Enter any two values (number of iterations, initial length, or total conductor length) into the calculator to estimate the total conductor (wire) length for a Koch-curve style fractal geometry.

Fractal Antenna Wire Length (Koch) Calculator

Enter any 2 values to calculate the missing variable

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Fractal Antenna Size Formula

The following equation is used to estimate the total conductor (wire) length for an ideal Koch-curve style fractal (a common fractal geometry used in “Koch” fractal antennas). This is a conductor-length estimate, not the antenna’s overall span or height.

L = L_0\left(\frac{4}{3}\right)^n
  • Where L is the total conductor (wire) length after n iterations (in meters, cm, inches, etc.)
  • L₀ is the initial straight length at iteration 0 (same units as L)
  • n is the number of iterations (typically a non‑negative integer)

To calculate the estimated conductor length, multiply the initial length by \(\left(\frac{4}{3}\right)^n\). (In the classic Koch construction, each iteration increases total length by a factor of \(4/3\).)

What is a Fractal Antenna?

Definition:

A fractal antenna is an antenna that uses a self-similar (fractal) geometry to pack a longer conductor path into a relatively compact area, often to help with multiband or wideband behavior compared with a simple straight element of the same overall size.

How to Calculate Fractal Antenna Size?

Example Problem:

The following example outlines the steps and information needed to estimate total conductor length for a Koch-curve style fractal.

First, determine the total number of iterations and the initial straight length. In this example, there are 6 iterations and the initial length is 10 cm.

Finally, calculate the estimated conductor length using the equation above:

L = L₀(4/3)^n

L = 10(4/3)^6

L = 56.1866 cm