Resonant Frequency Calculator

Calculate the resonant frequency of LC and series RLC circuits, or solve for the required inductance or capacitance.

Circuit Inputs

Result

Engineering Guide

Resonant Frequency Calculator

Learn how to use the resonant frequency calculator to size inductors and capacitors, interpret the results, and avoid the most common mistakes when working with LC and RLC circuits in filters, oscillators, and matching networks.

Approx. 8–10 min read Circuit design & analysis

Quick Start: Using the Resonant Frequency Calculator

The resonant frequency calculator is built around the standard LC and RLC formulas you already know from class or work. It helps you move quickly between “solve for frequency” and “solve for L or C” without re-arranging equations by hand.

  1. 1 Choose the circuit type the calculator is modeling: typically a series LC or series RLC branch (for filters and oscillators) or a parallel resonant tank (for notches and RF matching). The core formula is \(\displaystyle f_0 = \frac{1}{2\pi\sqrt{LC}}\) for the ideal LC case.
  2. 2 Pick what you want to solve for. The common choices are: resonant frequency \(f_0\), inductance \(L\), or capacitance \(C\). In an RLC mode you may also see quality factor \(Q\) and bandwidth \(\Delta f\).
  3. 3 Enter known values with the correct units. Typical inputs are: \(L\) in \(\mu\text{H}\) or \(\text{mH}\), \(C\) in \(\text{nF}\) or \(\text{pF}\), and \(f_0\) in \(\text{kHz}\) or \(\text{MHz}\). The calculator normalizes everything internally, so mixing units is fine as long as each field’s unit matches the value you type.
  4. 4 For RLC modes, enter the series resistance \(R\) if you care about damping and bandwidth. The ideal resonant frequency is still based on \(L\) and \(C\), but the calculator can derive \(\displaystyle Q = \frac{1}{R}\sqrt{\frac{L}{C}}\) and approximate \(\Delta f = \frac{f_0}{Q}\).
  5. 5 Press Calculate. The calculator computes the primary result (for example, \(f_0\) in \(\text{Hz}\)) and shows a few quick stats such as angular frequency \(\omega_0 = 2\pi f_0\), period \(T = 1/f_0\), or \(Q\) and bandwidth when resistance is included.
  6. 6 Open Calculation Steps to see line-by-line algebra: the symbolic equation, numerical substitution, and the final value with units. This is handy for debugging design spreadsheets and for showing work on homework or lab reports.
  7. 7 Use the result as a starting point, not an absolute truth. Real components have tolerance, parasitics, and temperature drift; you may need to adjust \(L\) or \(C\) and re-run the calculator after prototyping.

Tip: If your math gives a frequency that is off by a factor of about \(2\pi\), you probably mixed up angular frequency \(\omega_0\) (in \(\text{rad/s}\)) with ordinary frequency \(f_0\) (in \(\text{Hz}\)).

Watch out: The calculator assumes positive, real values for \(L\) and \(C\). If either is zero, negative, or left blank, the result will be invalid or undefined.

Choosing Your Method or Mode

There are several ways to use resonant frequency equations in practice. The resonant frequency calculator groups them into a few natural modes that match how engineers typically think about the problem.

Mode 1 — Solve for Resonant Frequency \(f_0\)

This is the classic design question: you already know the inductor and capacitor you want to use, and you simply need to know where the resonance lands.

  • Perfect for quick checks on existing LC filters, RF tanks, and oscillators.
  • Matches most textbook and exam problems.
  • Steps output make it easy to verify hand calculations.
  • You must already have reasonable values for both \(L\) and \(C\).
  • Does not directly answer “what component value do I need?”
Ideal LC: \(f_0 = \dfrac{1}{2\pi\sqrt{LC}}\)

Mode 2 — Solve for \(L\) or \(C\) from a Target \(f_0\)

Here you start from a desired resonant frequency and one known component, then let the calculator rearrange the equation and solve for the missing value.

  • Ideal when you are picking a capacitor from a standard series for a fixed inductor, or vice versa.
  • Helps you see how small changes in frequency affect the required component value.
  • Reduces algebra errors when rearranging formulas under time pressure.
  • Still assumes the ideal LC model; parasitics are not directly included.
  • Extreme frequencies may require unrealistic component values.
Solve for \(C\):\; \(C = \dfrac{1}{(2\pi f_0)^2 L}\)

Mode 3 — Series RLC with \(Q\) and Bandwidth

When a resistor is present (as it is in any real inductor or series path), you care about how sharp the resonance is. This mode keeps the same core resonance equation but adds quality factor and bandwidth.

  • Great for designing narrowband filters or tuned amplifiers.
  • Relates circuit values directly to selectivity.
  • Lets you experiment with the trade-off between loss (R) and sharpness (Q).
  • Assumes a simple lumped series RLC; distributed or multi-resonant systems are more complex.
  • Very low \(R\) may produce unrealistically high \(Q\) if other losses are ignored.
\(Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}},\quad \Delta f \approx \dfrac{f_0}{Q}\)

What Moves the Resonant Frequency

Resonant frequency is highly sensitive to the reactive elements in your circuit and only weakly affected by resistance. The resonant frequency calculator helps you see which levers matter most.

Inductance \(L\)

Increasing \(L\) decreases \(f_0\) because the term \(\sqrt{LC}\) grows. For a fixed capacitor, doubling \(L\) reduces \(f_0\) by a factor of \(\sqrt{2}\).

Capacitance \(C\)

Increasing \(C\) also decreases \(f_0\). Switching from a \(47\ \text{nF}\) capacitor to a \(100\ \text{nF}\) part can move your resonant frequency down by roughly \(\sqrt{100/47}\).

Resistance \(R\)

In an ideal series RLC, the simple formula for \(f_0\) only depends on \(L\) and \(C\), but adding \(R\) lowers \(Q\) and widens the bandwidth. Very large \(R\) effectively kills the resonance.

Parasitics & stray reactances

Winding capacitance in inductors, trace inductance on PCBs, and device input capacitances all change the effective \(L\) and \(C\). At high frequencies, these parasitics can dominate, shifting the true resonant point away from the ideal calculation.

Component tolerances

Real inductors and capacitors can vary by ±5% to ±20%. Because \(f_0\) depends on \(\sqrt{LC}\), a ±10% tolerance in both parts can easily translate to several percent uncertainty in frequency.

Temperature & bias

Ferrite cores, ceramic dielectrics, and semiconductor junctions change value with temperature, DC bias, and signal level. The calculator assumes fixed values, so always apply margin in RF and power designs.

Worked Examples

These examples mirror what the resonant frequency calculator does internally. You can follow the math by hand, then confirm the numbers using the calculator for faster iteration.

Example 1 — Resonant Frequency of an LC Tank

  • Series LC tuned circuit for an audio filter.
  • Inductance \(L = 10\ \text{mH}\).
  • Capacitance \(C = 100\ \text{nF}\).
  • Resistance is ignored for the frequency calculation.
1
Start from the ideal LC resonance formula:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
2
Convert units and substitute: \(L = 10\ \text{mH} = 10\times 10^{-3}\ \text{H}\), \(C = 100\ \text{nF} = 100\times 10^{-9}\ \text{F}\).
\[ f_0 = \frac{1}{2\pi\sqrt{(10\times 10^{-3})(100\times 10^{-9})}} = \frac{1}{2\pi\sqrt{1\times 10^{-9}}} \]
3
Evaluate the square root and denominator: \(\sqrt{1\times 10^{-9}} = 3.16\times 10^{-5}\).
\[ 2\pi\sqrt{LC} \approx 2\pi \times 3.16\times 10^{-5} \approx 1.99\times 10^{-4} \]
4
Take the reciprocal to get the frequency:
\[ f_0 \approx \frac{1}{1.99\times 10^{-4}} \approx 5.0\times 10^{3}\ \text{Hz} \]
So the resonant frequency is about 5.0 kHz.

Example 2 — Choosing a Capacitor for a Target Resonant Frequency

  • RF tank circuit for a small transmitter.
  • Target resonant frequency \(f_0 = 100\ \text{kHz}\).
  • Available inductor \(L = 47\ \mu\text{H}\).
  • Find the required capacitance \(C\).
1
Rearrange the resonance formula to solve for \(C\):
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \quad\Rightarrow\quad C = \frac{1}{(2\pi f_0)^2 L} \]
2
Substitute values with base units: \(f_0 = 100\ \text{kHz} = 100\times 10^{3}\ \text{Hz}\), \(L = 47\ \mu\text{H} = 47\times 10^{-6}\ \text{H}\).
\[ C = \frac{1}{(2\pi \cdot 100\times 10^{3})^2 \cdot 47\times 10^{-6}} \]
3
Evaluate the numeric expression (the calculator does this automatically):
\[ C \approx 5.39\times 10^{-8}\ \text{F} \]
which is about 54 nF. You would typically pick the nearest standard value (for example, \(56\ \text{nF}\)) and then re-compute the actual \(f_0\) using the calculator.

In both examples, the resonant frequency calculator follows exactly these steps, but it also tracks units, computes derived quantities like \(\omega_0\) and \(T\), and provides a consistent way to experiment with different component values.

Common Layouts & Variations

The same resonant frequency equations show up in many circuit topologies. The layout, however, changes how strongly the resonance appears, how wide the passband is, and where the power flows. This table summarizes a few practical configurations.

ConfigurationTypical UseBehavior Around \(f_0\)Design Notes
Series LC in series with loadNarrowband audio filters, notch filters in power linesMinimum impedance at \(f_0\); current peaks through the branch.Watch component current ratings and make sure the load does not excessively damp the resonance.
Parallel LC across a line (tank)RF tank circuits, oscillators, impedance matching networksMaximum impedance at \(f_0\); branch tends to block current at resonance.Parasitic resistance sets the achievable \(Q\). Layout and shielding matter at high frequency.
Series RLC (R in series with LC)Tuned amplifiers, audio crossovers, band-pass sectionsFinite peak in current or voltage at \(f_0\), with bandwidth set by \(Q\).Use the calculator’s \(Q\) and \(\Delta f\) outputs to balance sharpness against loss and component tolerance.
Multiple resonant sections cascadedHigher-order filters, steep skirts in RF front-endsSeveral resonances interacting; overall response is sharper but more sensitive to mismatch.Individual sections may not share exactly the same \(f_0\); tolerances can distort the combined response.
  • Sketch the impedance or magnitude response around \(f_0\) to see whether you want a peak or a null.
  • Check that component voltage and current ratings are not exceeded at resonance.
  • Consider worst-case tolerance on \(L\), \(C\), and \(R\) when defining acceptable frequency drift.
  • Remember that PCB traces add both inductance and capacitance at higher frequencies.
  • Verify that any nearby resonances (mechanical or electrical) will not interfere with your design.
  • Use the calculator for both nominal and corner cases to understand how robust your circuit is.

Specs, Logistics & Sanity Checks

The resonant frequency calculator gives you ideal values. Turning those into a real product means choosing practical components, reading data sheets, and checking that the circuit behaves as expected on the bench.

Selecting Inductors and Capacitors

Use the calculator’s result as a target, then pick the closest standard value for \(L\) or \(C\) that meets your voltage, current, and size constraints. Pay attention to:

  • Inductor core material: ferrite vs. powdered iron vs. air core affects stability and loss.
  • Capacitor dielectric: NP0/C0G for stability; X7R or Y5V for cost and compactness but higher drift.
  • Rated current and voltage: resonance can significantly increase stress on components.

Tolerance, Q and Losses

The calculator may show a very sharp resonance for ideal components, but real parts always introduce loss. When reading data sheets:

  • Look for Q factor or ESR/ESL specs at or near your operating frequency.
  • Assume that Q is lower at the extremes of the frequency range and under high current or voltage.
  • Derate target \(Q\) and resonant gain to leave headroom for aging and temperature variation.

Measurement & Sanity Checks

Once you build the circuit, compare measured resonance to the calculator’s prediction:

  • Use a network analyzer, signal generator + scope, or simple sweep to find the actual peak or notch.
  • If measured \(f_0\) is significantly off, re-estimate parasitic capacitance and inductance and update the calculator inputs.
  • Re-run worst-case scenarios in the calculator using min/max component values to ensure the design still meets spec.

Whenever you change a component footprint, layout, or vendor, it is good practice to re-enter the updated values into the resonant frequency calculator and verify that the circuit still resonates where you expect.

Frequently Asked Questions

What is resonant frequency in an LC or RLC circuit?
Resonant frequency is the frequency at which the net reactance of the inductor and capacitor cancels out, leaving the circuit purely resistive. In an ideal LC circuit it is given by \(f_0 = 1/(2\pi\sqrt{LC})\). At this point energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor.
Does resistance change the resonant frequency value?
In a simple series RLC circuit, moderate resistance mainly affects the quality factor \(Q\) and bandwidth rather than the resonant frequency itself, so the calculator still uses the ideal LC formula for \(f_0\). Very large resistance or more complex topologies can shift the effective resonance slightly, but for most practical designs the LC expression is a good approximation.
Why does the formula include the 2π term?
Many derivations start from the natural angular frequency \(\omega_0\) in radians per second, where \(\omega_0 = 1/\sqrt{LC}\). To convert from angular frequency to ordinary frequency in hertz you use \(f_0 = \omega_0 / (2\pi)\), which produces the familiar \(1/(2\pi\sqrt{LC})\) form used by the calculator.
Should I use a series or parallel resonant configuration?
Use a series resonant configuration when you want a low impedance path at the resonant frequency, such as a band-pass branch or tuned current path. Use a parallel resonant or tank configuration when you want a high impedance at resonance, such as an RF tuning network or oscillator tank. The resonant frequency calculator gives you \(f_0\) either way; the choice depends on how you want the circuit to behave around that frequency.
What units should I use for L, C and frequency in the calculator?
Internally the calculator works in henries, farads and hertz, but the inputs accept more convenient units such as microhenries, millihenries, nanofarads, picofarads, hertz, kilohertz and megahertz. The important thing is to match the numeric value with the selected unit for each field; the calculator takes care of all conversions before applying the equations.
Why does the calculator show NaN or an error for my inputs?
NaN (not a number) usually means that at least one input was missing, zero or negative when the formula expects a positive value. Check that both \(L\) and \(C\) are greater than zero, that the units match the magnitude you entered, and that you are not using unrealistic values. If you are solving for \(L\) or \(C\) from a very low or very high frequency, the required component may be outside a practical range.
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