# Resonant Frequency Calculator

Calculate the resonant frequency of an LC circuit from inductance and capacitance. Find angular frequency and impedance. Free electronics calculator.

## What this calculates

The resonant frequency of an LC circuit is the frequency at which the inductor and capacitor exchange energy with maximum efficiency, causing the circuit to oscillate. It is determined by the formula f = 1/(2π√(LC)). This calculator computes resonant frequency, angular frequency, and impedance behavior at resonance.

## Inputs

- **Inductance** (mH) — min 0 — Inductance of the inductor in millihenries.
- **Capacitance** (μF) — min 0 — Capacitance of the capacitor in microfarads.

## Outputs

- **Resonant Frequency** (Hz) — Resonant frequency in hertz.
- **Resonant Frequency** (kHz) — Resonant frequency in kilohertz.
- **Angular Frequency** (rad/s) — Angular frequency ω = 2πf.
- **Impedance at Resonance** — formatted as text — At resonance, impedance of an ideal LC circuit is zero (series) or infinite (parallel).

## Details

An LC circuit consists of an inductor (L) and a capacitor (C) connected together. At the resonant frequency, the inductive reactance XL = ωL equals the capacitive reactance XC = 1/(ωC), and the two cancel each other. The result depends on the circuit configuration.

In a series LC circuit, the impedance drops to zero at resonance (or to just the resistance in a real RLC circuit), allowing maximum current flow. In a parallel LC circuit, the impedance reaches a theoretical maximum (infinity for ideal components), blocking current at the resonant frequency. This is the operating principle of bandpass and band-stop filters.

LC resonance is fundamental to radio tuning, oscillators, filters, and impedance matching networks. AM radios use variable capacitors to tune the LC circuit's resonant frequency to different broadcast stations. The formula f = 1/(2π√(LC)) was derived by William Thomson (Lord Kelvin) in 1853 and remains one of the most important equations in electrical engineering.

## Frequently Asked Questions

**Q: What is resonant frequency in an LC circuit?**

A: It is the frequency at which the inductive reactance and capacitive reactance are equal and cancel each other. The circuit oscillates naturally at this frequency, exchanging energy between the magnetic field of the inductor and the electric field of the capacitor.

**Q: What happens at resonance in a series vs. parallel LC circuit?**

A: In a series LC circuit, impedance is minimized at resonance, allowing maximum current. In a parallel LC circuit, impedance is maximized, blocking current at the resonant frequency.

**Q: How do I increase the resonant frequency of an LC circuit?**

A: Decrease either the inductance or the capacitance (or both). Since f = 1/(2π√(LC)), smaller L or C values result in a higher resonant frequency.

**Q: What is the quality factor (Q) of an LC circuit?**

A: The Q factor measures how underdamped the circuit is; higher Q means sharper resonance and less energy loss per cycle. For a series RLC circuit, Q = (1/R)√(L/C). Ideal LC circuits (no resistance) have infinite Q.

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Source: https://vastcalc.com/calculators/physics/resonant-frequency
Category: Physics
Last updated: 2026-04-21