Resonant Frequency (LC)

f = \frac{1}{2\pi\sqrt{LC}}

Resonant frequency of LC circuit where X_L = X_C.

Variables

Resonant frequency

Natural frequency

In SI units: s⁻¹

Allowed values: greater than 0

Inductance

In SI units: kg·m²/(A²·s²)

Allowed values: greater than 0

Capacitance

In SI units: A²·s⁴/(kg·m²)

Allowed values: greater than 0

Derivation

At resonance: ωL = 1/(ωC), so ω = 1/√(LC), f = ω/(2π).

Your notes

0/5000

Check value

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L = 2 H (Inductance)
C = 3 F (Capacitance)

Result: f = 0.06497473 Hz

Other electricity & magnetism formulas with the same quantities

Capacitance (Capacitance) shares Capacitance
Parallel Plate Capacitor (Capacitance) shares Capacitance
Capacitor Energy (Capacitance) shares Capacitance
RC Time Constant (Capacitance) shares Capacitance
Self-Inductance (Electromagnetic Induction) shares Inductance
Inductor Energy (Electromagnetic Induction) shares Inductance

Where this formula is listed

Electricity & Magnetism formulas, under AC Circuits, alongside RMS Voltage/Current.
In the electricity & magnetism list it comes after Impedance (RLC Series).
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Resonant Frequency (LC) formula?

Resonant Frequency (LC) is written f = 1/(2π√(LC)). Resonant frequency of LC circuit where X_L = X_C. It belongs to Electricity & Magnetism, under AC Circuits.

What are the units in f = 1/(2π√(LC))?

In SI units, f is resonant frequency, measured in s⁻¹; L is inductance, measured in kg·m²/(A²·s²); C is capacitance, measured in A²·s⁴/(kg·m²).

How is the Resonant Frequency (LC) formula derived?

At resonance: ωL = 1/(ωC), so ω = 1/√(LC), f = ω/(2π). The result is f = 1/(2π√(LC)).