Resonant Frequency
f = 1 / (2π√(LC))
Quick answer
This calculator solves f = 1 / (2π√(LC)) for Frequency. With Inductance 100 µH, Capacitance 100 pF, the result is 1.592 MHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The resonant frequency of an LC tank circuit is where the inductive reactance exactly equals the capacitive reactance, causing them to cancel out. At this frequency the circuit impedance is purely resistive (determined only by parasitic resistance), and energy oscillates back and forth between the inductor's magnetic field and the capacitor's electric field. This principle is the foundation of radio tuning, oscillator circuits, and bandpass/bandstop filters. The formula shows that resonant frequency depends on the geometric mean of L and C, so halving one and doubling the other keeps the same frequency.
Variables
- f — Resonant frequency in hertz (Hz)
- L — Inductance in henries (H)
- C — Capacitance in farads (F)
Practical Notes
In series RLC circuits, resonance produces minimum impedance and maximum current. In parallel RLC circuits, resonance produces maximum impedance and minimum current. Crystal oscillators exploit the extremely high Q factor of piezoelectric resonance for precise frequency generation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | MHz | Hz, kHz, MHz, GHz |
| L | Inductance | µH | nH, µH, mH, H |
| C | Capacitance | pF | pF, nF, µF, mF, F |
Step by step
- 1. What you know: Inductance 100 µH, Capacitance 100 pF
- 2. The relation: f = 1 / (2π√(LC))
- 3. Substitute: L = 100 µH, C = 100 pF
- 4. Result: Frequency = 1.592 MHz
Worked examples
Minimum range
Given: Inductance 100 nH, Capacitance 1 pF
Result: Frequency = 0.5033 GHz
Low range
Given: Inductance 1 µH, Capacitance 10 pF
Result: Frequency = 50.33 MHz
Typical
Given: Inductance 100 µH, Capacitance 100 pF
Result: Frequency = 1.592 MHz
High range
Given: Inductance 0.47 mH, Capacitance 1 nF
Result: Frequency = 0.2322 MHz
Maximum range
Given: Inductance 4.7 mH, Capacitance 10 nF
Result: Frequency = 23.22 kHz
Solving for each variable
Solve for Frequency
Inductance 100 nH, Capacitance 1 pF → 0.5033 GHz
Solve for Inductance
Frequency 100 kHz, Capacitance 1 pF → 2.533 H
Solve for Capacitance
Frequency 100 kHz, Inductance 100 nH → 25.33 µF
How Frequency changes with Inductance
| Inductance (input) | Frequency (result) |
|---|---|
| 10 µH | 5.033 MHz |
| 25 µH | 3.183 MHz |
| 50 µH | 2.251 MHz |
| 75 µH | 1.838 MHz |
| 100 µH | 1.592 MHz |
| 150 µH | 1.299 MHz |
| 0.2 mH | 1.125 MHz |
| 0.4 mH | 0.7958 MHz |
| 0.7 mH | 0.6015 MHz |
| 1 mH | 0.5033 MHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 1592000 |
| kHz | 1592 |
| MHz | 1.592 |
| GHz | 0.001592 |
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<p><a href="https://vbatpower.com/formulas/resonant-frequency/">Resonant Frequency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Resonant Frequency?
Use f = 1 / (2π√(LC)). With Inductance 100 µH, Capacitance 100 pF, Frequency works out to 1.592 MHz.
What is the formula for Resonant Frequency?
The formula is f = 1 / (2π√(LC)). The resonant frequency of an LC tank circuit is where the inductive reactance exactly equals the capacitive reactance, causing them to cancel out.
How do you find Inductance when you know the other values?
Rearrange for Inductance: with Frequency 100 kHz, Capacitance 1 pF, Inductance is 2.533 H.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Frequency 100 kHz, Inductance 100 nH, Capacitance is 25.33 µF.
What units does Resonant Frequency use?
Frequency is shown in Hz, kHz, MHz, GHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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