LC Resonant Frequency and Reactance Calculator
Find the resonant frequency of an LC circuit and the reactance of each part at any frequency.
How it changes with frequency
Formulas
f0 = (1)/(2π·√LC). At resonance the inductive reactance XL = 2πfL equals the capacitive reactance XC = (1)/(2πfC). Below resonance the capacitor dominates, and above it the inductor does.
Try it: series RLC around resonance
Sweep the input frequency around f0 and watch XL and XC cancel. The chart shows the impedance of R, L and C in series.
- Resonant frequency f0
- 159 kHz
- Q
- 10
- Bandwidth (−3 dB)
- 15.9 kHz
- XL at this f
- 10 Ω
- XC at this f
- 10 Ω
- |Z| at this f
- 1 Ω
- Phase of Z
- 0° (resistive)
In a series RLC circuit the inductor's reactance XL rises with frequency and the capacitor's XC falls. At f0 they are equal and cancel, so only R is left: the impedance is at its minimum and the current at its peak. Below f0 the circuit is capacitive and the current leads the voltage; above f0 it is inductive and the current lags.
A smaller R gives a higher Q: a deeper, narrower dip and a sharper peak in current. The shaded band is where the current stays above 70.7% of its peak. The frequency slider keeps its position relative to f0 when you change L or C.
Worked example: 10 μH and 100 nF
- Resonant frequency: f0 = (1)/(2π·√LC) = (1)/(2π·√10 μH × 100 nF) = 159 kHz
- At this frequency both reactances are equal: XL = XC = (√L)/(√C) = 10 Ω
- With 1 Ω in series, Q = (XL)/(R) = 10 and the bandwidth is (f0)/(Q) = 15.9 kHz.
Resonant frequency by L and C
| L \ C | 1 nF | 10 nF | 100 nF | 1 µF |
|---|---|---|---|---|
| L \ C1 µH | 1 nF5.03 MHz | 10 nF1.59 MHz | 100 nF503 kHz | 1 µF159 kHz |
| L \ C10 µH | 1 nF1.59 MHz | 10 nF503 kHz | 100 nF159 kHz | 1 µF50.3 kHz |
| L \ C100 µH | 1 nF503 kHz | 10 nF159 kHz | 100 nF50.3 kHz | 1 µF15.9 kHz |
| L \ C1 mH | 1 nF159 kHz | 10 nF50.3 kHz | 100 nF15.9 kHz | 1 µF5.03 kHz |
Making L or C 100 times larger lowers the resonant frequency 10 times (it goes with one over the square root). Real circuits land a few percent off because of wiring inductance and part tolerances.
Using it in practice
Step by step
- Enter the inductance and capacitance with prefixes (10u, 100n and so on).
- Read the resonant frequency, the characteristic impedance and the reactance of each part at resonance.
- To tune to a target frequency, change one part and watch how the frequency moves: it follows the inverse square root, so halving C raises f by about 41%.
Common mistakes
- Forgetting stray capacitance. Breadboards, wiring and probes add several picofarads. With small capacitors the measured resonance comes out lower than calculated.
- Using an inductor above its self-resonant frequency. Every real inductor has winding capacitance; past its self-resonant frequency it behaves like a capacitor. Check the datasheet.
- Ignoring resistance. Wire and core losses set the Q. A low-Q circuit has a broad, shallow peak, so the resonance looks smeared out on a sweep.
Practical tips
At resonance the inductor and capacitor reactances are equal and cancel. A series LC then looks like a short (only its resistance remains); a parallel LC looks like a high impedance. Component tolerance matters: a 10% inductor and a 10% capacitor can shift the frequency by up to about 10% together. Use a trimmer capacitor when the frequency has to be exact.
Frequently asked questions
What is LC resonance used for?
Tuning radio receivers and oscillators, picking out a single frequency, and wireless charging coils. At resonance a series LC circuit has its lowest impedance and a parallel LC circuit has its highest.
Why does my measured resonance differ from the calculation?
Real parts have tolerance, and the board and leads add stray capacitance and inductance. The effect grows at higher frequencies.