What formula does the calculator use?

It uses f₀ = 1/(2π√(L·C)).

Can I solve for inductance or capacitance?

Yes. Select Inductance L or Capacitance C and enter the other two required values.

Which units are supported?

Inductance supports H, mH, and µH; capacitance supports F, µF, nF, and pF; frequency supports Hz, kHz, and MHz.

Is resonant frequency different for series and parallel RLC circuits?

No. The calculator uses the same LC resonant-frequency formula for both.

What additional values are returned?

The result includes angular resonance ω₀ and characteristic impedance √(L/C).

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RLC Resonant Frequency Calculator (f = 1/(2π√(LC)))

Compute the LC (RLC series/parallel) resonant frequency: f₀ = 1/(2π·√(L·C)). Resonant frequency is identical for series and parallel RLC; R only affects Q and bandwidth. Solves for f₀, L, or C from the other two, and returns angular resonance ω₀ and characteristic impedance √(L/C). L in H/mH/µH, C in F/µF/nF/pF, f in Hz/kHz/MHz.

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3 examples

L=100µH, C=100pF → f₀≈1.5915 MHz

f₀ = 1/(2π·√(L·C)) = 1/(2π·√(100e-6·100e-12)) = 1/(2π·1e-7) ≈ 1.5915 MHz. ω₀ = 2π·f₀ ≈ 10⁷ rad/s. Characteristic impedance √(L/C) = √(1e-4/1e-10) = 1000 Ω.

{"result":"RLC resonant frequency (solve f0). L=100 µH (0.0001 H), C=100 pF (1e-10 F). f0 = 1/(2π·√(L·C)) = 1591549.431 Hz (1.5915 MHz). ω0 = 10000000 rad/s. Characteristic impedance √(L/C) = 1000 Ω.","metadata":{"input":{"solveFor":"frequency","L":100,"inductanceUnit":"µH","C":100,"capacitanceUnit":"pF","frequencyUnit":"MHz"},"result":{"solveFor":"frequency","inductance_H":0.0001,"inductance_uH":100,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1591549.431,"frequency_MHz":1.5915,"angularFrequency_rad_s":10000000,"characteristicImpedance_ohm":1000}}}

f=1 MHz, C=100pF → L≈253.30 µH

L = 1/((2π·f)²·C) = 1/((2π·1e6)²·1e-10) = 1/(39.478e9·1e-10) ≈ 2.533e-4 H = 253.30 µH. Characteristic impedance √(L/C) = √(2.533e-4/1e-10) ≈ 1591.55 Ω.

{"result":"RLC resonant frequency (solve L). f0=1 MHz (1000000 Hz), C=100 pF (1e-10 F). L = 1/((2π·f)²·C) = 0.0002533 H (253.303 µH). ω0 = 6283185.3072 rad/s. Characteristic impedance √(L/C) = 1591.5494 Ω.","metadata":{"input":{"solveFor":"inductance","C":100,"capacitanceUnit":"pF","f":1,"frequencyUnit":"MHz"},"result":{"solveFor":"inductance","inductance_H":0.000253303,"inductance_uH":253.303,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1000000,"frequency_MHz":1,"angularFrequency_rad_s":6283185.3072,"characteristicImpedance_ohm":1591.5494}}}

f=1 MHz, L=253.30 µH → C=100 pF

C = 1/((2π·f)²·L) = 1/((2π·1e6)²·2.533e-4) = 1e-10 F = 100 pF. Verification: f₀ = 1/(2π·√(2.533e-4·1e-10)) = 1e6 Hz = 1 MHz. Characteristic impedance √(L/C) = √(2.533e-4/1e-10) ≈ 1591.55 Ω.

{"result":"RLC resonant frequency (solve C). f0=1 MHz (1000000 Hz), L=253.3029591 µH (0.0002533 H). C = 1/((2π·f)²·L) = 0.0000000001 F (100 pF). ω0 = 6283185.3072 rad/s. Characteristic impedance √(L/C) = 1591.5494 Ω.","metadata":{"input":{"solveFor":"capacitance","L":253.3029591,"inductanceUnit":"µH","f":1,"frequencyUnit":"MHz"},"result":{"solveFor":"capacitance","inductance_H":0.0002533,"inductance_uH":253.303,"capacitance_F":0.0000000001,"capacitance_pF":100,"frequency_Hz":1000000,"frequency_MHz":1,"angularFrequency_rad_s":6283185.3072,"characteristicImpedance_ohm":1591.5494}}}

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8 options

SettingsAdjust formats, ranges, numbers, and modes.8

Solve ForselectOptionalWhich quantity to compute: f₀ from L+C, L from f+C, or C from f+L.Inductance LnumberOptionalRequired when solving for f₀ or C. Enter in the selected Inductance Unit.Inductance UnitselectOptionalCapacitance CnumberOptionalRequired when solving for f₀ or L. Enter in the selected Capacitance Unit.Capacitance UnitselectOptionalFrequencynumberOptionalRequired when solving for L or C. Enter in the selected Frequency Unit.Frequency UnitselectOptionalDecimal PlacesnumberOptional

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RLC Resonant Frequency Calculator (f = 1/(2π√(LC)))

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Examples

1. Calculate resonant frequency from L and C

2. Find inductance for a 1 MHz circuit

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3. Find capacitance for known L and frequency