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Wire-above-plane inductance calculator

When you need this

At UHF any length of wiring above a ground plane is already a piece of transmission line, not just a piece of wire.

Wire above a conducting plane: length b, height h, diameter d
b — length of the run parallel to the plane, h — height of the wire axis, d — wire diameter
Section length b (mm)
Height of the wire axis above the substrate h (mm)
Wire diameter d (mm)
Result
Inductance L
The same in microhenries
Characteristic impedance of this line Z₀
Reactance at 1 GHz

📐 Formulas​

The inductance is set by the height above the plane: the plane carries the return current, and the loop area is set by the distance between the wire and its mirror image.

L = (μ₀ / 2π) · b · arcosh(2h/d)

In convenient units (b in metres, h and d in the same units as each other):

L [µH] = 0.2 · b · arcosh(2h/d)

The same geometric factor sets the characteristic impedance of this line in air:

Z₀ = 59.95 · arcosh(2h/d)   Ω

Notation:​

  • b — length of the run parallel to the plane [mm]
  • h — height of the axis of the wire above the plane [mm]
  • d — wire diameter [mm]
  • Z₀ — characteristic impedance of such a line [Ω]
Limits of the calculator:
  • This is a lumped-element model: it holds as long as the electrical length of the run is no more than a few degrees
  • Closer to a quarter wavelength the run already transforms impedance, and beyond it turns capacitive — then it is a line that has to be calculated, not an inductance
  • The height h is measured to the axis of the wire, so it is always greater than d/2
  • The dielectric of the board is not taken into account — the formula is for air

🎯 Where it is used​

  • Estimating the wiring inductance in RF assemblies.
  • Working out the inductance of leads and jumpers.
  • Checking the characteristic impedance of a line the layout has formed by accident.
Practical notes:
  1. The characteristic impedance here is not a footnote: if it is far from the impedance of the chain, the run will spoil the match before it starts «adding inductance».
  2. 50 mm of 1 mm wire at a height of 5 mm gives 30 nH — at 1 GHz that is already 188 Ω. Which is exactly why UHF wiring is kept as short as possible.
  3. Bringing the wire closer to the ground plane is the simplest way to cut the stray inductance without shortening it.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Wire-above-plane inductance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/wire_above_plane (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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