RLC Resonance Calculator

A series RLC resonance calculation identifies the frequency at which an inductor and capacitor have equal, opposing reactance. The primary result, Resonant frequency, is used to set or check the operating frequency of tuned circuits, passive filters, impedance-matching networks, signal-selective branches, and resonant power circuits.

Enter Inductance, Capacitance, and Series resistance to calculate the ideal resonant frequency and first-order series-RLC quality metrics. The calculator returns:

• Resonant frequency in hertz (Hz)
• Quality factor, or Q
• Bandwidth in hertz (Hz)

At series resonance, inductive reactance and capacitive reactance cancel:

\(X_L=X_C\)

The circuit’s remaining impedance is primarily its series resistance. In an idealized series RLC circuit, this produces minimum impedance and maximum current at the resonant frequency.

Series Resonance

Inductance is entered in millihenries (mH), and Capacitance is entered in microfarads (uF). The calculator converts both values to base SI units before calculating resonance:

\(L_{\text{H}}=L_{\text{mH}}\times10^{-3}\)

\(C_{\text{F}}=C_{\text{uF}}\times10^{-6}\)

The ideal resonant frequency is:

\(f_0=\frac{1}{2\pi\sqrt{LC}}\)

Where:

Symbol	Electrical quantity	Unit
\(f_0\)	Resonant frequency	Hz
(L)	Inductance	H
(C)	Capacitance	F
\(\pi\)	Mathematical constant	—

Increasing inductance or capacitance lowers the resonant frequency. Reducing either value raises it. Series resistance does not change the calculator’s ideal reactance-cancellation frequency; it determines the calculated Q and bandwidth.

Quality Factor and Bandwidth

Series resistance is entered in ohms. It represents the total series loss used for the first-order estimate, including intended resistance and, where applicable, inductor winding resistance, capacitor equivalent series resistance, source resistance, conductor resistance, and other series losses.

For a series RLC circuit:

\(Q=\frac{1}{R}\sqrt{\frac{L}{C}}\)

This can also be expressed as:

\(Q=\frac{\omega_0L}{R}\)

Where \(\omega_0=2\pi f_0\).

The Quality factor describes resonance sharpness. A higher Q indicates lower series loss and a narrower frequency range around resonance. A lower Q indicates more damping and a wider response.

The calculator determines bandwidth from:

\(BW=\frac{f_0}{Q}\)

For this ideal series-RLC relationship, bandwidth can also be written as:

\(BW=\frac{R}{2\pi L}\)

Bandwidth is the separation between the lower and upper half-power, or −3 dB, frequencies. For a series resonant circuit, Q is the ratio of resonant frequency to bandwidth.

Calculation Example

Using the displayed values:

Input	Value
Inductance	10 mH
Capacitance	10 uF
Series resistance	10 ohm

First convert the reactive components:

\(L=10\text{ mH}=0.010\text{ H}\)

\(C=10\text{ uF}=0.000010\text{ F}\)

Calculate resonant frequency:

\(f_0=\frac{1}{2\pi\sqrt{(0.010)(0.000010)}}\)

\(\mathbf{f_0=503.2921\text{ Hz}}\)

Calculate quality factor:

\(Q=\frac{1}{10}\sqrt{\frac{0.010}{0.000010}}\)

\(\mathbf{Q=3.1623}\)

Calculate bandwidth:

\(BW=\frac{503.2921}{3.1623}\)

\(\mathbf{BW=159.1549\text{ Hz}}\)

The circuit is therefore centered at approximately 503.3 Hz with a relatively broad 159.2 Hz first-order bandwidth. A Q of 3.1623 indicates substantial series damping rather than a sharply selective tuned circuit.

Circuit and Field Limits

This calculation applies to an ideal lumped series RLC model. It does not determine circuit current, voltage across the inductor or capacitor, power dissipation, component heating, insulation suitability, conductor ampacity, branch-circuit protection, feeder capacity, voltage drop, raceway fill, or equipment listing requirements.

Use the actual installed or specified component data when finalizing a design. Inductor DC resistance, capacitor ESR, component tolerance, temperature, frequency-dependent core loss, skin effect, lead length, wiring inductance, source impedance, load impedance, and parasitic capacitance can materially change measured Q, bandwidth, and resonant behavior.

For power or building-electrical installations, the resonant calculation is separate from the field and code review. Verify conductor size, terminal rating, insulation temperature rating, overcurrent protection, available fault current, grounding and bonding, equipment instructions, and AHJ requirements independently.