manufacturer’s measured figures for a manufactured cable, and have safety-related or regulated installations designed and verified by a qualified engineer.
