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LC resonant frequency calculator

A coil and a capacitor together swap energy back and forth at one natural frequency: their resonant frequency. It's how a radio picks out one station. Type L and C to find it, or pick a frequency and get the capacitor or coil that tunes to it.

µ or u = micro, m = milli.

p = pico, n = nano.

Resonant frequency, f₀ = 1 ÷ (2π√(LC))

1.07 MHz
Each part's reactance there, √(L ÷ C)
674 Ω
One swing takes
932 ns

How sharp: Q and bandwidth

Bigger R, sharper peak.

Quality factor, Q = R × √(C ÷ L)

14.8
Bandwidth, f₀ ÷ Q
72.3 kHz
Passes about
1.04 MHz to 1.11 MHz

The formula

f0 = 1 over 2π √(L × C)

L is in henries and C in farads. At f0 the coil's reactance, 2π f L, equals the capacitor's, 1 ÷ (2π f C), and the two cancel. To tune to a frequency, rearrange it:

C = 1 over (2π f)² × L and L = 1 over (2π f)² × C

Bigger parts swing more slowly. C sits under a square root, so four times the capacitance halves f0.

A worked example

Tune a radio to the AM station at 1,070 kHz with a 100 µH coil:

C = 1 over (2π × 1.07 MHz)² × 100 µH ≈ 221 pF

The nearest E6 value, 220 pF, tunes the tank to 1,073 kHz. Fed through 10 kΩ, its Q is 10 kΩ × √(220 pF ÷ 100 µH) ≈ 14.8, so it passes a band about 72 kHz wide, and a station at 1,500 kHz is cut to about a tenth.

Q and bandwidth

How sharp the peak is depends on the quality factor, Q. For a parallel tank fed through a resistor R, Q = R × √(C ÷ L): a bigger R gives a sharper peak. For a series LC with resistance R in the loop, Q = √(L ÷ C) ÷ R: there a smaller R is sharper. Either way the band between the two −3 dB edges is about f0 ÷ Q wide.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“LC resonance” is lesson 6 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 26 before it first.

Or start from the very first lesson, no account needed

The ideas behind it

Questions people ask

What is the formula for LC resonant frequency?

f₀ = 1 ÷ (2π × √(L × C)), with L in henries and C in farads. At that frequency the coil's reactance and the capacitor's are equal, so they cancel each other.

How do I find the capacitor for a resonant frequency?

Rearrange the formula: C = 1 ÷ ((2π × f)² × L). For 1,070 kHz with a 100 µH coil that's about 221 pF, so you'd fit 220 pF. An old radio's tuning dial is a variable capacitor doing exactly this.

What is the difference between series and parallel resonance?

A series LC's impedance drops to almost nothing at f₀, so the current through it peaks. A parallel tank's impedance soars at f₀, so fed through a resistor it passes f₀ and shorts other frequencies to ground. Both resonate at the same f₀.

What does Q mean for an LC circuit?

Q says how sharp the peak is: the band it passes, between the two −3 dB edges, is about f₀ ÷ Q wide. A tank fed through R has Q = R × √(C ÷ L); a series LC with R in the loop has Q = √(L ÷ C) ÷ R.

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