Resonant Frequency Calculator

Inductance:

Enter the tank inductor value and select the matching unit.

Capacitance:

Enter the capacitor value that resonates with the inductor.

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Inductor tolerance:

Enter a percent tolerance such as 5, 10, or 20.

Capacitor tolerance:

Set zero when you only need the ideal LC result.

Resistance model:

Choose series ESR or parallel load only when you have a real resistance value.

Loss resistance:

Optional resistance used only for Q and bandwidth estimates.

ohm

Display precision:

Adjust output precision without changing the calculation.

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Check	Value	Design note	Copy
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An LC resonant circuit is a small energy exchanger. The capacitor stores energy in an electric field, the inductor stores energy in a magnetic field, and the circuit has a natural rate at which energy moves back and forth between them. That natural rate is the resonant frequency, usually written as f0.

Resonance matters because many circuits are built to favor one frequency region and reject others. A radio tuner, a simple oscillator, a notch or band-pass filter, and a matching network all depend on the same idea: at one frequency, the inductor and capacitor have equal reactance magnitudes. Below that point the circuit looks more capacitive. Above it the circuit looks more inductive.

Reactance plot showing capacitive behavior below f0, inductive behavior above f0, and the XL equals XC crossing at resonance.

The first number people usually want is the ideal resonant frequency from inductance and capacitance. That value is useful, but it is not the same as a finished design answer. Real components have tolerances, resistance, parasitic capacitance, lead inductance, temperature drift, and a self-resonant frequency of their own. Those details decide whether the calculated center is a close prediction, a tuning starting point, or only a classroom-scale estimate.

Three terms make the rest of the calculation easier to read:

Reactance: The opposition an inductor or capacitor presents to alternating current. Inductive reactance rises with frequency, while capacitive reactance falls.
Q: A selectivity measure. Higher Q means a narrower resonant response when the loss model matches the real circuit.
Bandwidth: The approximate frequency width around resonance, often estimated from f0 divided by Q for simple resonant responses.

A careful LC estimate therefore has two jobs. It finds the ideal f0 from L and C, then it asks whether tolerance spread and loss make that number too fragile for the circuit being planned. For low-frequency examples, the ideal result may be close enough for learning or rough sizing. For RF work, part datasheets, layout parasitics, and measurement usually matter as much as the arithmetic.

How to Use This Tool:

Start with the two energy-storage values, then add optional tolerance and resistance values only when you have real numbers for them.

Enter Inductance and choose nH, uH, mH, or H. Use the inductor value that applies near the expected operating frequency when the datasheet gives frequency-dependent behavior.
Enter Capacitance and choose pF, nF, uF, mF, or F. Include the effective capacitance across the inductor, including known tuning and stray capacitance.
Read the summary first. A valid input set shows the calculated center frequency, the period, a reactance badge, and a frequency-context badge.
Open LC Frequency Ledger for the normalized L and C values, Resonant frequency, Angular frequency, Oscillation period, Reactance at f0, and Characteristic impedance.
Use Advanced for Inductor tolerance and Capacitor tolerance. Tolerance Loss Check then shows the low edge, high edge, and total frequency span from worst-case component drift.
Select Series resistance / ESR or Parallel load resistance only when the loss value is known. That enables Loaded Q and -3 dB bandwidth.
If the validation message appears, fix the named field before interpreting the results. Inductance and capacitance must be greater than zero, tolerances must stay from 0% to 80%, loss resistance cannot be negative, and display precision must stay from 2 to 6 decimals.

After the ledger looks sensible, open Reactance Crossing Plot to compare how the inductive and capacitive reactance curves meet at the calculated f0.

Interpreting Results:

Resonant frequency is the ideal center from the entered L and C values. Treat it as the first design estimate, not a promise that a physical circuit will peak at exactly that frequency.

Reactance at f0 and Characteristic impedance are the same magnitude in this ideal model. They are the bridge between the LC values and the optional Q estimate, because the selected resistance is compared with that reactance.

Frequency span warns how far the ideal center can move if both component tolerances shift in the worst direction.
Loaded Q is useful only when the chosen resistance model matches the actual circuit. A guessed ESR or load resistance can make bandwidth look more certain than it is.
Frequency context is a sanity label, not a standards certificate. RF, VHF, and microwave-range results need component self-resonance and layout checks.

The chart should show inductive reactance rising and capacitive reactance falling as frequency increases. If the plotted crossing is far above an inductor's self-resonant frequency, use a different part model or a measured network response before relying on the result.

Technical Details:

In the ideal LC model, energy moves between the capacitor's electric field and the inductor's magnetic field with no resistance and no radiation loss. The model is mathematically similar to a mass-spring oscillator: inductance plays the role of inertia, capacitance sets the electrical compliance, and the product L times C sets the time scale.

The frequency result comes from the point where the reactance magnitudes match. Inductive reactance is proportional to frequency, and capacitive reactance is inversely proportional to frequency. Setting those magnitudes equal gives the resonant angular frequency, then dividing by 2 pi gives frequency in hertz.

Formula Core:

Inductance is converted to henries and capacitance is converted to farads before the equations are applied.

\begin{array}{lll} f_{0} & = & \frac{1}{2 π \sqrt{L C}} \\ ω_{0} & = & 2 π f_{0} \\ Z_{0} & = & \sqrt{\frac{L}{C}} \\ T & = & \frac{1}{f_{0}} \end{array}

LC resonance variable meanings
Symbol	Meaning	Displayed result
L	Inductance in henries	Normalized from the entered inductance and unit.
C	Capacitance in farads	Normalized from the entered capacitance and unit.
f0	Ideal resonant frequency	Resonant frequency
ω0	Angular frequency in radians per second	Angular frequency
Z0	Characteristic impedance, equal to reactance magnitude at f0	Characteristic impedance and Reactance at f0
T	One ideal oscillation period	Oscillation period

With 10 mH and 0.1 uF, the normalized values are 0.01 H and 0.0000001 F. The LC product is 0.000000001, so f0 is about 5.033 kHz. The period is about 198.7 us, and Z0 is about 316.2 ohm.

Tolerance and Loss Rules:

Tolerance drift is modeled by recalculating f0 at the worst low and high component extremes. Loss modeling uses the characteristic impedance at resonance and the selected resistance model.

Resonance tolerance and loaded Q rules
Quantity	Rule used	Interpretation
Low frequency edge	Recalculate f0 with L and C both increased by their tolerance percentages.	Higher L and C lower resonance.
High frequency edge	Recalculate f0 with L and C both decreased by their tolerance percentages.	Lower L and C raise resonance.
Frequency span	(High edge - low edge) divided by nominal f0, shown as a percent.	Shows component tolerance spread, not measured passband width.
Series loaded Q	Q = Z0 / R for series resistance or ESR.	More series resistance lowers Q and widens bandwidth.
Parallel loaded Q	Q = R / Z0 for a parallel load resistance.	A larger parallel resistance raises Q and narrows bandwidth.
-3 dB bandwidth	Bandwidth = f0 / Q when Q is modeled.	Approximate for simple resonant responses; topology and loading still matter.

Frequency Context Bands:

Frequency context bands used by the resonant frequency result
Band label	Frequency range	Practical note
Sub-audio	< 20 Hz	Large inductors or capacitors may have losses that dominate the ideal model.
Audio range	20 Hz to < 20 kHz	Common for learning circuits, audio filters, and low-frequency oscillators.
Ultrasonic / LF	20 kHz to < 300 kHz	Tolerance, winding resistance, and capacitor type often become visible.
RF / HF	300 kHz to < 30 MHz	Check Q, self-resonant frequency, and layout capacitance.
VHF to microwave	30 MHz to < 3 GHz	Parasitics can move measured resonance substantially.
Microwave range	>= 3 GHz	Use component models and layout extraction rather than lumped ideal values alone.

Validation Bounds:

Input validation bounds for the resonant frequency calculator
Input	Accepted values	Why it matters
Inductance	Greater than zero; nH, uH, mH, or H.	Zero or negative inductance cannot produce a physical LC frequency.
Capacitance	Greater than zero; pF, nF, uF, mF, or F.	Zero or negative capacitance breaks the square-root term.
Component tolerances	0% to 80%.	Limits the worst-case edge calculation to a bounded, interpretable range.
Loss resistance	Zero or positive.	Negative resistance is not valid for the simple passive Q estimate.
Display precision	2 to 6 decimal places.	Controls displayed values and exports without changing the underlying calculation.

The reactance crossing data samples fixed frequency ratios around f0. At 0.25x f0 the capacitive reactance magnitude is four times Z0 and the inductive reactance is one quarter of Z0. At 4x f0 those roles reverse. The 1x row is the resonance point where both magnitudes equal Z0.

Limitations:

The calculation is an ideal lumped-element estimate with optional first-order tolerance and loss checks. It is useful for planning, comparison, and sanity checks, but it does not replace datasheet review or measurement when parasitics are significant.

Check inductor self-resonant frequency before trusting an RF or microwave result.
Use measured or specified resistance for Q; guessed resistance can make -3 dB bandwidth misleading.
Include known stray capacitance, lead inductance, and loading when those effects are a meaningful share of the tank values.
Confirm the actual topology. Series and parallel resonant circuits use the same ideal f0, but their impedance peaks, current peaks, and loading behavior differ.

Worked Examples:

A small audio-range tank with Inductance set to 10 mH and Capacitance set to 0.1 uF produces a Resonant frequency near 5.033 kHz. The LC Frequency Ledger also reports an Oscillation period near 198.7 us and Reactance at f0 near 316.2 ohm, which makes the result easy to check against the equation.

With the same L and C values, 5% inductor tolerance and 5% capacitor tolerance move the Low frequency edge to about 4.793 kHz and the High frequency edge to about 5.298 kHz. The Frequency span is roughly 504.5 Hz wide, so a narrow filter should not be judged from the nominal f0 alone.

An RF-style estimate with 100 uH and 100 pF lands near 1.592 MHz, which falls in the RF / HF context band. That label is a prompt to check inductor Q, self-resonant frequency, and layout capacitance before treating the ideal value as a final tuning point.

A common input failure is entering 0 for capacitance while experimenting with units. The summary changes to Check input, and the validation list asks for capacitance greater than zero. Fix that field before reading Tolerance Loss Check or the chart, because no frequency, Q, or bandwidth value is meaningful until both L and C are positive.

FAQ:

Why does a larger capacitor lower the resonant frequency?

The frequency is divided by the square root of L times C. Increasing capacitance makes that product larger, so the energy exchange takes longer and Resonant frequency falls.

Should I choose series or parallel resistance for Q?

Use Series resistance / ESR when the loss is in the tank path, such as winding resistance or equivalent series resistance. Use Parallel load resistance when the tank is being loaded by a resistance across it.

Why is bandwidth shown as not modeled?

-3 dB bandwidth needs Loaded Q, and loaded Q needs a positive Loss resistance with either the series or parallel resistance model selected.

Why does the summary say Check input?

The calculation needs positive inductance and capacitance, valid units, tolerances from 0% to 80%, nonnegative loss resistance, and display precision from 2 to 6 decimals. Fix the named validation message before using the ledger or chart.

Does the calculation leave my browser?

The LC math, tables, JSON, and chart data are calculated in the browser. The entered component values do not need to be uploaded for the resonance calculation.

Can this replace a measured RF design check?

No. The calculator gives ideal LC resonance plus simple tolerance and loss estimates. For RF work, compare the result with self-resonant frequency, component models, layout parasitics, and measured response.

Glossary:

Resonant frequency: The ideal frequency where an LC tank's inductive and capacitive reactance magnitudes match.
Angular frequency: The same oscillation rate expressed in radians per second.
Characteristic impedance: The square root of inductance divided by capacitance, used here as the reactance magnitude at f0.
Loaded Q: A selectivity estimate based on the selected resistance model and the reactance magnitude at resonance.
Self-resonant frequency: The frequency where a real inductor's parasitic capacitance resonates with its inductance and changes how the part behaves.
Parasitics: Unwanted capacitance, inductance, or resistance from component construction, leads, traces, dielectric materials, and layout.

References:

Oscillations in an LC Circuit, OpenStax.
RLC Series AC Circuits, OpenStax.
Q Factor and Bandwidth of a Resonant Circuit, All About Circuits.
ADALM2000 Activity: Inductor Self Resonance, Analog Devices, December 2023.