# Resonant Frequency Calculator

## Calculate the resonant frequency, inductance, or capacitance of a coil from any two values with the Resonant Frequency Calculator

The resonant frequency calculator can calculate the resonant frequency of a coil from the inductance and capacitance, calculate the inductance from the frequency and capacitance, or calculate the capacitance from the frequency and inductance.

The formula for the resonant frequency of a circuit shows that the same frequency will always be obtained as long as the product of the inductance and capacitance is constant. The relation between the two for a fixed frequency is called the L/C ratio. The resonant frequency formula is: $F=\frac{1}{2\pi\sqrt{LC}}$

Where
L = Inductance in Henrys (H)
C = Capacitance in Farads (F)
F = Frequency in cycles per second (C.P.S.) or Hertz (Hz)

These units may be inconvenient when dealing with radio frequencies. An alternative formula is: $F=\frac{10^6}{2\pi\sqrt{LC}}$

Where
L = Inductance in microhenrys (µH)
C = Capacitance in picofarads (pF)
F = Frequency in kilocycles (kc) or kilohertz (kHz)

Example 1: Using the resonant frequency formula, find the resonant frequency of a circuit with an inductance of 3.2 µH and capacitance of 970pF $F=\frac{10^6}{6.28\sqrt{3.2*970}}=\frac{10^6}{6.28*55.71}$ $=\frac{10^6}{350.05}=2856.667\; kc$

Example 2: Using the LC Constant formula, find the capacitance required to resonate at 1860 kc (1.86 Mc) with an inductance of 250 µH $LC=\frac{25,330}{1.86^2}=\frac{25,330}{3.4596}=7321.7$ $C=\frac{7321.7}{L}=\frac{7321.7}{250}=29.29\; pF$

### LC Constant

The Resonant Frequency Calculator also uses the LC Constant to calculate the inductance or capacitance when the frequency is known. The LC Constant formula is: $LC=\frac{25,330}{F^2}$

Where
L = Inductance in microhenrys (µH)
C = Capacitance in picofarads (pF)
F = Frequency in megacycles (Mc) or megahertz (MHz)

### Using the Resonant Frequency Calculator

Select the value that you would like to calculate

Inductance: Input the inductance and select your preferred units

Capacitance: Input the capacitance and select your preferred units

Frequency: Input the frequency and select your preferred units

Selecting units: You can choose your preferred units of measurement through selecting the units cells and clicking the downwards pointing arrow to display a list of available options

Learn As You Go: This feature displays a live example of how to perform the calculation using the figures that you enter

Reference: ARRL – The Radio Amateur’s Handbook