Resonant Frequency Calculator

Inductance:

Enter the tank inductance and choose the unit printed on the source value.

Capacitance:

Enter the capacitance that resonates with the inductor.

Inductor tolerance:

Zero keeps the nominal LC answer unchanged.

Capacitor tolerance:

Set zero when component tolerance is not part of the estimate.

Loss model:

Leave disabled when AC series resistance or parallel loading is unknown.

Loss resistance:

Used only for loaded Q and approximate bandwidth.

ohm

Display precision:

Choose a compact or detailed presentation.

Quantity	Value	Calculation basis	Copy
{{ row.label }}	{{ row.value }}	{{ row.note }}

Check	Value	Design meaning	Copy
{{ row.label }}	{{ row.value }}	{{ row.note }}

A tuned circuit is useful only when its natural frequency lands where the surrounding circuit needs it. In an LC network, that frequency is set by inductance and capacitance. At resonance, inductive reactance and capacitive reactance have the same magnitude, so a filter, oscillator, tuner, or matching network changes behavior around a well-defined electrical center.

The ideal center is not the whole design. Larger inductance or capacitance lowers the resonant frequency, but real parts also bring tolerance, alternating-current loss, stray capacitance, lead inductance, temperature drift, and their own self-resonance. Those effects matter most when the required passband is narrow or the circuit operates near radio frequencies.

Resonant frequency: The ideal frequency where the magnitudes of inductive and capacitive reactance are equal.
Characteristic impedance: The common reactance magnitude at resonance, found from the ratio of inductance to capacitance.
Loaded Q: A first-order measure of how sharply the circuit responds after a series loss or parallel load is included.
Bandwidth: The approximate frequency width associated with loaded Q for a simple resonant response.

Tolerance spread and bandwidth answer different questions. Tolerance estimates where the center frequency could move as component values vary. Bandwidth estimates how broad one loaded response may be. A circuit can have a narrow bandwidth and still miss its intended center because component tolerances or parasitics shifted the actual resonance.

Use the ideal result for component selection and early checks, then compare it with part datasheets and measurement. An inductor operating near or above its self-resonant frequency no longer behaves like the simple lumped inductance assumed by the LC equation.

How to Use This Tool:

Enter the effective component values first. Add tolerance and loss only when those numbers describe the parts and loading near the expected frequency.

Enter Inductance and Capacitance with the units printed on the source values. Include known tuning or stray capacitance when it is material.
Check the calculated frequency, period, and characteristic impedance. If an input is zero, negative, outside the supported normalized range, or paired with an invalid unit, correct the named field before using any result.
Open Advanced and enter the inductor and capacitor tolerances to estimate worst-case low and high frequency edges. Leave both at 0% for a nominal-only result.
Select Series resistance / ESR or Parallel load resistance only when the corresponding positive AC resistance is known. The selected model determines loaded Q and approximate bandwidth.
Compare the reactance curve around the 1× frequency point. Use Display precision to change visible decimals without changing the underlying calculation.

Interpreting Results:

Resonant frequency is the ideal LC center. The low and high edges are worst-case component-value limits, not measured cutoff frequencies. If the tolerance span is wider than the acceptable tuning error, use tighter parts, provide adjustment range, or verify the assembled circuit.

Loaded Q and Approximate -3 dB bandwidth are meaningful only when the chosen resistance represents the real loss or load at resonance. Series resistance lowers Q as it rises; a larger parallel load resistance raises Q. Neither simple model includes every source, load, coupling, or topology effect.

On the reactance curve, the two magnitudes meet at 1× the calculated frequency. The samples from 0.5× to 2× illustrate the ideal crossing; they do not predict an actual gain, impedance, or phase response for a complete circuit.

Technical Details:

Ideal inductive reactance rises with frequency, while ideal capacitive reactance falls. Equating their magnitudes gives the LC resonant frequency. All inductance values are converted to henries and capacitance values to farads before the equations are evaluated.

Formula Core:

The primary equations produce frequency, angular frequency, period, and the reactance magnitude at resonance.

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

Symbols and units for LC resonance equations
Symbol	Meaning	Unit
L	Effective inductance	henry (H)
C	Effective capacitance	farad (F)
f₀	Ideal resonant frequency	hertz (Hz)
ω₀	Angular frequency	radian per second
T	Oscillation period	second (s)
Z₀	Characteristic impedance and ideal reactance magnitude at resonance	ohm

For 10 mH and 0.1 µF, L is 0.01 H and C is 0.0000001 F. Substitution gives about 5,032.92 Hz, a period of about 198.69 µs, and a characteristic impedance of about 316.23 ohms.

Tolerance and Loss Rules:

Worst-case tolerance edges move both components in the direction that produces the lowest or highest frequency. The loss calculation then compares the selected resistance with Z₀.

\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})}} \\ Tolerance span & = & \frac{f_{high} - f_{low}}{f_{0}} \times 100 % \\ Q_{series} & = & \frac{Z_{0}}{R} \\ Q_{parallel} & = & \frac{R}{Z_{0}} \\ BW & = & \frac{f_{0}}{Q} \end{array}

The reactance samples use frequency ratios 0.5, 0.75, 1, 1.5, and 2. At ratio x, ideal inductive reactance is Z₀ × x and capacitive reactance is Z₀ ÷ x, so both equal Z₀ at x = 1.

The tolerance inputs accept 0% through 80%. Normalized inductance must stay from 1 pH through 1 MH, normalized capacitance from 1 fF through 1 kF, and loss resistance from 0 through 1 teraohm. A positive resistance is required whenever a loss model is active. Calculations retain full numeric precision; the precision choice changes presentation only.

Limitations:

The equations describe an ideal lumped LC network plus optional first-order tolerance and resistance models. They do not determine the response of a complete filter or oscillator.

Check the inductor's self-resonant frequency, Q curve, and AC resistance at the intended frequency.
Include meaningful source, load, winding, dielectric, trace, lead, and fixture effects.
Use the actual circuit topology when interpreting impedance peaks, current peaks, and -3 dB points.
Confirm narrowband or RF designs with a suitable circuit model and measurement.

References:

Resonance-Based Capacitive Sensing Using LDC2114, Texas Instruments, December 2017.
LC Filter Design, Texas Instruments, revised November 2016.
ADALM2000 Activity: Inductor Self Resonance, Analog Devices, December 2023.