RLC Resonant Frequency Calculator
This calculator finds the resonant frequency of an RLC circuit from the inductance (L) and capacitance (C). It also calculates the angular frequency in radians per second, and if you enter the resistance (R) as well, it returns the Q factor (quality factor) which tells you how sharply the circuit resonates. An RLC circuit contains a resistor, an inductor and a capacitor. At the resonant frequency, the inductive and capacitive reactances are equal and opposite, leaving only the resistance to limit the current. In a series RLC circuit this means impedance is at its lowest and current is at its highest. In a parallel RLC circuit the opposite is true: impedance is highest and current is lowest at resonance. The resonant frequency is determined solely by L and C, not by R. The formula is f0 = 1 / (2 x pi x square root of (L x C)), where L is in henries and C is in farads. The angular frequency is omega0 = 2 x pi x f0 = 1 / square root of (L x C). The Q factor for a series circuit is Q = (1/R) x square root of (L/C); a higher Q means a sharper, more selective resonance and less energy lost per cycle. RLC circuits are used in radio tuners to select a specific frequency, in notch and bandpass filters, in oscillator circuits, and in switched-mode power supply design. Enter L in millihenries and C in microfarads for typical audio and power circuits, or adjust the units in the fields below.
L and C inputs are in mH and uF. Q factor requires resistance. Higher Q = sharper, more selective resonance.
How it works
L is converted from millihenries to henries (divide by 1000) and C from microfarads to farads (divide by 1,000,000). The angular resonant frequency is omega0 = 1 / square root of (L x C) rad/s. The resonant frequency in hertz is f0 = omega0 / (2 x pi). If R is entered, the series Q factor is Q = (1/R) x square root of (L/C) and the bandwidth is BW = f0 / Q = R / (2 x pi x L) in hertz. The bandwidth is the range of frequencies between the two -3 dB points on either side of resonance.
Worked example
An LC circuit has L = 10 mH (0.010 H) and C = 100 uF (100 x 10^-6 F). The product L x C = 0.010 x 100 x 10^-6 = 1 x 10^-6. The square root is 1 x 10^-3. The angular frequency is omega0 = 1 / (1 x 10^-3) = 1000 rad/s. The resonant frequency is f0 = 1000 / (2 x pi) = 159.15 Hz. With R = 10 ohms, the series Q factor would be Q = (1/10) x square root of (0.010 / 100 x 10^-6) = (1/10) x 10 = 1.0 and the bandwidth would be 159.15 / 1.0 = 159.15 Hz. These match the default L and C values above.
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