RLC Series Resonance Frequency, Reactance & Q-Factor Calculator

Find RLC resonant frequency f₀ = 1 / (2π√(LC)), Q-factor, and bandwidth.

Resonant Frequency (f₀)
670.16 kHz
Quality Factor (Q) 42.11 Q
Characteristic Reactance (Z₀) 505.29 Ω
−3 dB Passband Bandwidth 15.92 kHz
Inputs
μH
Series inductance (L) in microhenries (μH).
pF
Series capacitance (C) in picofarads (pF).
Ω
Series resistance (R) in Ohms (Ω).
Results & Graph
Resonant Frequency (f₀)
670.16 kHz
Quality Factor (Q)
42.11 Q
Characteristic Reactance (Z₀)
505.29 Ω
−3 dB Passband Bandwidth
15.92 kHz

Resonant Frequency (f₀)

Graph 1 • Inductance Micro Henry Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 kHz 511.8 kHz 1.0k kHz 50%: 947.75 kHz 947.8 50% 75%: 773.84 kHz 773.8 75% 100%: 670.16 kHz 670.2 100% 125%: 599.41 kHz 599.4 125% 150%: 547.19 kHz 547.2 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Resonant Frequency (f₀) 670.16 kHz Quality Factor (Q) 42.11 Q Characteristic Reactance (Z₀) 505.29 Ω −3 dB Passband Bandwidth 15.92 kHz
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Resonant Frequency (f₀)670.16 kHzQuality Factor (Q)42.11 QCharacteristic Reactance (Z₀)505.29 Ω−3 dB Passband Bandwidth15.92 kHz
Summary: With L=120 μH, C=470 pF, and R=12 Ω, resonance occurs at 670.16 kHz with Q=42.11 and −3 dB bandwidth 15.92 kHz.
Summary: With L=120 μH, C=470 pF, and R=12 Ω, resonance occurs at 670.16 kHz with Q=42.11 and −3 dB bandwidth 15.92 kHz.
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Formula & Mathematical Methodology: RLC Resonance & Q Physics & Engineering Equation

f₀ = 1 / [ 2π × L × C ]
Z₀ = L / C
Q = Z₀ / R
BW = f₀ / Q
f₀ = 1 / [ 2π × √(L × C) ]; Z₀ = √(L / C); Q = Z₀ / R; BW = f₀ / Q
  • inductanceMicroHenry: Inductance Micro Henry (μH)
  • capacitancePicoFarad: Capacitance Pico Farad (pF)
  • resistanceOhms: Resistance Ohms (Ω)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: RLC Resonance & Q

Find RLC resonant frequency f₀ = 1 / (2π√(LC)), Q-factor, and bandwidth.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: f₀ = 1 / [ 2π × √(L × C) ]; Z₀ = √(L / C); Q = Z₀ / R; BW = f₀ / Q.
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes RLC Resonance & Q via f₀ = 1 / [ 2π × √(L × C) ]; Z₀ = √(L / C); Q = Z₀ / R; BW = f₀ / Q.

Frequently Asked Questions

What equation powers the RLC Series Resonance Frequency, Reactance & Q-Factor Calculator?

It evaluates f₀ = 1 / [ 2π × √(L × C) ]; Z₀ = √(L / C); Q = Z₀ / R; BW = f₀ / Q using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Electrical & RF Engineering

RLC Series Resonance Frequency, Reactance & Q-Factor Calculator: inputs, method, and how to read the result

Find RLC resonant frequency f₀ = 1 / (2π√(LC)), Q-factor, and bandwidth.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Inductance Micro Henry: Series inductance (L) in microhenries (μH).
  • Capacitance Pico Farad: Series capacitance (C) in picofarads (pF).
  • Resistance Ohms: Series resistance (R) in Ohms (Ω).

What the calculation includes

With the default values shown, Resonant Frequency (f₀) is 670.16 kHz. The calculation follows RLC Resonance & Q Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Inductance Micro Henry from 120 μH to 132 μH changes Resonant Frequency (f₀) from 670.16 kHz to 638.98 kHz. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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