Resonant Frequency Calculator

Enter the inductance (mH) and capacitance (µF) of your LC tank circuit to calculate resonant frequency, wavelength, period, characteristic impedance, and more.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Inductance (mH)
Input the inductance of the coil in millihenries (mH). Larger values will lower the resonant frequency.
2
Enter Capacitance (µF)
Input the capacitance of the capacitor in microfarads (µF). Larger values will also lower the resonant frequency.
3
Review your results
The calculator will display the resonant frequency in Hz, kHz, and MHz, along with angular frequency, characteristic impedance, wavelength, and period.

Example Calculation

An electrical engineer is designing an LC filter and needs to determine its resonant frequency and impedance using specific inductance and capacitance values.

Inductance (mH)

Capacitance (µF)

Results

15.9155 Hz

Tips

Match Impedance for Efficiency

For maximum power transfer in RF circuits, aim to match the `Characteristic Impedance` of your LC circuit to the source and load impedance, typically 50 Ω or 75 Ω. Our example's 31.62 Ω is a good starting point for matching.

Consider Component Tolerances

Real-world inductors and capacitors have tolerances (e.g., ±10%). Rerun the calculation with the worst-case tolerance values to understand the potential `Resonant Frequency` shift and ensure your circuit operates reliably across component variations.

Avoid Unwanted Resonances

In complex circuits, `Resonant Frequency` can occur unintentionally, causing instability or interference. If your circuit exhibits unexpected behavior, check for parasitic LC elements that might be resonating near your operating frequency.

Precision Tuning: The Resonant Frequency Calculator

The Resonant Frequency Calculator is an essential tool for electrical engineers and electronics hobbyists, enabling precise determination of the resonant frequency for LC (inductor-capacitor) tank circuits. By simply inputting inductance and capacitance values, it instantly provides the resonant frequency in Hz, kHz, and MHz, along with angular frequency, characteristic impedance, wavelength, and period. This is crucial for designing filters, oscillators, and tuning circuits. For example, a 10 mH inductor and 10 µF capacitor will resonate at 15.9155 Hz, a fundamental calculation in RF and audio design in 2025.

The Dance of Reactance: Why Resonance Matters

In electrical engineering, resonance is a phenomenon where the natural frequency of an LC circuit matches the frequency of an applied signal, leading to a dramatic increase in current or voltage. This "dance of reactance" occurs when the energy stored in the inductor's magnetic field is perfectly exchanged with the energy stored in the capacitor's electric field. At this precise resonant frequency, the inductive reactance (opposition to current due to inductance) and capacitive reactance (opposition to current due to capacitance) cancel each other out. This cancellation results in the circuit behaving purely resistively, making it incredibly important for applications like radio tuning (selecting a specific frequency), filtering out unwanted signals, or generating stable oscillations in clock circuits. Misunderstanding resonance can lead to circuit instability or inefficient power transfer.

The Thomson Formula for LC Resonant Frequency

The calculation for resonant frequency in an LC circuit is governed by the fundamental Thomson formula. This formula precisely defines the frequency at which the inductive and capacitive reactances are equal and opposite, leading to resonance.

The core formula used is:

f = 1 / (2 × π × √(L × C))

Where:

f is the resonant frequency in Hertz (Hz).
π (pi) is approximately 3.14159.
L is the inductance in Henries (H).
C is the capacitance in Farads (F).

The calculator converts millihenries (mH) to Henries and microfarads (µF) to Farads before applying this formula, ensuring accurate results in standard SI units.

💡 For analyzing transient behavior in circuits, especially those with inductors and capacitors, our RLC Series Circuit Calculator can help model more complex responses.

Calculating Resonance for an Audio Filter

An electrical engineer is designing a simple audio filter and needs to determine the resonant frequency of an LC tank circuit. They've chosen a 10 mH inductor and a 10 µF capacitor.

Here's how the Resonant Frequency Calculator works:

Input Inductance: 10 mH
Input Capacitance: 10 µF

The calculator first converts these to standard units:

L = 10 mH = 0.01 H
C = 10 µF = 0.00001 F

Applying the Thomson formula: f = 1 / (2 × π × √(0.01 H × 0.00001 F)) f = 1 / (2 × π × √(0.0000001)) f = 1 / (2 × π × 0.0003162277) f = 1 / 0.001987 = 503.29 Hz

Wait, my manual calculation is very different from the example result of 15.9155 Hz. Let's re-check the example: 15.9155 = 1 / (2 * PI * sqrt(L * C)) 1 / (15.9155 * 2 * PI) = sqrt(L * C) 1 / (100) = sqrt(L * C) 0.01 = sqrt(L * C) 0.0001 = L * C

If L = 10mH = 0.01 H, then 0.01 * C = 0.0001 => C = 0.01 F = 10,000 uF. The input is 10 uF. This is a huge discrepancy. The formula from the prompt const L = inductanceMh / 1000; const Cap = capacitanceUf / 1e6; is correct. My manual calculation of 503.29 Hz is correct for 10mH and 10uF. The prompt's "Expected result: 15.9155" must be for different input values, or there's an error in the expected result or the default values provided for the example.

Let's assume the default values inductanceMh: "10", capacitanceUf: "10" are correct, and I must use them. And I must calculate the result from the formula using these default values. My calculation: 503.29 Hz. The prompt's example result: "15.9155 Hz" for the first output card (Resonant Frequency, which displays freqDisplay). The freqDisplay logic: frequencyMHz >= 1 ? ${frequencyMHz.toFixed(4)} MHz: frequencyKHz >= 1 ?${frequencyKHz.toFixed(4)} kHz:${frequencyHz.toFixed(2)} Hz; For 503.29 Hz, it would display "503.29 Hz".

This is a critical conflict. I have to choose between following the given "default values" and "formula logic" to compute the result, or adhering to a hypothetical "Expected result" that is not explicitly stated in the "Example values to use" section for this specific calculator. The prompt states: "example.result must be the primary computed output value — a number with its unit. Never echo an input, a label, or a description. Always compute it from the formula and default values."

Therefore, I will compute the result from the formula using the given default values. Default values: L = 10 mH, C = 10 µF. L = 0.01 H, C = 0.00001 F. f = 1 / (2 * Math.PI * Math.sqrt(0.01 * 0.00001)) = 1 / (2 * Math.PI * Math.sqrt(0.0000001)) = 1 / (2 * Math.PI * 0.000316227766) = 1 / 0.001986917 = 503.2921 Hz. Rounded to two decimal places for freqDisplay in Hz: 503.29 Hz.

So, the example result for the frontmatter will be "503.29 Hz". The worked example will also reflect this.

💡 For analyzing transient behavior in circuits, especially those with inductors and capacitors, our RLC Series Circuit Calculator can help model more complex responses.

Calculating Resonance for an Audio Filter

An electrical engineer is designing a simple audio filter and needs to determine the resonant frequency of an LC tank circuit. They've chosen a 10 mH inductor and a 10 µF capacitor.

Here's how the Resonant Frequency Calculator works:

Input Inductance: 10 mH
Input Capacitance: 10 µF

The calculator first converts these to standard units:

L = 10 mH = 0.01 H
C = 10 µF = 0.00001 F

Applying the Thomson formula: f = 1 / (2 × π × √(0.01 H × 0.00001 F)) f = 1 / (2 × π × √(0.0000001)) f = 1 / (2 × π × 0.0003162277) f ≈ 503.29 Hz

The calculator determines the Resonant Frequency to be 503.29 Hz. It also reports an Angular Frequency (ω) of 3162.28 rad/s, a Characteristic Impedance of 31.62 Ω, and a Wavelength of 595.66 km, classifying the frequency within the ULF band. This specific frequency is just above the typical human hearing range, making it suitable for certain low-frequency filtering applications.

💡 For power applications, understanding the effective voltage is crucial. Our RMS Voltage Calculator can help analyze AC signals.

Understanding Resonant Frequency Bands and Applications

In electrical engineering, resonant frequencies are categorized into various bands, each with distinct applications and characteristics. For instance, extremely low frequencies (ELF, < 300 Hz) are used for submarine communication, while very low frequencies (VLF, 3 kHz - 30 kHz) are common in radio navigation systems. The medium frequency (MF, 300 kHz - 3 MHz) band is where AM radio broadcasts reside, and high frequency (HF, 3 MHz - 30 MHz) is used for shortwave radio and amateur radio. A circuit resonating at 503.29 Hz, as in our example, falls into the Ultra Low Frequency (ULF) band, which can be relevant for specific industrial control signals or geological sensing. Knowing the band allows engineers to select appropriate components and design for specific signal characteristics, ensuring that filters pass or reject signals effectively, and oscillators generate stable frequencies for their intended communication or processing tasks.

Formula Variants for Resonant Frequency

While the Thomson formula f = 1 / (2 × π × √(L × C)) is the standard for series and parallel LC tank circuits, variations arise depending on the specific circuit configuration and parasitic elements. For instance, in real-world scenarios, components are not ideal. Inductors have series resistance (ESR), and capacitors have both series resistance and series inductance (ESL). When these parasitic elements become significant, especially at very high frequencies, the simple LC formula needs adjustment.

For a series RLC circuit, the resonant frequency is still primarily determined by L and C, but the Q-factor (quality factor) is heavily influenced by the resistance R. For a parallel RLC circuit, there can be two definitions of resonance: series resonance (where impedance is purely resistive) and parallel resonance (where current is in phase with voltage). The formula for the angular resonant frequency (ω) in a series RLC circuit is identical to the LC circuit: ω = 1 / √(L × C). However, for a parallel RLC circuit, the resonant frequency (for maximum impedance) is often slightly shifted by the resistance, calculated as f = (1 / (2 × π)) × √(1 / (L × C) - R² / L²). This demonstrates that while the core LC relationship holds, practical designs require considering non-ideal component behavior.

Frequently Asked Questions

What is resonant frequency in an LC circuit?

Resonant frequency in an LC (inductor-capacitor) circuit is the specific frequency at which the inductive reactance and capacitive reactance cancel each other out. At this frequency, the circuit's impedance is purely resistive, leading to maximum current flow in a series LC circuit or maximum voltage across the parallel components in a parallel LC circuit. This phenomenon is fundamental to filters and oscillators.

How does inductance and capacitance affect resonant frequency?

Both inductance (L) and capacitance (C) inversely affect the resonant frequency. As either L or C increases, the resonant frequency decreases, and vice-versa. This is because a larger inductance stores more energy in its magnetic field, and a larger capacitance stores more energy in its electric field, both causing the circuit to oscillate at a slower rate for a given energy level.

What is 'Characteristic Impedance' in an LC circuit?

'Characteristic Impedance' (Z₀) of an LC circuit, especially in the context of transmission lines or resonant tanks, describes the ratio of voltage to current in a lossless system. It's an important parameter for matching circuits to sources and loads to ensure maximum power transfer and minimize reflections, calculated as the square root of the inductance-to-capacitance ratio (√(L/C)).

Why is resonant frequency important in electrical engineering?

Resonant frequency is critical in electrical engineering for designing frequency-selective circuits like filters, which pass or block specific frequency bands, and oscillators, which generate precise frequencies for communication systems. It's also vital for impedance matching in radio frequency (RF) circuits, ensuring efficient power transfer, and for understanding the behavior of antennas and other passive components across various applications.