PhysicsCalcs
Electricity

Resonant Frequency Calculator

Calculate LC and RLC resonant frequency, find L or C for a target frequency, Q factor, bandwidth, and reactance at resonance.

Interactive calculator

Resonant Frequency Calculator

Calculate LC/RLC resonant frequency, find L or C for target resonance, Q factor, bandwidth, and reactance at resonance.

Inductor value

Capacitor value

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: find f\u2080, find L, find C, Q & BW, or reactance at resonance.
  • Enter inductance, capacitance, and/or resistance.
  • Click Calculate for results.

Table of Contents

Key Takeaways

  • Resonant frequency f₀ = 1/(2π√LC) depends only on L and C, not R.
  • At resonance, inductive and capacitive reactances cancel (XL = Xc).
  • Below resonance, the circuit is capacitive; above resonance, it is inductive.
  • The quality factor Q determines resonance sharpness and bandwidth.
  • Resonance is used in radio tuning, filters, oscillators, and impedance matching.

What Is Resonant Frequency?

Resonant frequency is the natural frequency at which an LC or RLC circuit oscillates with maximum energy transfer between the inductor and capacitor. At this frequency, the inductive reactance (XL) exactly equals the capacitive reactance (Xc), and they cancel each other in a series circuit.

Resonant Frequency Infographic

Resonance Formulas

f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}

Resonant frequency

Q=1RLCQ = \frac{1}{R}\sqrt{\frac{L}{C}}

Quality factor (series RLC)

Below, At, and Above Resonance

ConditionBehaviorPhase
f < f\u2080Xc > XL \u2192 CapacitiveCurrent leads voltage
f = f\u2080XL = Xc \u2192 ResistiveIn phase
f > f\u2080XL > Xc \u2192 InductiveVoltage leads current

How to Use the Resonant Frequency Calculator

  1. 1Choose a calculation mode.
  2. 2Enter inductance and/or capacitance values.
  3. 3For Q factor, also enter resistance.
  4. 4Click Calculate to see frequency, Q, bandwidth, or reactance.
  5. 5Review the step-by-step solution.

Example Calculations

LC Resonance

L = 10 mH, C = 100 nF. f&sub0; = 1/(2π√(0.01 × 10−7)) ≈ 5.03 kHz.

Find C for 1 MHz

f&sub0; = 1 MHz, L = 10 μH. C = 1/((2π × 10&sup6;)² × 10−5) ≈ 2.53 nF.

Where Resonant Frequency Calculations Are Used

AM/FM radio tuning, antenna design, bandpass filters, oscillators, wireless power transfer, impedance matching networks, crystal oscillators, and LC tank circuits in amplifiers.

Common Mistakes

  • Confusing resonant frequency with cutoff frequency.
  • Forgetting unit conversions (mH to H, nF to F).
  • Using series RLC Q formula for parallel circuits.
  • Assuming R affects resonant frequency.

Accuracy and Limitations

This calculator assumes ideal components. Real inductors have winding resistance and core losses, real capacitors have ESR and parasitic inductance. At very high frequencies, distributed effects and transmission-line behavior become important.

Frequently Asked Questions

What is resonant frequency?›

Resonant frequency is the frequency at which the inductive and capacitive reactances in an LC or RLC circuit are equal and cancel each other. At this frequency, energy oscillates freely between the inductor and capacitor.

Does resistance affect resonant frequency?›

No. The resonant frequency f₀ = 1/(2π√LC) depends only on inductance and capacitance. Resistance affects the Q factor, bandwidth, and damping, but not the resonant frequency itself.

What happens at resonance in a series RLC?›

At resonance, impedance is minimized and equals R. Current is maximized. The voltage across L and C can each be Q times the source voltage.

How do I choose L and C for a target frequency?›

Use f₀ = 1/(2π√LC). Pick one component, then calculate the other. This calculator’s “Find L” and “Find C” modes do this automatically.

What is the difference between resonance and cutoff frequency?›

Resonant frequency is where XL = Xc in an LC/RLC circuit. Cutoff frequency is the −3 dB point in a filter. They use different formulas and have different physical meanings.

Can I use this for parallel LC circuits?›

The formula f₀ = 1/(2π√LC) applies to both series and parallel LC circuits for the ideal case. However, the Q factor and bandwidth formulas differ for parallel RLC.

Sources / References

  1. OpenStax University Physics Vol 2: RLC Circuits
  2. HyperPhysics: Resonance
  3. NIST: SI Units
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish