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Loaded vertical calculator

How it works

A vertical shorter than a quarter wave looks capacitive, and a coil cancels that. The question is not how much inductance you need but what it costs you: a short antenna has a radiation resistance of a few ohms, and next to that the losses in the coil and in the ground stop being a detail.

Lradialsh 5 m
The coil cancels the capacitive reactance of a short vertical
Frequency (MHz)
Physical height (m)
Mast diameter (mm)
Coil position
Coil Q factor
Ground loss resistance (Ω)
Capacitance hat
Result
Coil inductance
Coil reactance
Antenna reactance without the coil
Mast characteristic impedance Z₀
Electrical length
Where the power goes
Radiation resistance
Coil loss resistance
Antenna efficiency

📐 The formulas​

Average characteristic impedance of the mast:

Z₀ = 60 × [ ln(2h/a) − 1 ]

Reactance of a shortened vertical:

Xa = − Z₀ × cot(β·h),     β = 2π/λ

Inductance of a base loading coil:

L = |Xa| / (2π·f)

At the centre of the mast you need about 1.6 times the inductance, and at 2/3 height about 2.3 times.

Radiation resistance of a short antenna:

Rr = 40π² × (h/λ)²  ≈ 394.8 × (h/λ)²

Where the power goes:

R_coil = X_L / Q
Efficiency = Rr / (Rr + R_coil + R_ground)

Symbols:​

  • h — physical height, a — mast radius
  • Q — coil Q: a real air-cored coil on HF gives 150–300
  • R_ground — the loss resistance of the radial system
Where this calculator stops:
  • Rr = 394.8·(h/λ)² holds roughly up to 0.15 λ: at 0.25 λ it gives 24.7 Ω instead of the real ~36
  • The corrections for coil position (1.6 and 2.3) are engineering factors, not an exact calculation
  • The hat's effect on radiation resistance is estimated with a factor of 1.6; the real gain depends on its size
  • Ground resistance is not calculated but entered: take it from the radial system calculator

🎯 In practice​

  • A 5 m vertical for 40 m. You need about 8.6 µH at the base — and an honest answer about how much efficiency is left.
  • A mobile whip. The same arithmetic: a short mast, a coil, and the bodywork playing a large part as “ground”.
  • Comparing options. Switch the coil position and watch what happens to the efficiency at the same height.
Practical advice:
  1. A centre coil wins on efficiency but is heavier and harder to build — a trade-off, not an obvious choice.
  2. A capacitance hat is almost always a better buy than a bigger coil: it raises the radiation resistance rather than merely cancelling reactance.
  3. Coil Q depends on the wire and former diameters: thin wire on a ferrite rod is the worst of all worlds.
  4. Ground losses are usually greater than coil losses. More radials buy you more than rewinding the coil.

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

How to cite this calculator
UR3PKI. «Loaded vertical calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/antennas/loaded_vertical (licence CC BY-NC-SA 4.0).

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