LC Circuit Resonance Frequency Calculator – Find Resonant Frequency Free

How to use the LC resonance frequency calculator

1. Enter the inductance (L) in henrys — convert millihenrys by dividing by 1,000 and microhenrys by dividing by 1,000,000.
2. Enter the capacitance (C) in farads — convert microfarads by dividing by 1,000,000 and nanofarads by dividing by 1,000,000,000.
3. Click “Calculate Resonance Frequency”.
4. Read the result in hertz, shown on the page.

A worked example

Take a 10 mH inductor (0.01 henrys) and a 100 nF capacitor (0.0000001 farads). The formula is f₀ = 1 ÷ (2 × π × √(L × C)). First multiply: 0.01 × 0.0000001 = 0.000000001. The square root of that is 0.0000316. Multiply by 2π to get 0.000199, and 1 ÷ 0.000199 = 5,033. So the circuit resonates at about 5.03 kHz. At exactly that frequency, the inductive reactance (about 316 ohms) equals the capacitive reactance (also about 316 ohms), they cancel, and the circuit’s impedance is at its minimum for a series circuit — which is why a radio tuned to that frequency picks up one station strongly and the rest weakly.

Where resonance is used

• Radio tuning: a variable capacitor paired with a fixed inductor lets a radio select one station’s frequency and reject the others.
• Filters and crossovers: resonant circuits sharpen a filter’s response around the frequency you want to keep or remove.
• Wireless power and induction: chargers and induction hobs work best at the resonant frequency of their coils, where energy transfers most efficiently.
• Oscillators: many signal generators and clocks use an LC tank circuit to set their operating frequency.

Series and parallel resonance behave differently

The resonant frequency itself is the same for series and parallel LC circuits — the formula does not change — but what happens at resonance is opposite. In a series circuit, impedance is at its lowest at resonance, so current is at its highest. In a parallel circuit, impedance is at its highest, so current drawn from the source is at its lowest while a large current circulates between the inductor and capacitor. This calculator gives the frequency for both cases; which behaviour you get depends on how you wired the parts. Keep that distinction in mind when you design, because choosing the wrong arrangement gives you the opposite of the effect you wanted.

Honest limitations

• The calculator assumes ideal parts. Real inductors have resistance, which lowers the sharpness of resonance (the Q factor) and slightly shifts the peak.
• Unit mistakes are the most common error: a 100 nF capacitor entered as 100 farads gives a nonsense answer, so convert to henrys and farads first.
• Stray capacitance in wiring and on circuit boards adds to your capacitor’s value, which matters most at high frequencies with small capacitors.
• This tool gives the resonant frequency only. For bandwidth, Q factor or impedance at other frequencies, you need the resistance and the circuit arrangement too.

LC circuit resonance frequency calculator – frequently asked questions

What is the formula for resonant frequency?

f₀ = 1 ÷ (2π√(LC)), where L is inductance in henrys and C is capacitance in farads. The answer comes out in hertz.

Does a bigger capacitor raise or lower the resonant frequency?

Lower. Increasing either L or C lowers the resonant frequency, because the square root of their product sits in the denominator.

Is the formula the same for series and parallel circuits?

Yes, the resonant frequency is the same. What differs is the impedance at resonance: lowest for series, highest for parallel.

How do I work out the reactances at resonance?

At resonance XL equals XC. Use the inductive reactance calculator and the capacitive reactance calculator at the resonant frequency to confirm they match.