Coaxial cable impedance calculator

Enter both diameters in any shared unit, such as millimetres or inches, because only their ratio affects the result. The calculator returns impedance in ohms using the standard lossless coaxial-line relationship, making it useful for early cable design, geometry checks, and comparisons between dielectric materials.

Enter the conductor geometry correctly

Use the inside diameter of the outer conductor for outer_diameter and the outside diameter of the centre conductor for inner_diameter. These are the two conductive surfaces facing the dielectric, so jacket thickness and the outside size of the shield do not belong in the calculation. Both diameter values must use the same unit. Millimetres, inches, or any other linear unit work equally well because the formula uses the ratio between them, not their absolute scale. The outer diameter must be strictly greater than the inner diameter; otherwise there is no annular dielectric region and the proposed coaxial geometry is invalid. Enter diameter rather than radius unless you consistently convert both values. Using both radii would produce the same ratio, but mixing one radius with one diameter would give a misleading result. Measurements should describe a concentric cable. Significant eccentricity, deformation, braid structure, or manufacturing tolerance can make a physical cable differ from this ideal estimate.

Understand the dielectric constant and formula

The dielectric_constant input is relative permittivity, often written as epsilon r. It is dimensionless and must be positive. Use the effective value for the material and construction between conductors rather than an unrelated bulk-material figure when accurate design work matters. The calculator evaluates 60 times the natural logarithm of the outer-to-inner diameter ratio, divided by the square root of relative permittivity. This is the standard closed-form expression for the characteristic impedance of an ideal, uniform, lossless coaxial transmission line with nonmagnetic materials. A larger diameter ratio raises impedance, while a higher dielectric constant lowers it. The result is rounded to six decimal places for stable machine-readable output. The calculation does not model conductor resistance, dielectric loss tangent, surface roughness, frequency-dependent dispersion, connectors, or discontinuities. Those effects influence real insertion loss and impedance behaviour, but they are separate from the ideal geometric characteristic impedance calculated here.

Use the result in cable and RF design

Compare the returned impedance with the target impedance of the source, load, connector, and surrounding transmission system. Common systems are designed around a consistent nominal impedance, and an unintended mismatch can create reflections, standing waves, and reduced power transfer. During preliminary design, vary one input at a time to see whether changing the centre conductor, shield spacing, or dielectric brings the geometry closer to the target. Keep realistic production tolerances in mind: a mathematically exact result does not guarantee every manufactured length will have that exact impedance. For an existing cable, use dimensions taken at the conductor boundaries and the best available effective permittivity, then treat the answer as an engineering estimate. Precision verification still calls for appropriate measurement, such as a time-domain reflectometer or vector network analyser, especially across a required frequency band. The API uses the same deterministic calculation as the browser tool and costs $0.002 per request, which makes repeated design sweeps and automated validation straightforward.