LC Circuit Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit from inductance and capacitance.
Shows frequency in Hz, kHz, and angular frequency in rad/s.
Resonant Frequency
How LC Resonance Frequency Is Calculated
An LC circuit consists of an inductor (L) and capacitor (C) connected together. At the resonant frequency, the circuit oscillates with maximum amplitude — the basis of radio tuning, oscillators, and filters.
Resonance Frequency Formula:
f = 1 / (2π × √(L × C))
Where:
- f = resonant frequency in Hertz (Hz)
- L = inductance in Henries (H)
- C = capacitance in Farads (F)
- 2π ≈ 6.2832
Angular Resonance Frequency:
ω₀ = 1 / √(L × C) (in radians/second)
Worked Example: AM radio tuning circuit: L = 250 µH (250×10⁻⁶ H), C = 365 pF (365×10⁻¹² F):
- f = 1 / (2π × √(250×10⁻⁶ × 365×10⁻¹²))
- LC = 9.125×10⁻¹⁴
- √LC = 9.553×10⁻⁷
- f = 1 / (2π × 9.553×10⁻⁷) = 1 / 6.003×10⁻⁶ = 166,600 Hz ≈ 166.6 kHz
By reducing capacitance to 50 pF (top of AM band):
- f = 1 / (2π × √(250×10⁻⁶ × 50×10⁻¹²)) = 1,422 kHz — sweeping the entire AM band (535–1605 kHz) with variable capacitor.
Quality Factor (Q):
Q = (1/R) × √(L/C)
Higher Q = sharper resonance, better frequency selectivity. Typical radio circuits: Q = 50–200.