LC Resonance Calculator
LC resonant frequency, period, and reactance.
What it does
Inductors and capacitors trade energy back and forth fastest at one frequency. At resonance their reactances match and cancel, leaving minimum impedance with zero phase. Ten millihenries with 100 nanofarads rings at 5032.9 Hz with 316.2 ohms each side.
The tool above runs ideal series resonance. Enter millihenries and nanofarads, and it prints frequency with auto Hz/kHz/MHz units, period with s/ms/us units, and the balanced reactance. Defaults give 5.03 kHz at 198.7 microseconds.
Course texts derive the identical form. OpenStax works 3.00 mH with 5.00 uF to 1.30 kHz from f0 equals 1 over 2 PI root(LC), HyperPhysics frames minimum impedance with zero phase, and MIT 8.02 zeroes omega L minus 1 over omega C for the same condition.
Resistance rules real sharpness outside this page. The Q factor divides reactance by series resistance, setting bandwidth and peak currents that ideal math omits. Tolerances on L and C drift production boards off nominal frequency.
How to use
- Enter inductance in mH.
- Enter capacitance in nF.
- Read frequency first.
- Read period for timing.
- Read balanced reactance.
- Add resistance analysis for Q.
Formula
- mH
- Inductance in millihenries.
- nF
- Capacitance in nanofarads.
OpenStax derives f0 explicitly (3.00 mH + 5.00 uF = 1.30 kHz check); HyperPhysics and MIT 8.02 confirm the resonance condition.
Worked example
Example: 10 mH, 100 nF
Defaults: 10 mH with 100 nF.
- Inputs: 10 mH inductor, 100 nF capacitor.
- Product: 0.01 x 0.0000001 = 1e-9.
- Root: sqrt(1e-9) = 0.0000316.
- Frequency: 1 / (2 PI x 0.0000316) = 5032.9 Hz.
- Period 198.7 us, XL=XC 316.2 ohms. Tool shows 5.03 kHz.
Reference table
| L / C | Frequency | Reactance |
|---|---|---|
| 10 mH / 100 nF | 5.03 kHz | 316.2 ohms |
| 1 mH / 10 uF | 1.59 kHz | 10 ohms |
| 3 mH / 5 uF | 1.30 kHz | ~24 ohms |
| 100 uH / 10 nF | 159.15 kHz | 100 ohms |
Limits
- Ideal only. Resistance and Q excluded.
- Lumped model; parasitics ignored.
- Tolerance drift unmanaged.
- Series topology assumed.
Common mistakes
- Mixing mH/nF with H/F directly.
- Reading kHz as Hz (1000x errors).
- Ignoring tolerance drift.
- Forgetting resistance damps peaks.
- Assuming parallel matches series.
Try it yourself
Quick checks. Answers sit tucked under each question.
1 mH with 10 uF?
LC = 1e-8, root 0.0001. f = 1591.55 Hz, shown as 1.59 kHz. T 628.3 us. XL 10 ohms.
100 uH with 10 nF?
LC = 1e-12, root 1e-6. f = 159154.9 Hz, shown as 159.15 kHz. T 6.3 us. XL 100 ohms.
Questions
How is resonant frequency figured?
One over 2 PI root(LC) with SI units. Here 1/(6.2832 x 0.0000316) = 5032.9 Hz.
How is the period figured?
One over frequency: 198.7 microseconds here.
What is the reactance?
2 PI f L, equal to 1/(2 PI f C) at resonance: 316.2 ohms here.
What happens at resonance?
Minimum impedance with zero phase in the ideal series circuit; the sharpness (Q) depends on resistance.
Which units do I enter?
Yes. Enter mH and nF; the tool converts to henries and farads inside.
Are real circuits exact?
No. Real parts add resistance, tolerance, and parasitics around these ideals.
Sources
- HyperPhysics: Resonant RLC Circuits
- OpenStax 23.12: RLC Series AC Circuits (1.30 kHz check)
- MIT OCW 8.02: Electricity and Magnetism (LRC circuits)