How to use it
- Type the two values you know into Frequency, Inductance and Capacitance, and leave the third box empty. For example, type Inductance 1 mH and Capacitance 1 µF, and leave Frequency empty.
- Read Resonant frequency f0, the frequency at which the reactances of L and C cancel.
- To see how sharp the peak is, type a Resistance R and read the Q factor and Bandwidth.
- Choose Series RLC or Parallel RLC under Circuit: the Q and bandwidth formulas differ.
The formulas
An inductor and a capacitor pass energy back and forth at one frequency, where their reactances are equal and opposite. That is the resonant frequency. A resistor in the same circuit damps the swing: the Q factor measures how sharp the resonance is, and the bandwidth is the width of the band between the two half-power points.
f0 = 1 ÷ (2π√(LC))
L = 1 ÷ ((2πf0)² × C)
C = 1 ÷ ((2πf0)² × L)
Series RLC: Q = (1 ÷ R)√(L ÷ C), Δf = R ÷ (2πL)
Parallel RLC: Q = R√(C ÷ L), Δf = 1 ÷ (2πRC)
Q = f0 ÷ Δf- A Q of 10 means the bandwidth is a tenth of the resonant frequency.
- A high Q gives a narrow, selective peak, as in a radio tuner. A low Q gives a wide, flat response.
What the calculator does not cover
- A circuit with more than one capacitor, inductor or resistor in one branch. Enter the equivalent values, or treat each branch on its own.
- Real parts: the resistance of an inductor's wire and the losses of a capacitor are part of R only when you enter them.
- The effect of the source and the load on the Q of a filter. In complex networks the true peak can sit a little away from f0.
Worked example: 1 mH and 1 µF with R 10 Ω
The resonant frequency is f0 = 1 ÷ (2π√(1 mH × 1 µF)) = 1 ÷ (2π × 31.62 µs) = 5.033 kHz.
With R = 10 Ω in series, Q = (1 ÷ 10) × √(1 mH ÷ 1 µF) = 0.1 × 31.62 = 3.16, and the bandwidth is Δf = 10 ÷ (2π × 1 mH) = 1.592 kHz.
As a check, f0 ÷ Q = 5.033 kHz ÷ 3.16 = 1.592 kHz, the same bandwidth.
Frequently asked questions
What is the resonant frequency of an LC circuit?
It is f0 = 1 ÷ (2π√(LC)). For 1 mH and 1 µF that is about 5.03 kHz. At this frequency the reactances of the inductor and the capacitor are equal, so in a series circuit they cancel.
What does a high Q factor mean?
A high Q means a sharp resonance with a narrow bandwidth, so the circuit responds strongly to one frequency and little to nearby ones. A low Q gives a broad, flat response.
Why do I have to leave one box empty?
The frequency, L and C are linked by one formula, so two of them fix the third. The empty box tells the calculator which value to work out. If all three are typed in, the result is over-determined and the calculator refuses it.
What is the difference between series and parallel RLC?
In a series circuit the resistor is in line with L and C, and a larger R lowers Q. In a parallel circuit the resistor sits across the L and C tank, and a larger R raises Q. Choose the one that matches your drawing.
Can I type 5k or 10µ in the boxes?
Yes. 5k in the frequency box is 5 kHz, and 10µ in the inductance or capacitance box is 10 µH or 10 µF. A unit typed after the number, such as 1mH or 1µF, is ignored.
Sources
Figures and text last checked on Tuesday, November 10, 2026.