What is resonant frequency and why does it matter?

Resonant frequency is the natural frequency at which a system oscillates with maximum amplitude when given an impulse. In circuits it determines which frequency a filter passes or blocks. In mechanics it's the frequency at which vibration amplitude peaks — which can cause structural failure (e.g., Tacoma Narrows bridge). Understanding and controlling resonant frequency is essential in RF design, audio, mechanical engineering, and medical devices.

How do I calculate the resonant frequency of an LC circuit?

Use f = 1/(2π√(LC)). Convert L to henries and C to farads first. Example: L = 10 µH = 10×10⁻⁶ H, C = 470 pF = 470×10⁻¹² F → LC = 4.7×10⁻¹⁵ → √(LC) = 6.856×10⁻⁸ → f = 1/(2π × 6.856×10⁻⁸) = 2.322 MHz.

What is Q factor and how does it affect resonance?

The Q (quality) factor measures how underdamped a resonant system is. For a series RLC: Q = (1/R)√(L/C). High Q (e.g., 100) means a very sharp resonance peak and narrow bandwidth — ideal for selective filters. Low Q (e.g., 1) means broad, less selective response. Bandwidth BW = f₀/Q. A higher Q also means lower energy loss per cycle.

How do I calculate the natural frequency of a spring-mass system?

f_n = (1/2π)√(k/m) where k is the spring constant in N/m and m is the mass in kg. Example: k = 1000 N/m, m = 2 kg → f_n = (1/2π)√(500) = (1/2π)(22.36) = 3.56 Hz. This is the frequency at which the system will oscillate after being displaced.

What is the difference between resonant frequency and natural frequency?

Natural frequency (f_n) refers to the undamped oscillation frequency of a mechanical system. Resonant frequency (f_r) is the frequency at which maximum response amplitude occurs — in lightly damped systems these are nearly equal. For heavily damped systems, resonant frequency is slightly lower than natural frequency. In electrical circuits, both terms are used interchangeably for the LC resonance frequency.

Resonance Frequency Calculator

Resonance occurs when a system oscillates at maximum amplitude at a specific frequency — the resonant (or natural) frequency. In LC circuits, energy alternates between the inductor's magnetic field and the capacitor's electric field: f = 1/(2π√(LC)). Adding resistance forms an RLC circuit with finite bandwidth and a quality factor Q = (1/R)√(L/C) for series circuits. For mechanical systems, a mass on a spring oscillates at its natural frequency f_n = (1/2π)√(k/m), where k is the spring constant and m is the mass. Understanding resonance is critical in electronics (tuned filters, oscillators, radio receivers), mechanical engineering (vibration isolation, structural analysis), and acoustics (musical instruments, speaker design). This calculator covers all three scenarios with selectable units and full formula display.

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calendar_today Updated: April 2026

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LC Circuit Inputs

Inductance (L)

Capacitance (C)

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Enter L and C to calculate resonant frequency

RLC Circuit Inputs

Inductance (L)

Capacitance (C)

Resistance (R)

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Enter L, C, and R to calculate

Spring-Mass System

Spring Constant (k)

Mass (m)

Results

Enter spring constant and mass to calculate

lightbulb Tips

•f = 1/(2π√(LC)) for LC circuits
•Q = (1/R)√(L/C) — higher Q = narrower bandwidth
•f_n = (1/2π)√(k/m) for spring-mass systems
•Halve L or C → frequency rises by √2 ≈ 1.414×

How to Use This Calculator

tune

Choose Calculator Mode

Select LC Circuit for a simple inductor-capacitor tank circuit, RLC Circuit to also get Q factor and bandwidth with a resistor, or Mechanical for a spring-mass natural frequency.

input

Enter Component Values

Type the inductance (H/mH/µH/nH), capacitance (F/mF/µF/nF/pF), or spring constant and mass. All common unit prefixes are supported.

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Read Resonant Frequency

The resonant frequency is displayed in Hz, kHz, MHz, or GHz automatically scaled to the most readable unit. The period (1/f) is also shown.

band_pass

Check Q Factor & Bandwidth (RLC)

For RLC mode, the Q factor and bandwidth tell you how selective your circuit is. High Q = narrow bandwidth = more selective filter.

The Formula

In an LC circuit, energy oscillates between the inductor (magnetic) and capacitor (electric) at f = 1/(2π√(LC)). Adding resistance (RLC) damps the oscillation — the Q factor Q = (1/R)√(L/C) describes how sharp the resonance peak is. High Q means narrow bandwidth and low energy loss. For a spring-mass system, the analogous formula is f_n = (1/2π)√(k/m), where k is the spring stiffness and m is the suspended mass. Both formulas share the same mathematical structure.

f = 1/(2π√(LC)) | f_n = (1/2π)√(k/m) | Q = (1/R)√(L/C)

lightbulb Variables Explained

f Resonant frequency (Hz)
L Inductance (H — henries)
C Capacitance (F — farads)
R Resistance (Ω — ohms) for RLC circuits
k Spring constant (N/m) for mechanical systems
m Mass (kg) for mechanical spring-mass system
Q Quality factor — sharpness of resonance peak (dimensionless)
BW Bandwidth (Hz) — frequency range around resonance: BW = f/Q

tips_and_updates Pro Tips

Halving L or C raises frequency by √2 (≈1.414×). To double frequency, reduce L or C to ¼ of original value.

High Q (>10) means a sharp, selective resonance — ideal for radio filters. Low Q (<1) means broad, overdamped response.

For spring-mass: doubling the mass lowers natural frequency by √2. Doubling spring stiffness raises it by √2.

A Q factor of 1/(2ζ) relates to the damping ratio ζ — critical damping is ζ=1 (Q=0.5), underdamped is ζ<1 (Q>0.5).

Real LC circuits always have some resistance (wire/coil ESR) — the Q factor drops and bandwidth widens with higher R.

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Resonance Frequency Calculator

LC Circuit Inputs

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RLC Circuit Inputs

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Spring-Mass System

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How to Use This Calculator

Choose Calculator Mode

Enter Component Values

Read Resonant Frequency

Check Q Factor & Bandwidth (RLC)

The Formula

lightbulb Variables Explained

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Frequently Asked Questions

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