Coaxial Cable Impedance Calculator

A coaxial cable impedance calculator helps estimate the characteristic impedance and other transmission-line properties of a coaxial cable from its physical dimensions and dielectric material. This is useful when designing RF systems, checking cable geometry, studying transmission lines, or estimating signal propagation characteristics.

This calculator uses three primary inputs: the inner shield diameter, centre conductor diameter, and dielectric constant (εr). From these values, it calculates characteristic impedance, diameter ratio, velocity factor, propagation velocity, signal delay, estimated capacitance, and an approximate cable type.

For an ideal coaxial transmission line, characteristic impedance is calculated using:

Where D is the inner diameter of the shield, d is the centre conductor diameter, and ϵ_r is the dielectric constant.

What Is Coaxial Cable Impedance?

Coaxial cable impedance, more precisely called characteristic impedance, is an electrical property of a transmission line. It describes the relationship between voltage and current associated with a travelling electromagnetic wave along the cable.

Characteristic impedance is measured in ohms (Ω), but it should not be confused with the DC resistance of the cable. A coaxial cable can have a characteristic impedance of 50 Ω while its DC resistance is much lower.

Characteristic impedance is especially important in RF, telecommunications, video, and other high-frequency systems. When the impedance of the source, transmission line, and load are appropriately matched, signal reflections can be reduced.

Common coaxial cable impedance values include 50 Ω and 75 Ω. The appropriate impedance depends on the equipment and application rather than simply the physical appearance of the cable.

The characteristic impedance of an ideal coaxial cable is primarily determined by two factors:

• The ratio between the shield and conductor diameters
• The dielectric constant of the insulating material

That relationship is what makes a coaxial cable impedance calculator useful. Instead of manually working through the logarithmic equation, you can enter the physical dimensions and dielectric constant and immediately obtain an estimated result.

How Does a Coaxial Cable Work?

A coaxial cable normally consists of a centre conductor surrounded by a dielectric material, a conductive shield, and an outer protective jacket.

The centre conductor carries the signal. The shield provides the return path and helps contain the electromagnetic field around the cable. The dielectric separates the conductors and influences how electromagnetic energy propagates through the transmission line.

The geometry is important because the electromagnetic field exists primarily in the region between the centre conductor and the surrounding shield.

Changing the spacing between these conductors changes the electrical characteristics of the cable. Increasing or decreasing the conductor diameter or shield diameter changes the ratio between them, which changes characteristic impedance.

The dielectric material also has a major influence. A material with a different relative permittivity changes both the impedance and propagation speed.

This means that two coaxial cables with similar physical dimensions can have different electrical characteristics if their dielectric materials are different.

Coaxial Cable Impedance Formula

The calculator uses the following formula for characteristic impedance:

Where:

• Z₀ = characteristic impedance in ohms
• D = inner diameter of the shield
• d = centre conductor diameter
• ϵ_r = relative dielectric constant
• ln = natural logarithm

The formula works with the ratio D/d, so the two diameter measurements must use the same unit.

For example, you can use:

• mm/mm
• inch/inch
• m/m

The individual unit cancels when the ratio is calculated.

Step 1: Calculate the Diameter Ratio

First calculate:

This ratio compares the internal shield diameter with the centre conductor diameter.

Step 2: Calculate the Natural Logarithm

Next calculate:

Step 3: Account for the Dielectric

Calculate:

The dielectric constant influences how the electromagnetic field behaves inside the cable.

Step 4: Calculate Characteristic Impedance

Finally, combine the values:

The result is the estimated characteristic impedance in ohms.

Coaxial Cable Impedance Calculator Inputs

The calculator requires three inputs.

Inner Shield Diameter

The Inner Shield Diameter represents the internal diameter of the conductive outer shield.

The calculator uses millimeters as the input unit. For example, you might enter:

4.6 mm

It is important to use the relevant internal shield dimension rather than the external diameter of the complete cable jacket.

The jacket diameter can be substantially larger because it includes insulation and protective material that are not part of the D/d geometry used in this formula.

Centre Conductor Diameter

The Centre Conductor Diameter is the diameter of the central conductive element.

For example:

1.0 mm

This value directly affects the diameter ratio.

With the shield diameter held constant, increasing the centre conductor diameter decreases D/d. Because the impedance equation contains ln(D/d), this changes the calculated characteristic impedance.

Dielectric Constant

The third input is the Dielectric Constant (εr).

Relative dielectric constant describes an important electrical property of the material surrounding the centre conductor.

The calculator requires a positive value. A common example used with the calculator is:

εr = 2.25

The dielectric constant affects both characteristic impedance and propagation speed.

How to Use the Coaxial Cable Impedance Calculator

Using the calculator is straightforward.

1. Measure or obtain the inner shield diameter.
2. Measure or obtain the centre conductor diameter.
3. Determine the dielectric constant of the cable's dielectric material.
4. Enter all three values into the calculator.
5. Calculate the characteristic impedance.
6. Review the diameter ratio.
7. Check the velocity factor and propagation velocity.
8. Review the estimated signal delay and capacitance.
9. Compare the calculated impedance with the impedance required by your RF or transmission system.

For accurate engineering work, use reliable dimensional measurements and the appropriate dielectric value. If manufacturer specifications are available, they should also be considered because real cables include physical and electrical effects that an idealized formula does not fully represent.

Real-Life Example: Calculating Coaxial Cable Impedance

Consider a technician evaluating a coaxial cable used in an RF project.

Suppose the cable has:

• Inner shield diameter: 4.6 mm
• Centre conductor diameter: 1.0 mm
• Dielectric constant: 2.25

We can use these values to calculate the transmission-line characteristics.

Step 1: Calculate the Diameter Ratio

Therefore:

The diameter ratio is 4.600.

Step 2: Calculate Characteristic Impedance

Using:

Because:

the equation becomes:

The resulting impedance is approximately:

The calculator therefore reports approximately 49.91 Ω, depending on the exact calculation and rounding.

This falls inside the calculator's 48–52 Ω classification range, so its approximate recommendation is:

50 ohms RF Cable

Step 3: Calculate Velocity Factor

The calculator uses:

For εr = 2.25:

So the calculated velocity factor is approximately 0.667.

Step 4: Calculate Propagation Velocity

The calculator uses the speed of light:

Propagation velocity is:

Therefore:

The calculator displays approximately 199,861,639 m/s after rounding to a whole number.

Step 5: Calculate Signal Delay

The delay per metre is:

After converting seconds to nanoseconds, the result is approximately:

So a 10-metre cable would have an approximate one-way propagation delay of:

under this calculation model.

Step 6: Estimate Capacitance

The calculator uses:

With the example values, the estimated capacitance is approximately:

This example shows how one set of physical dimensions can provide several useful transmission-line parameters.

Understanding the Calculator Results

Characteristic Impedance

Characteristic impedance is the main output of the calculator.

It is expressed in ohms and represents the impedance of the idealized transmission line to a travelling wave.

For example:

49.91 Ω

is close to a nominal 50 Ω transmission line.

This value can be useful when evaluating whether a cable's geometry is approximately suitable for a system designed around a particular characteristic impedance.

Diameter Ratio (D/d)

The diameter ratio is:

It is dimensionless because both measurements have the same unit.

For the example:

A change in either conductor diameter or shield diameter changes this ratio and therefore changes the calculated impedance.

Velocity Factor

Velocity factor describes propagation speed relative to the speed of light.

The calculator uses:

A result of 0.667 means the calculated propagation speed is approximately 66.7% of the speed of light.

Propagation Velocity

Propagation velocity is calculated as:

It is reported in metres per second.

This value is useful for understanding how quickly a signal travels through the cable and for estimating transmission-line delay.

Signal Delay

The calculator reports signal delay in ns/m.

It represents the approximate time required for a signal to travel one metre through the cable.

For longer cable lengths, multiply the delay per metre by the cable length.

Estimated Capacitance

The calculator estimates capacitance per unit length in pF/m.

Capacitance is another important transmission-line parameter because it affects the electrical behaviour of the cable.

The result should be treated as an estimate based on the calculator's mathematical model rather than a replacement for a manufacturer's measured capacitance specification.

Recommended Cable Type

The calculator provides an approximate classification based on the calculated impedance:

• 48–52 Ω → 50 ohms RF Cable
• 73–77 Ω → 75 ohms Video/CATV Cable
• 90–100 Ω → 95 ohms Data Cable
• Other values → Custom

This classification is only a convenient interpretation of the calculated impedance. It does not identify a specific commercial cable.

50 Ohm vs 75 Ohm Coaxial Cable

Two commonly encountered coaxial cable impedance classes are 50 Ω and 75 Ω.

50 Ω Coaxial Cable

50 Ω coaxial systems are widely associated with RF and measurement applications.

When the calculator produces a result between 48 Ω and 52 Ω, this particular calculator classifies it as a 50 ohms RF Cable.

75 Ω Coaxial Cable

75 Ω coaxial cables are commonly encountered in video and CATV-related systems.

The calculator classifies calculated impedance between 73 Ω and 77 Ω as:

75 ohms Video/CATV Cable

Which One Should You Use?

The system specification should determine the required impedance.

A calculator should not be used by itself to decide which cable belongs in a particular system. Other characteristics can matter, including frequency range, attenuation, power handling, connector compatibility, shielding, environmental requirements, and the specifications of the connected equipment.

Practical Use Cases

RF Cable Design

An engineer can use the calculator during an early cable-design process to understand how conductor and shield dimensions affect characteristic impedance.

This is especially useful when experimenting with different coaxial geometries.

Antenna Feedline Design

Coaxial cable is frequently used as a feedline between an antenna and radio equipment.

The calculator can estimate the characteristic impedance from the cable geometry and dielectric constant, helping users understand whether the physical structure is approximately consistent with the intended transmission-line impedance.

For practical installations, the antenna system, feedline, connectors, and equipment should be evaluated as a complete RF system.

RF Prototyping

During prototyping, users may need to evaluate custom coaxial structures before manufacturing or selecting a cable.

Entering different dimensions allows rapid comparison of theoretical impedance values.

Cable Analysis

A technician who has access to the internal dimensions of a coaxial cable can use the calculator to estimate its characteristic impedance.

However, this should not be treated as definitive cable identification because real-world cables have additional properties that are not represented by the basic equation.

Propagation Delay Estimation

The calculator can estimate signal delay per metre.

For example, if the calculated delay is approximately 5 ns/m, a 20-metre cable would have an approximate one-way propagation delay of:

This can be useful when considering signal timing and transmission-line length.

Transmission-Line Education

The calculator is also useful for students learning about:

• Transmission lines
• Characteristic impedance
• Dielectric materials
• RF engineering
• Propagation velocity
• Signal delay
• Cable capacitance

Instead of manually calculating every parameter, students can change the input values and observe how the results change.

What Affects Coaxial Cable Impedance?

Several factors influence characteristic impedance.

Centre Conductor Diameter

The centre conductor is represented by d in the equation.

Changing its diameter changes the D/d ratio and therefore changes calculated impedance.

Inner Shield Diameter

The shield's internal diameter is represented by D.

Increasing or decreasing it changes the distance between the conductors and affects impedance.

Dielectric Constant

The dielectric constant is represented by ϵ_r.

For the same geometry, the calculator's formula shows that increasing εr increases the denominator:

This decreases the calculated characteristic impedance.

Cable Geometry

Real cable construction also depends on how consistently the conductors and dielectric are positioned.

Manufacturing tolerances, concentricity, and dimensional variation can affect actual cable characteristics.

Dielectric Material

Different dielectric materials have different electrical properties.

This is why knowing the correct dielectric constant is important when using a theoretical coaxial impedance calculation.

Frequency and Real-World Effects

The calculator is based on an idealized transmission-line relationship. Real cables also experience frequency-dependent loss and other effects.

For high-performance applications, manufacturer specifications or direct measurement should be used alongside theoretical calculations.

Coaxial Cable Impedance vs Resistance

Characteristic impedance and electrical resistance are different concepts.

Resistance describes opposition to current flow, particularly in a DC context. It is normally measured in ohms.

Characteristic impedance describes the voltage-to-current relationship associated with travelling waves on a transmission line.

Therefore, a cable described as a 50 Ω coaxial cable does not mean that a multimeter will measure 50 Ω resistance across its conductors.

A basic resistance measurement cannot directly determine characteristic impedance.

Characteristic impedance is instead related to the distributed inductance and capacitance of the transmission line and, for an ideal coaxial geometry, can be calculated from the conductor dimensions and dielectric properties.

Coaxial Cable Impedance and Impedance Matching

Impedance matching is an important consideration in transmission-line systems.

A simplified RF system can be represented as:

Source → Coaxial Cable → Load

If the source, cable, and load have compatible characteristic impedances, signal reflections can be minimized.

If the impedances differ, part of the travelling wave can be reflected back toward the source.

For example, connecting equipment designed for a 50 Ω transmission system to a 75 Ω cable introduces an impedance mismatch.

The practical impact depends on the complete system and operating frequency, but impedance mismatch can result in reflections and degraded signal transfer.

The coaxial cable impedance calculator can help estimate the cable's characteristic impedance from its physical geometry, making it useful as an initial design and analysis tool.

Coaxial Cable Velocity Factor and Propagation Velocity

Velocity factor and propagation velocity are closely related.

The calculator uses:

Then:

where c is the speed of light.

The relationship can be summarized as:

Higher dielectric constant → lower calculated velocity factor → lower propagation velocity → greater calculated delay per metre.

For example, with εr = 2.25:

The propagation velocity is approximately:

The calculator then determines the corresponding delay per metre.

These calculations are useful for estimating cable delay in RF and signal-transmission applications.

Coaxial Cable Capacitance Calculation

The calculator estimates capacitance using:

The output is expressed in pF/m.

Capacitance per unit length is an important property of a transmission line. It contributes to the cable's overall electrical behaviour and is related to how the transmission line stores electric energy.

The calculated capacitance depends on both:

• Dielectric constant
• Conductor geometry

The result should be considered an estimated value based on the calculator's idealized geometry. Actual cable capacitance can differ because of manufacturing details and material properties.

Limitations of the Coaxial Cable Impedance Calculator

A mathematical calculator is useful, but it does not reproduce every characteristic of a physical coaxial cable.

The calculation assumes an idealized coaxial transmission-line geometry.

Real cables can also be affected by:

• Conductor losses
• Dielectric losses
• Surface roughness
• Frequency-dependent behaviour
• Manufacturing tolerances
• Shield construction
• Connector transitions
• Temperature
• Cable bending
• Non-uniform geometry

The calculator also does not account for every parameter used to specify a commercial cable.

For critical RF systems, calculated values should be compared with manufacturer specifications or measured using appropriate test equipment.

For example, a vector network analyzer (VNA) can be used for RF characterization, while time-domain measurement techniques can provide information about transmission-line discontinuities and delay.

Input Validation

The calculator also includes basic validation.

The shield diameter must be greater than the centre conductor diameter. Both diameter values must be positive, and the dielectric constant must also be positive.

If the shield diameter is less than or equal to the conductor diameter, the calculator returns an error rather than producing a misleading impedance result.

How to Design a Coaxial Cable for a Target Impedance

The same impedance relationship can be used conceptually for coaxial cable design.

The equation is:

Suppose the target is approximately 50 Ω.

A designer can select a dielectric material and then adjust the relationship between D and d until the calculated impedance approaches the desired value.

The basic process is:

1. Select a dielectric material.
2. Determine its relative dielectric constant.
3. Choose initial conductor dimensions.
4. Calculate the resulting impedance.
5. Adjust the conductor or shield geometry.
6. Recalculate the impedance.
7. Compare the result with the target.

The calculator in its current form is primarily a forward calculator. It takes physical dimensions and dielectric constant and calculates impedance.

It does not directly solve the reverse problem of entering a target impedance and automatically calculating the required conductor diameter or shield diameter.

Common Mistakes When Calculating Coaxial Impedance

Using the Outer Jacket Diameter

The formula requires the relevant inner diameter of the conductive shield. The complete outside diameter of the cable includes the protective jacket and should not simply be substituted for D.

Mixing Units

If the shield diameter is entered in millimeters and the conductor diameter is entered in inches, the resulting D/d ratio will be wrong.

Always use the same unit for both dimensions.

Using an Incorrect Dielectric Constant

The dielectric constant must correspond to the relevant dielectric material.

Using an incorrect value can significantly change the calculated result.

Confusing Resistance With Impedance

A resistance measurement with a multimeter does not directly provide characteristic impedance.

These are different electrical properties.

Ignoring Manufacturer Specifications

For a commercially manufactured cable, the manufacturer's electrical specifications are generally more appropriate for final system design than an estimate based only on dimensions.

Coaxial Cable Impedance Calculator vs Manual Calculation

Manual calculation requires several steps:

1. Determine shield diameter.
2. Determine conductor diameter.
3. Calculate D/d.
4. Determine the dielectric constant.
5. Calculate the square root of εr.
6. Calculate the natural logarithm of D/d.
7. Calculate characteristic impedance.
8. Calculate additional transmission-line parameters separately.

The calculator automates these calculations and provides multiple outputs at once.

This makes it useful when testing multiple cable geometries, teaching transmission-line concepts, performing preliminary design work, or checking calculations.

Frequently Asked Questions

What is a coaxial cable impedance calculator?

A coaxial cable impedance calculator estimates the characteristic impedance of a coaxial transmission line from its inner shield diameter, centre conductor diameter, and dielectric constant. This calculator also estimates diameter ratio, velocity factor, propagation velocity, signal delay, capacitance, and an approximate cable type.

How do you calculate coaxial cable impedance?

Use:

Measure the inner shield diameter and centre conductor diameter using the same unit, then enter the dielectric constant.

What is the formula for coaxial cable impedance?

The ideal coaxial cable characteristic impedance formula used by this calculator is:

Here, D is the inner shield diameter, d is the centre conductor diameter, and εr is the dielectric constant.

What is a typical coaxial cable impedance?

50 Ω and 75 Ω are common characteristic impedance values. The correct impedance depends on the equipment and application.

How do I calculate 50 ohm coaxial cable?

Choose a suitable dielectric and conductor geometry, then adjust the D/d ratio until the calculated characteristic impedance approaches 50 Ω. The actual cable design should also account for manufacturing and application requirements.

What is the velocity factor of coaxial cable?

Velocity factor describes the signal propagation speed in the cable relative to the speed of light. In this calculator, it is estimated as:

How is coaxial cable propagation velocity calculated?

The calculator uses:

where c is the speed of light and VF is the calculated velocity factor.

What is signal delay in coaxial cable?

Signal delay is the approximate time required for a signal to travel through a given length of cable. This calculator expresses it as nanoseconds per metre.

What is coaxial cable capacitance?

Coaxial cable capacitance is the capacitance between the centre conductor and shield per unit length. This calculator estimates it in pF/m from cable geometry and dielectric constant.

Can I calculate coax impedance from cable diameter?

Yes, provided you know the relevant inner shield diameter, centre conductor diameter, and dielectric constant. The two diameter measurements must use the same unit.

Does a 50 Ω coax cable have 50 Ω resistance?

No. A cable's characteristic impedance is different from its DC resistance. A 50 Ω characteristic impedance does not mean that the cable will measure 50 Ω with a multimeter.

What happens when coaxial cable impedance does not match the system?

An impedance mismatch can cause signal reflections. Depending on the system and frequency, this can affect signal transfer and create standing-wave behaviour.

Can this calculator identify my exact coaxial cable?

No. It estimates electrical properties from the supplied dimensions and dielectric constant. Exact cable identification requires manufacturer information or appropriate electrical measurement.

Final Takeaway

A Coaxial Cable Impedance Calculator provides a fast way to estimate the characteristic impedance of an idealized coaxial transmission line from its physical geometry and dielectric constant.

The primary equation is:

But impedance is only one part of the calculation. The same inputs can also be used to estimate the diameter ratio, velocity factor, propagation velocity, signal delay, and capacitance.

The tool can support RF prototyping, antenna feedline analysis, cable design, transmission-line education, and preliminary engineering calculations.

For critical or production RF applications, treat calculator results as theoretical estimates and verify them against manufacturer specifications or appropriate measurement equipment.

Enter your inner shield diameter, centre conductor diameter, and dielectric constant to calculate the estimated coaxial cable impedance and related transmission-line parameters.