LC resonant frequency calculator
Tank circuit frequency from inductance and capacitance.
Fill in the fields and the result will appear here automatically.
Find the natural frequency, period and characteristic impedance ρ=√(L/C) of an ideal LC circuit. Inputs are µH and nF. The product LC fixes frequency;ρ relates capacitor peak voltage to current amplitude. It is not the circuit input impedance at resonance and does not specify a permissible or matched load.
How it works
Formula and logic
L=LµH·10⁻⁶ H, C=CnF·10⁻⁹ F; f₀=1/(2π√LC), T=2π√LC, ρ=√(L/C). Equal peak energies CU_Cmax²/2=LImax²/2 give U_Cmax/Imax=ρ. Both values must be positive; resistance and parasitic elements are absent.
Example
100 µH and 100 nF give 50329.21 Hz, period 1.987·10⁻⁵ s and ρ=31.623 Ω. 10 µH and 1000 nF keep the frequency but give ρ=3.162 Ω. Quadrupling only L halves frequency and doubles ρ.
Fields and units
- Inductance — µH
- Capacitance — nF
How to use
- — Enter µH and nF; conversion to H and F is internal.
- — Check component self-resonance and actual specifications separately.
- — The characteristic-impedance row means ρ=√(L/C), not the impedance of a load to connect.
- — Q, damping and loaded resonance require losses and topology that are not entered here.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: ideal LC energy and frequency OpenStax: free damped RLC oscillation OpenStax: forced-current resonance in series RLC
- Limitation
- Ideal lossless LC; no Q, loaded input impedance or parasitic parameters.
FAQ
Why do different pairs give one frequency?
Because the formula takes the L·C product, not the values themselves. The pairs 100 µH + 100 nF and 10 µH + 1000 nF share a product, so the frequency matches — what differs is the characteristic impedance.
What is the characteristic impedance for?
ρ is capacitor peak voltage divided by current amplitude during ideal free oscillation. Those peaks occur at different instants. It is neither instantaneous U/I nor input impedance.
Is wire resistance accounted for?
No. Free underdamped series RLC has ωd=√(1/LC−(R/2 L)²). The forced current maximum in an ideal series RLC remains at ω₀=1/√LC. Loss does not imply one universal downward shift for every resonance definition.
Does a series circuit differ from a parallel one?
Ideal series and parallel configurations with the same L, C have f₀. Their input impedances depend on topology and losses: ideally series impedance tends to zero and parallel impedance to infinity.