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.

Quantity	Value	Detail	Copy
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Check	Value	Design note	Copy
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Resonant frequency is the natural oscillation point of an inductor-capacitor circuit. At that point, energy moves back and forth between the inductor's magnetic field and the capacitor's electric field, and the inductive and capacitive reactance magnitudes match. For a radio tuner, filter, oscillator, sensor coil, or classroom tank circuit, that frequency is the number that tells you where the LC pair wants to respond most strongly.

The same inductance and capacitance can behave differently once real parts are mounted on a board. Tolerance changes the center frequency, winding resistance and load resistance reduce selectivity, and stray capacitance can move high-frequency work away from the ideal value. A 10 mH inductor with a 0.1 uF capacitor lands near 5.033 kHz in the ideal calculation, but 5% component tolerances already spread that result by about 10% from low edge to high edge.

LC reactance crossing diagram with inductive reactance rising and capacitive reactance falling at resonant frequency.

The ideal LC formula is a useful starting point because it shows the main direction of change: increasing either inductance or capacitance lowers the resonant frequency, while reducing either value raises it. That starting point does not prove that a practical circuit will peak at exactly the calculated number. At RF and above, component self-resonance, lead length, board dielectric, probe loading, and the surrounding circuit can matter as much as the printed L and C values.

A resonant-frequency result is therefore best read as an engineering estimate with a clear set of assumptions. It is strong for first-pass component selection, tolerance comparison, and quick Q or bandwidth checks. It still needs measurement, simulation, or vendor models before it becomes a release value for a tuned filter, oscillator, antenna match, or sensor front end.

Technical Details:

An LC circuit reaches ideal resonance when inductive reactance and capacitive reactance have equal magnitude. Inductive reactance grows with frequency. Capacitive reactance shrinks with frequency. Where they meet, their reactive effects cancel in the ideal math, leaving a series circuit at minimum impedance or a parallel tank at maximum impedance, depending on topology.

The calculation uses lumped inductance in henries and capacitance in farads. It does not model winding capacitance, equivalent series resistance beyond the optional Q estimate, dielectric loss, magnetic core behavior, coupling to nearby conductors, or active oscillator conditions. Those omissions are acceptable for a first-pass LC number, but they explain why measured RF resonance can move away from the nominal result.

Formula Core:

The primary equation computes the ideal resonant frequency from inductance and capacitance. The companion quantities describe the same point in angular frequency, time period, and reactance terms.

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

LC resonance symbols and result fields
Symbol	Meaning	Unit	Shown as
L	Inductance after unit conversion	H	Inductance
C	Capacitance after unit conversion	F	Capacitance
f0	Ideal resonant frequency	Hz, kHz, MHz, or GHz	Resonant frequency
omega0	Angular frequency at resonance	rad/s	Angular frequency
T	One ideal oscillation cycle	s, ms, us, ns, or ps	Oscillation period
X0	Reactance magnitude where XL and XC match	ohm, kohm, or Mohm	Reactance at f0 and Characteristic impedance

Tolerance drift is calculated as a worst-case spread around the nominal LC value. The low-frequency edge assumes both inductance and capacitance are high. The high-frequency edge assumes both are low. The percentage span is the high-low difference compared with the nominal frequency.

\begin{array}{lcl} f_{low} & = & \frac{1}{2 π \sqrt{L (1 + t_{L}) C (1 + t_{C})}} \\ f_{high} & = & \frac{1}{2 π \sqrt{L (1 - t_{L}) C (1 - t_{C})}} \end{array}

Optional loss math estimates loaded Q and bandwidth when a real resistance value is known. A series resistance or ESR reduces Q as resistance rises. A parallel load resistance raises Q as resistance rises. The bandwidth estimate uses the common approximation bandwidth equals resonant frequency divided by Q.

Loss model formulas for loaded Q and bandwidth
Selected resistance model	Loaded Q formula	Bandwidth formula	When to use it
No loss model	Not modeled	Not modeled	Use when ESR or load resistance is unknown.
Series resistance / ESR	Q = X0 / R	BW = f0 / Q	Use for winding resistance or series loss near the LC pair.
Parallel load resistance	Q = R / X0	BW = f0 / Q	Use for a shunt load across a tank circuit.

The frequency context label is a coarse planning cue, not a standards classification. It flags where parasitics become harder to ignore.

Frequency context labels and boundaries
Displayed context	Boundary	Practical reading
Sub-audio	Below 20 Hz	Large L or C values can make practical losses dominate.
Audio range	20 Hz to below 20 kHz	Useful for audio filters, oscillators, and teaching examples.
Ultrasonic / LF	20 kHz to below 300 kHz	Tolerance and winding resistance often become visible.
RF / HF	300 kHz to below 30 MHz	Inductor self-resonance, Q, and layout capacitance need review.
VHF to microwave	30 MHz to below 3 GHz	Measured resonance can shift substantially with board geometry.
Microwave range	3 GHz and above	Use component models and layout extraction rather than only ideal lumped values.

Everyday Use & Decision Guide:

Start with the values that the circuit will actually see. Use the inductor value at the operating frequency when a datasheet gives frequency-dependent behavior, and use the effective capacitance across the inductor. For a tuned circuit, effective capacitance includes the deliberate capacitor plus known stray capacitance from layout, device pins, and fixtures when those values are available.

For a first pass, leave Resistance model at No loss model unless you have a measured ESR, winding resistance, or load resistance. The nominal LC Resonant Frequency and LC Frequency Ledger remain useful without a loss model. Add resistance only when you want the Loaded Q and -3 dB bandwidth rows to reflect a real loss assumption.

Use Inductance units of nH, uH, mH, or H, and Capacitance units of pF, nF, uF, mF, or F.
Set Inductor tolerance and Capacitor tolerance to zero for an ideal result, or enter part tolerances up to 80% to see worst-case frequency spread.
Use Series resistance / ESR for resistance in series with the tank current path, and Parallel load resistance for a shunt load across the resonant circuit.
Open Reactance Crossing Plot when you want to see XL rising and XC falling around f0. The plotted ratios run from 0.25x to 4x the resonant frequency.
Adjust Display precision only for displayed decimals. It does not change the underlying calculation.

Do not treat a narrow bandwidth estimate as proof that a physical circuit will be selective. A high calculated Q can disappear when the inductor is near self-resonance, the capacitor has high loss, the source or load is too heavy, or the board adds unexpected capacitance. Check the Component SRF guard and Layout parasitics rows before using an RF result as a design target.

After the nominal frequency looks right, compare Low frequency edge, High frequency edge, Frequency span, Loaded Q, and -3 dB bandwidth. Those rows tell you whether the part values are only close in theory or still reasonable after tolerance and loss assumptions.

Step-by-Step Guide:

Work from nominal LC values first, then add tolerance and loss only when those assumptions are known.

Enter Inductance and choose nH, uH, mH, or H. The input must be greater than zero before the summary can calculate.
Enter Capacitance and choose pF, nF, uF, mF, or F. Once both main values are valid, the summary heading changes to LC Resonant Frequency and the primary number shows f0.
Open Advanced when tolerance or loss matters. Enter Inductor tolerance and Capacitor tolerance as percent values from 0 to 80.
Choose Resistance model only when you have a real resistance value. Enter Loss resistance in ohms to calculate Loaded Q and -3 dB bandwidth.
Review LC Frequency Ledger for Resonant frequency, Angular frequency, Oscillation period, Reactance at f0, Characteristic impedance, and Frequency context.
Review Tolerance Loss Check for Low frequency edge, High frequency edge, Frequency span, Loaded Q, -3 dB bandwidth, Component SRF guard, and Layout parasitics.
Use Reactance Crossing Plot to confirm the visual crossing. At 1.00x f0, inductive and capacitive reactance values meet at the calculated reactance.
If a validation message appears, fix that field before using any result. Common messages include Inductance must be greater than zero, Capacitance must be greater than zero, tolerance outside 0 to 80%, negative loss resistance, or display precision outside 2 to 6 decimals.

Interpreting Results:

Resonant frequency is the headline result. Reactance at f0 and Characteristic impedance explain the impedance scale of the LC pair at that frequency, which matters when estimating Q, source loading, or coupling strength.

Low frequency edge and High frequency edge are worst-case tolerance estimates, not measured production limits. They assume both components move in the direction that creates the edge. A design that only works at the nominal frequency may fail once ordinary 5%, 10%, or 20% part tolerances are included.

How to read resonant frequency result fields
Result field	Trust cue	Follow-up
Resonant frequency	Use as the ideal center from the entered L and C values.	Measure or simulate the assembled circuit before committing an RF or high-Q design.
Frequency span	Shows how wide the tolerance window is around nominal.	Choose tighter parts or a tuning method when the span overlaps an unwanted band.
Loaded Q	Appears only when a positive loss resistance and a series or parallel model are selected.	Confirm that the selected resistance model matches the physical circuit.
-3 dB bandwidth	Estimated as f0 divided by loaded Q.	Use measured response for final passband or notch width.
Frequency context	Warns when RF, VHF, microwave, or very low-frequency behavior needs extra review.	Check datasheet self-resonance, Q curves, and layout parasitics when the context row says to slow down.

The most common false confidence is reading a clean nominal number as a measured circuit peak. The corrective check is simple: keep Component SRF guard, Layout parasitics, and the tolerance edge rows beside the headline frequency whenever the circuit will be built or ordered.

Worked Examples:

Audio-range LC example

With Inductance set to 10 mH and Capacitance set to 0.1 uF, the Resonant frequency row returns about 5.033 kHz. The Oscillation period is about 198.692 us, and Reactance at f0 is about 316.228 ohm. The Frequency context row reads Audio range, so ordinary tolerance is usually a bigger first concern than microwave layout behavior.

Same parts with 5% tolerance

Keeping the 10 mH and 0.1 uF values, set both tolerance fields to 5%. Low frequency edge falls near 4.793 kHz when L and C are high, while High frequency edge rises near 5.298 kHz when L and C are low. Frequency span is about 504.554 Hz wide, or about 10.03% of nominal. That span is large enough to matter for a narrow filter even though the nominal result did not change.

Small RF tank with series loss

A 100 nH inductor with a 47 pF capacitor gives a Resonant frequency near 73.413 MHz and a Reactance at f0 near 46.127 ohm. Choose Series resistance / ESR and enter 0.8 ohm for Loss resistance. Loaded Q becomes about 57.66 and -3 dB bandwidth becomes about 1.273 MHz. The Frequency context row reads VHF to microwave, so the inductor's self-resonant frequency and board layout need review.

Input problem caught before calculation

If Capacitance is left at zero or a negative value, the form reports Capacitance must be greater than zero and the summary stays in the input-check state. Fixing the capacitance to 100 nF with a 10 mH inductor restores the 5.033 kHz result. A similar correction applies when tolerance is outside 0 to 80% or Loss resistance is negative.

FAQ:

Why does a larger capacitor lower the frequency?

The ideal equation places L and C inside a square root in the denominator. Increasing capacitance increases that denominator, so Resonant frequency goes down. Increasing inductance has the same direction of effect.

Should I use nominal or tolerance values?

Enter nominal values in Inductance and Capacitance, then add part tolerance in Advanced. The nominal value drives Resonant frequency, while Low frequency edge, High frequency edge, and Frequency span show the worst-case spread.

What resistance model should I choose?

Use No loss model when resistance is unknown. Use Series resistance / ESR for winding resistance or series capacitor ESR. Use Parallel load resistance when a load sits across the tank circuit.

Why is loaded Q missing?

Loaded Q appears only when Resistance model is set to a series or parallel model and Loss resistance is greater than zero. With no model or zero resistance, the row reads Not modeled.

Why does the result warn about self-resonance?

Real inductors include parasitic capacitance, so each inductor has a self-resonant frequency. If the calculated LC frequency approaches that datasheet limit, the inductor may no longer behave like the intended inductance.

Are entered values sent away for the calculation?

The LC math runs in the browser. Treat shared page addresses with care if they include filled-in values, especially when the component values come from proprietary hardware work.

Glossary:

Resonant frequency: The ideal frequency where inductive and capacitive reactance magnitudes match.
Inductance: The L value in henries that stores energy in a magnetic field.
Capacitance: The C value in farads that stores energy in an electric field.
Reactance: The frequency-dependent opposition from an inductor or capacitor, reported in ohms.
Loaded Q: A selectivity estimate that combines reactance with a series or parallel resistance model.
Self-resonant frequency: The frequency where an inductor resonates with its own parasitic capacitance.

References:

Activity: Resonance in RLC Circuits, Analog Devices Wiki, approved February 7, 2022.
Measuring Self Resonant Frequency, Coilcraft.
LC Resonant Frequency Calculator, All About Circuits.
Q Factor and Bandwidth of a Resonant Circuit, All About Circuits.