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.

The capacitance is set by the plate area and their number, the voltage by the gap between them

What to compute	Capacitance from the geometryGeometry for a given capacitance and voltage
Plate shape	Sector (ordinary variable)Full circle (fixed)
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: C and Voltage». 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.