Calculate resonant frequency from inductance and capacitance, or solve for the missing L, C, or f when you enter any two values with unit options.
Resonant Frequency Formula
The resonant frequency of an ideal LC circuit is found from inductance and capacitance. The calculator can also rearrange the same relationship to solve for inductance or capacitance when you enter the other two values.
f = 1/(2*pi*sqrt(L*C))
L = 1/((2*pi*f)^2*C)
C = 1/((2*pi*f)^2*L)
- f = resonant frequency, in hertz (Hz)
- L = inductance, in henrys (H)
- C = capacitance, in farads (F)
- pi = 3.14159265…
If you leave frequency blank, the calculator uses inductance and capacitance to find the resonant frequency. If you leave inductance blank, it uses capacitance and frequency to solve for the required inductance. If you leave capacitance blank, it uses inductance and frequency to solve for the required capacitance.
Common LC Circuit Unit Conversions
The formulas use base units: henrys, farads, and hertz. The calculator converts selected units before applying the formula.
| Quantity | Unit | Equivalent base unit |
|---|---|---|
| Inductance | 1 mH | 0.001 H |
| Inductance | 1 μH | 0.000001 H |
| Capacitance | 1 μF | 0.000001 F |
| Capacitance | 1 pF | 0.000000000001 F |
| Frequency | 1 kHz | 1,000 Hz |
| Frequency | 1 MHz | 1,000,000 Hz |
Example Calculations
Example 1: Find resonant frequency
Suppose you have an inductor of 10 μH and a capacitor of 100 pF.
Convert the values:
- 10 μH = 0.00001 H
- 100 pF = 0.0000000001 F
f = 1/(2*pi*sqrt(0.00001*0.0000000001))
The result is about 5,032,921 Hz, or 5.033 MHz.
Example 2: Find capacitance
Suppose you want a resonant frequency of 159.155 kHz with an inductance of 1 mH.
Convert the values:
- 159.155 kHz = 159,155 Hz
- 1 mH = 0.001 H
C = 1/((2*pi*159155)^2*0.001)
The result is about 0.000000001 F, or 1 nF. Since the calculator supports pF, that is about 1,000 pF.
FAQ
Does this formula work for both series and parallel LC circuits?
Yes, for an ideal LC circuit, the resonant frequency formula is the same for series and parallel resonance. Real circuits can differ because of resistance, coil losses, capacitor ESR, and stray capacitance.
Why does the measured resonant frequency differ from the calculated value?
The calculated value assumes ideal parts. Real inductors and capacitors have tolerances and parasitic effects. Circuit board layout, nearby conductors, lead length, and probe capacitance can also shift the actual resonant frequency.
What happens if inductance or capacitance increases?
If inductance increases, resonant frequency decreases. If capacitance increases, resonant frequency also decreases. The frequency depends on the square root of the product of L and C, so changes are not one-to-one.
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