RLC Resonant Frequency Calculator
Enter inductance (L) and capacitance (C) to calculate the ideal resonance: f0 = 1 / (2π√(LC)). Optionally add resistance (R) for damped behavior in a series RLC circuit.
Tip: For RF designs, small changes in nH and pF can cause large frequency shifts.
What is resonant frequency in an RLC circuit?
Resonant frequency is the frequency at which an RLC circuit naturally oscillates. At this point, the inductor’s reactance and the capacitor’s reactance are equal in magnitude and opposite in sign, so they cancel each other out. The circuit then behaves as if only resistance is left (for a series configuration), and energy moves back and forth between the electric field of the capacitor and the magnetic field of the inductor.
This behavior is central in filters, oscillators, impedance matching networks, radio tuners, and sensor interfaces. If you pick L and C carefully, you can target almost any frequency range—from low-frequency power systems up to high-frequency RF applications.
Core formulas used by this calculator
1) Ideal resonance (most common)
The ideal resonant angular frequency and frequency are:
ω0 = 1 / √(LC)
f0 = 1 / (2π√(LC))
where:
- L is inductance in henries (H)
- C is capacitance in farads (F)
- f0 is in hertz (Hz)
2) Damped series RLC oscillation (optional R input)
If resistance is included, the oscillation frequency can shift lower:
ωd = √(1/(LC) - (R/(2L))2), when underdamped.
If the quantity inside the square root becomes zero or negative, the circuit is critically damped or overdamped and does not oscillate sinusoidally.
How to use this RLC calculator
- Enter your inductor value and pick the correct unit (H, mH, µH, nH).
- Enter your capacitor value and pick the correct unit (F, mF, µF, nF, pF).
- (Optional) Enter resistance in ohms for damped series analysis.
- Click Calculate Resonant Frequency.
- Review ideal resonance, angular frequency, period, and damping outputs.
Series vs parallel resonance (quick intuition)
Series RLC
At resonance, total impedance is minimum (ideally just R), so current peaks. This is useful when you want a frequency-selective current path.
Parallel RLC
At resonance, impedance is maximum, so source current can dip while internal branch currents can still be significant. This is useful for tank circuits and frequency-selective loads.
Example calculation
Suppose you have:
- L = 10 mH
- C = 100 µF
Convert to SI units:
- L = 0.01 H
- C = 0.0001 F
Then:
f0 = 1 / (2π√(0.01 × 0.0001)) ≈ 159.15 Hz
If R = 5 Ω is added in a series model, the damped oscillation remains close to this value, and the quality factor can also be estimated.
Common mistakes to avoid
- Unit mismatch: confusing mH with µH or nF with µF causes huge errors.
- Ignoring parasitics: in real circuits, capacitor ESR and inductor winding resistance shift behavior.
- Assuming no tolerance: L and C components often vary by ±5% to ±20%.
- Forgetting layout effects: PCB traces introduce stray inductance and capacitance, especially at high frequency.
When this calculator is most useful
- Designing LC and RLC filters
- Estimating tank frequencies in oscillators
- Checking tuning in analog front-ends
- Educational labs and homework verification
- Rapid prototyping before simulation
Final note
This tool gives fast and reliable first-pass results for resonant frequency. For precision work—especially in RF, power electronics, or high-Q systems—follow up with circuit simulation and bench measurement. Real components and layout details always matter.