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Capacitance hat calculator

What it actually does

A hat does not “add height” — it adds capacitance at the top. That raises the current in the lower part of the mast, evens out the distribution, and the antenna radiates better at the same height. The smaller loading coil is a pleasant side effect, not the point.

r 0.5 mC
The hat adds capacitance at the top — the current along the mast evens out and the radiation resistance rises
Frequency (MHz)
Hat type
Hat radius (m)
Mast height (m)
Mast diameter (mm)
The hat itself
Hat capacitance
Capacitance of a solid disc of the same radius
Hat reactance
What this does for the antenna
Coil without a hat
Coil with a hat
Difference
Radiation resistance without a hat
Radiation resistance with a hat

📐 The formulas​

Capacitance of an isolated disc:

C = 8 × ε₀ × r  ≈  70.8 × r    [pF, r in metres]

A spoked ring — a fraction of the capacitance of a solid disc:

4 spokes  → 0.55 C        8 spokes  → 0.73 C
16 spokes → 0.85 C        solid disc → 1.00 C

What this does for the antenna:

X_hat = −1 / (2πf·C)
The reactance of the mast and of the hat combine as parallel capacitances,
so the inductance the coil has to provide falls.

Symbols:​

  • r — hat radius, ε₀ = 8.854·10⁻¹² F/m
Where this calculator stops:
  • C = 8ε₀r is for an isolated disc in free space. Near the ground and the mast the capacitance is somewhat higher
  • The spoke fractions are engineering factors, not an exact calculation
  • The rise in radiation resistance is estimated with a factor of 1.6 — the real figure depends on how the hat and the mast compare in size
  • If the hat radius approaches the mast height the model stops working, and the calculator says so

🎯 In practice​

  • A mobile whip. A few spokes at the top do more than a fatter coil.
  • A balcony vertical. The hat can be made of horizontal spokes — there is usually more room sideways than upwards.
  • Testing the idea. Compare the coil before and after: sometimes the hat removes it altogether.
Practical advice:
  1. Eight spokes is the sensible compromise: sixteen add only 12 % more capacitance for twice the work.
  2. Keep the spokes radial and equal, or you will get a horizontal component in the radiation.
  3. The higher the hat sits the better it works: at the top of the mast, not halfway up.
  4. Mechanics matter: a hat is a sail on the end of a lever.

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

How to cite this calculator
UR3PKI. «Capacitance hat calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/capacity_hat (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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