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RLC Resonant Frequency Calculator

Calculate f₀ = 1 / (2π√LC)

Inductance L (H)
Capacitance C (F)
Quick Entry

Resonant Frequency Formula

f₀ = 1 / (2π√LC)
ω₀ = 1 / √LC (angular frequency, rad/s)
At resonance: XL = Xc, φ = 0, Z = R (series)
Period: T₀ = 1/f₀ = 2π√LC

Resonant frequency is the natural frequency at which an LC circuit oscillates. At this frequency, the inductive and capacitive reactances are equal, causing the circuit to appear purely resistive. The energy alternately stores in the inductor's magnetic field and the capacitor's electric field.

Resonance requires both L and C. Ideal LC (no R) oscillates forever. Real circuits have resistance that damps the oscillation. Higher Q = sharper resonance = less damping.

Understanding Resonance

Resonance occurs when the energy stored in the inductor equals the energy stored in the capacitor each cycle. At this point, the circuit offers minimum opposition (series) or maximum opposition (parallel) to current flow. The resonant frequency depends only on the product LC, not on resistance.

Resonance Condition

XL = Xc → 2πfL = 1/(2πfC) → f² = 1/(4π²LC) → f₀ = 1/(2π√LC). Simple derivation from reactance equality.

Series Resonance

Z = R (minimum). Current is maximum. Voltage across L and C can be Q×Vin (resonant step-up). Used in radio tuning.

Parallel Resonance

Z = ∞ (maximum, ideally). Current is minimum. Tank circuit stores energy. Used in oscillators and filters.

LC Oscillation

Energy oscillates between L and C at f₀. Peak inductor current = peak capacitor voltage. No power consumed (ideal).

Teaching Example: L=10mH, C=1μF.
f₀ = 1/(2π√(0.01×1e-6)) = 1/(2π×0.0001) = 1/(0.0006283) = 1591.5 Hz.
ω₀ = 1/√(0.01×1e-6) = 1/0.0001 = 10000 rad/s. T₀ = 1/1591.5 = 0.628 ms.
At f₀: XL = 2π×1591.5×0.01 = 100Ω, Xc = 1/(2π×1591.5×1e-6) = 100Ω. Equal!

Applications

Radio Tuners Oscillators Bandpass Filters Wireless Charging RFID Tags

Frequently Asked Questions

What is resonant frequency?
f₀ = 1/(2π√LC). Natural frequency where XL = Xc. Circuit appears purely resistive. Used in tuning and filtering.
Does R affect resonant frequency?
No. f₀ depends only on L and C. Resistance R affects damping, Q factor, and impedance at resonance, but not the resonant frequency itself.
How to increase resonant frequency?
Decrease L or C. Halving either value doubles f₀. Use smaller inductor (fewer turns) or smaller capacitor. f₀ ∝ 1/√(LC).
What is the difference between f₀ and ω₀?
f₀ in Hz (cycles per second). ω₀ in rad/s (radians per second). ω₀ = 2πf₀ = 1/√LC. ω₀ is used in calculus/physics equations.

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