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Coil self-capacitance calculator

When you need this

Self-capacitance cannot be measured directly, but it can be worked out from a series of resonances. Unlike the «two-frequency method», the line here is fitted through three or more points — and how well they sit on it is visible straight away.

LCsCf₀
Cs — self-capacitance of the coil, C — the tuning capacitor the measurement is made with
Measurements: capacitor value and resonant frequency
Measurement 1: C (pF) and f (MHz)
Measurement 2: C (pF) and f (MHz)
Measurement 3: C (pF) and f (MHz)
Measurement 4: C (pF) and f (MHz)
Measurement 5: C (pF) and f (MHz)
Measurement 6: C (pF) and f (MHz)
Measurement 7: C (pF) and f (MHz)
Measurement 8: C (pF) and f (MHz)
Result
Coil inductance L
Confidence interval for L (95 %)
Self-capacitance C₀
Confidence interval for C₀ (95 %)
Estimated self-resonant frequency f₀
How well the points fit a straight line, R²
Points used

📐 Formulas​

Capacitors of known value C are connected to the coil one after another and the resonant frequency f is measured each time. The self-capacitance C₀ adds to every C:

f = 1 / (2π·√(L·(C + C₀)))

Square it and invert:

1/f² = 4π²L·C + 4π²L·C₀

So in the coordinates (C; 1/f²) the points fall on a straight line y = a·x + b. After that it is ordinary least squares:

L  = a / 4π²
C₀ = b / a

In convenient units (C in picofarads, f in megahertz) the formula works with no extra factors:

1/f[MHz]² = 4π² · L[H] · (C + C₀)[pF]

The confidence interval from Student's distribution (n − 2 degrees of freedom):

s² = Σ(yᵢ − a·xᵢ − b)² / (n − 2)
SE(a) = s / √Sxx
SE(b) = s·√(1/n + x̄²/Sxx)
ΔL  = t₉₅ · SE(a) / 4π²
ΔC₀ ≈ |C₀| · t₉₅ · √( (SE(b)/b)² + (SE(a)/a)² )

Notation:​

  • C — capacitance of the tuning capacitor [pF]
  • f — measured resonant frequency [MHz]
  • L — inductance of the coil [µH]
  • C₀ — self-capacitance of the coil [pF]
  • R² — how well the points fit the line
Limits of the calculator:
  • You are measuring the whole setup, not the coil: the stray capacitance of the jig and the input capacitance of the instrument add to C₀
  • A confidence interval measures spread, not correctness: if every measurement is biased the same way, the interval will be narrow and the answer wrong
  • Keep the measuring frequencies an order of magnitude below the self-resonance of the coil
  • A high ESR smears out the resonance and makes the frequency reading imprecise

🎯 Where it is used​

  • Finding the self-resonance of a coil before putting it into a tuned circuit.
  • Measuring inductance without an inductance meter — a grid dip oscillator and a capacitance meter are enough.
  • Checking that a coil is not working too close to its self-resonance.
Practical notes:
  1. The «two-frequency method» is the same line through two points. A line through two points is unique, so there is simply nothing to show the error: one bad measurement tilts the line and the result comes out tidy and wrong.
  2. Measure the capacitors rather than reading the printed value. That is the commonest cause of a poor R²: the real capacitance can be tens of per cent off the nominal one.
  3. Do not use very small values of C: once the capacitor is comparable with C₀, the error grows sharply.

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

How to cite this calculator
UR3PKI. «Coil self-capacitance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/self_capacitance (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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