What this coaxial cable calculator does
This calculator estimates the core transmission-line properties of an ideal coaxial cable from geometry and material inputs. You provide the inner conductor diameter (d), the shield inner diameter (D), dielectric constant (εr), magnetic permeability (μr), length, and frequency. It returns:
- Characteristic impedance (Z0) in ohms
- Capacitance per meter (pF/m)
- Inductance per meter (µH/m)
- Velocity factor and propagation velocity
- Delay per meter and one-way delay for your cable length
- Wavelength in cable and electrical length at the chosen frequency
This is useful for RF design, antenna feedline planning, pulse timing, and understanding how cable geometry drives impedance matching behavior.
Coaxial cable formulas used
For a homogeneous dielectric, the classic TEM (transverse electromagnetic) coax equations are:
where ln is the natural logarithm, c is the speed of light in vacuum, and ε0, μ0 are vacuum permittivity and permeability.
How to use the inputs correctly
1) Diameters: keep units consistent
Because the formulas use the ratio D/d, any consistent unit works (mm, inches, etc.). In this page, inputs are labeled in mm. The only strict geometric rule is D must be greater than d.
2) Dielectric constant (εr)
Typical values:
- Air: ~1.0006
- Foamed polyethylene: roughly 1.3 to 1.7
- Solid polyethylene: about 2.25
- PTFE: around 2.0 to 2.1
Lower εr gives higher velocity factor and, for fixed geometry, higher characteristic impedance.
3) Relative permeability (μr)
For most practical coax dielectrics, μr is very close to 1. Leave it at 1 unless you are modeling specialty magnetic materials.
Design intuition: why impedance depends on geometry ratio
In a coax structure, electric and magnetic field distributions are set by the spacing between the center conductor and shield. The logarithmic term ln(D/d) captures this geometry. Making the shield diameter larger (for fixed center conductor) increases Z0. Making the center conductor larger (for fixed shield ID) decreases Z0.
For common RF systems, 50 Ω is popular for power handling and mixed-loss optimization, while 75 Ω is common for lower attenuation in receive/video distribution contexts.
Example workflow
Suppose you are prototyping a feedline with a solid polyethylene dielectric:
- d = 0.9 mm
- D = 2.95 mm
- εr = 2.25, μr = 1
- Length = 10 m, Frequency = 100 MHz
The calculator will produce a characteristic impedance close to a classic 50 Ω cable, plus delay and electrical length. That helps you estimate phase shift in matching networks, phased arrays, and timing-sensitive RF paths.
Practical limits of this simple model
Real cables are not ideal. This calculator intentionally focuses on foundational line parameters. It does not include:
- Frequency-dependent conductor loss (skin effect)
- Dielectric loss tangent and temperature drift
- Connector discontinuities and launch effects
- Braid coverage imperfections and leakage/shielding effectiveness
- Maximum voltage and power ratings
If you are building high-power, high-frequency, or very long runs, combine these results with manufacturer datasheets and measurement (VNA, TDR, insertion loss sweeps).
Quick troubleshooting checklist
- Calculator error: Ensure all values are positive and D > d.
- Unexpected impedance: Re-check dielectric constant and unit consistency.
- Phase issues in system: Verify frequency entry and physical cable length.
- Mismatch in practice: Include connector/adaptor effects and real cable tolerances.
Bottom line
A coaxial cable is more than a passive wire. It is a controlled transmission line where geometry and dielectric material define impedance, delay, and phase behavior. Use this calculator early in design to make smarter choices, reduce mismatch risk, and speed up RF troubleshooting.