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Air variable capacitor calculator

The capacitance is not the point here

For a magnetic loop the capacitor has to be home-made: nothing rated for kilovolts is on sale. And the number that decides the design is not the capacitance but the voltage. Six kilovolts means a six-millimetre gap; a six-millimetre gap means few plates; few plates mean a large area. That is where the size comes from.

d 0.5 mmC21 plates
The capacitance is set by the plate area and their number, the voltage by the gap between them
What to compute
Plate shape
Plate radius (mm)
Overlap angle (°)
Number of plates
Plate spacing (mm)
Result
Capacitance
Number of plates
Gap
Overlap area of one pair
Voltage
Ideal breakdown (3 kV/mm)
Practical limit (1 kV/mm)
Permissible RMS voltage

📐 Formulas​

C = ε₀ · (n − 1) · A / d          n is the total number of plates

The overlap area for sector plates:

A = (θ · r²) / 2        θ in radians

Hence the capacitance varies linearly with the angle of rotation.

Breakdown voltage:

ideal (smooth plates, dry air):       3 kV/mm
practical (edges, damp, dust):        1 kV/mm
permissible RMS voltage = practical / √2

Check point:​

21 plates, a 30 mm sector (180°), a 0.5 mm gap → 501 pF, ≈ 500 V. The same stack with a 6 mm gap → 41.7 pF, ≈ 6 kV.

Limits of the calculator:
  • Fringing, which adds 5–15 % to the capacitance, is not included — the real value is a little higher
  • The minimum capacitance (with the rotor fully out) and the stray capacitance of the wiring are not included
  • 3 kV/mm is for ideal conditions; the practical limit is three times lower, and that is the figure used in the calculation
  • A magnetic loop needs a capacitor with no sliding contact — a butterfly; an ordinary tuning capacitor arcs at the wiper

🎯 Where it is used​

  • A capacitor for a magnetic loop — the main application.
  • A transmitter tank circuit, where the voltage is high.
  • Judging a ready-made capacitor: what voltage it will stand, given its gap.
Practical notes:
  1. For a loop use a butterfly: it has two stators and its rotor touches nothing — no arcing and no loss at a contact.
  2. The edges of the plates must be smooth and rounded: a sharp edge halves the breakdown voltage.
  3. A vacuum capacitor withstands 10–20 times the voltage at the same spacing.
  4. Check the voltage you actually need with the magnetic loop calculator — it usually turns out higher than it looks.

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

How to cite this calculator
UR3PKI. «Air variable capacitor calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/air_capacitor (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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