LC Resonant Frequency Calculator
Enter inductance and capacitance to get the resonant frequency of an LC tank circuit, with the period and angular frequency alongside.
How it works
At resonance the inductor's reactance and the capacitor's reactance are equal and opposite, so they cancel. What is left is only the circuit's real resistance, which is why a tank circuit responds so strongly at one particular frequency and weakly everywhere else.
The frequency depends on the product of L and C, under a square root. That has a practical consequence: to halve the resonant frequency you must quadruple either component, not double it. Tuning is coarser than it first appears.
This is the basis of radio tuning, oscillators and filters. A variable capacitor across a fixed coil sweeps the resonant point across a band, which is how an analogue receiver selects a station.
The formula
Resonant frequency
f = 1 ÷ (2π × √(L × C))
Angular frequency
ω = 2πf = 1 ÷ √(L × C)
Period
T = 1 ÷ f
Inductance for a target frequency
L = 1 ÷ ((2πf)² × C)
Worked examples
| Scenario | Working | Result |
|---|---|---|
| 1 mH with 1 µF | 1 ÷ (2π√(0.001 × 0.000001)) | 5.033 kHz |
| 100 µH with 100 pF | 1 ÷ (2π√(1e−4 × 1e−10)) | 1.592 MHz — the AM band |
| Quadrupling the capacitance | √4 = 2 in the denominator | Frequency halves, not quarters |
When you'd use it
- Tuning a receiver or transmitter to a band
- Designing an oscillator around a target frequency
- Building a notch or band-pass filter
- Checking whether stray inductance and capacitance will resonate in range
Common questions
Does it matter whether the L and C are in series or parallel?
The resonant frequency is the same for both. What differs is the behaviour at that frequency: a series LC presents minimum impedance and passes the signal, while a parallel LC presents maximum impedance and blocks it. Same frequency, opposite effect.
Why does resistance not appear in the formula?
It does not shift the resonant frequency appreciably, but it does control how sharp the peak is. That sharpness is the Q factor — low resistance gives a narrow, selective response; high resistance gives a broad, lossy one.
My real circuit resonates at a different frequency. Why?
Stray capacitance and lead inductance. At high frequencies the board itself contributes, and inductors have self-capacitance between turns. Calculated values get you close; a real tuned circuit almost always needs trimming.
Is anything I enter sent to a server?
No. Every calculation runs in your browser, so component values, circuit figures and measurements are never uploaded, logged or stored. There is no account and no record of what you typed.