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LC resonance calculator

When you need this

Four quantities of a tuned circuit are tied together by two formulas. Enter any two — the rest follow.

L 2.611 µHC 22 pFfρ
L — inductance, C — capacitance, f — resonant frequency, ρ — characteristic impedance
What is given → what is wanted
Inductance L (µH)
Capacitance C (pF)
Resonant frequency f (MHz)
Characteristic impedance ρ (Ω)
Result
Inductance L
Capacitance C
Resonant frequency f
Characteristic impedance ρ

📐 Formulas​

f = 1 / (2π·√(L·C))                  resonant frequency
ρ = √(L / C) = 2πfL = 1/(2πfC)       characteristic impedance

Hence all four modes:

L, C → f = 1/(2π√(LC)),      ρ = √(L/C)
L, f → C = 1/(L·(2πf)²),     ρ = √(L/C)
C, f → L = 1/(C·(2πf)²),     ρ = √(L/C)
ρ, f → L = ρ/(2πf),          C = 1/(2πfρ)

Internally everything is worked out in SI (H, F, Hz, Ω); the units in the form are only a convenient wrapper. That is deliberate: most errors in calculators of this kind come precisely from hard-coded multipliers.

Notation:​

  • L — inductance [µH]
  • C — capacitance [pF]
  • f — resonant frequency [MHz]
  • ρ — characteristic impedance of the circuit [Ω]
Limits of the calculator:
  • This is an ideal loss-free circuit: the real resonant frequency is lower because of the self-capacitance of the coil and of the wiring
  • The self-capacitance of the coil is not taken into account — a separate calculator will estimate it
  • For high-Q circuits the difference between resonance by current and by voltage is negligible; for low-Q ones it is not

🎯 Where it is used​

  • Designing the tuned circuit of a local oscillator, a filter or an amplifier.
  • Choosing the capacitance for a coil that is already wound.
  • Choosing the characteristic impedance for the Q and the matching you need — the «ρ, f → L, C» mode.
Practical notes:
  1. The characteristic impedance ρ sets the Q of the circuit, Q = ρ/r, and the resonant impedance of a parallel circuit, R₀ = ρ·Q. That is where a design should start, not with component values.
  2. The computed values are written back into the fields — you can switch straight to another mode and carry on with the same numbers.
  3. The higher ρ is, the more lightly the circuit has to be coupled to the rest of the design so as not to spoil its Q.

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

How to cite this calculator
UR3PKI. «LC resonance calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/lc_resonance (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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