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RLC Resonance Calculator

Calculate RLC resonant frequency f₀, Q factor, bandwidth, and reactance at resonance for series or parallel circuits from L, C, and R. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (series, parallel, invalid-domain) · Matrix
Known limitations
  • Ideal L/C; no parasitics
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Ideal series/parallel RLC resonant frequency, Q, −3 dB bandwidth, and reactance at resonance from L, C, R.
Scope
Lumped ideal R, L, C.
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
7/7 property · digest 1afc159d02bc
Legacy regression
14/14 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
2/2 golden · 5/5 CVP boundary · 4/4 invalid · 7/7 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • IEC 60050 — International Electrotechnical Vocabulary — Resonance, quality factor, and bandwidth
  • Horowitz & Hill — The Art of Electronics — RLC resonance, Q, and bandwidth
  • NIST Guide to the SI (SP 811) — SI units for inductance, capacitance, and frequency
Sources
Evidence
2 legacy golden · 5 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 4/4 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Resonant frequencyf₀ = 1 ÷ (2π √(L C))
Angular frequencyω₀ = 1 ÷ √(L C) = 2π f₀
Q (series)Qₛ = (1/R) √(L/C) = ω₀ L / R
Q (parallel)Qₚ = R √(C/L) = R / (ω₀ L)
BandwidthBW = f₀ ÷ Q
Reactance at resonanceX₀ = ω₀ L = 1 ÷ (ω₀ C)
iAPI uses SI units (H, F, Ω). Ideal models: series RLC and parallel R with L∥C. Real coils have ESR; parallel tanks often need a more detailed model.

How to use

1

Choose series or parallel

Q formulas differ; f₀ from L and C is the same for both ideal topologies.

2

Enter L, C, and R

Use the unit selectors (mH, µF, …) or enter SI values via the API.

3

Read f₀, Q, and BW

Also shown: ω₀, X₀ at resonance, and Z_res = R for the ideal model.

Example calculations

Common configurations with formula and result.

ϟ

Series tank

L = 1 mH · C = 1 µF · R = 10 Ω

f₀ = 1/(2π√(LC))
f₀ ≈ 5.033 kHz · Qₛ ≈ 3.162 · BW ≈ 1.592 kHz
ϟ

Parallel (same LCR)

L = 1 mH · C = 1 µF · R = 10 Ω

Qₚ = R √(C/L)
f₀ ≈ 5.033 kHz · Qₚ ≈ 0.316 · BW ≈ 15.92 kHz
ϟ

Higher Q series

L = 1 mH · C = 1 µF · R = 1 Ω

Qₛ = (1/R)√(L/C)
Qₛ ≈ 31.62 · BW ≈ 159.2 Hz
ϟ

Audio LC

L = 10 mH · C = 100 nF · R = 50 Ω (series)

f₀ from LC
f₀ ≈ 5.033 kHz

Illustrative series RLC

Common values at a glance.

LCRf₀ (approx.)Qₛ
1 mH1 µF10 Ω5.03 kHz3.16
1 mH1 µF1 Ω5.03 kHz31.6
100 µH100 nF5 Ω50.3 kHz20
10 mH100 nF50 Ω5.03 kHz6.32
i Parallel Q uses Qₚ = R√(C/L) — larger R increases Q.

RLC Resonance calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
An RLC circuit resonates when inductive and capacitive reactances cancel. The resonant frequency is f₀ = 1/(2π√(LC)). Quality factor Q and −3 dB bandwidth depend on whether the network is series or parallel. This calculator returns f₀, ω₀, Q, BW, and the reactance magnitude at resonance.
What it calculates
Ideal series/parallel RLC resonant frequency, Q, −3 dB bandwidth, and reactance at resonance from L, C, R.
Inputs
  • mode: series or parallel (default series)
  • L > 0 (H), C > 0 (F), R > 0 (Ω)
Outputs
  • f0 (Hz), omega0 (rad/s)
  • Q, BW (Hz)
  • X0 (Ω), Z_res (= R)
  • Echoed L, C, R, mode
Formula
f0=1/(2π√(LC)); Qₛ=(1/R)√(L/C); Qₚ=R√(C/L); BW=f0/Q
Assumptions
  • Lumped ideal R, L, C.
  • Parallel mode is ideal R across LC (no coil ESR).
Units
  • H, F, Ω → Hz, rad/s
Boundary conditions
  • Missing L/C/R → MISSING_REQUIRED_INPUT
  • ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Non-finite → INVALID_NUMBER
  • Unknown mode → INVALID_MODE
Example
series, L=1 mH, C=1 µF, R=10 Ω → f0≈5032.92 Hz, Q≈3.162
Validation cases

5 published on this page · 14/14 tests · Production surface contract 4/4 · View evidence

  • series, L=1e-3, C=1e-6, R=10 → f0≈5032.92, Q≈3.162, BW≈1591.55
  • parallel, same LCR → f0≈5032.92, Q≈0.3162, BW≈15915.5
  • missing L → error MISSING_REQUIRED_INPUT
  • L=0 → error VALUE_MUST_BE_POSITIVE
  • mode=dc → error INVALID_MODE
Sources
  • IEC 60050 — International Electrotechnical Vocabulary — Resonance, quality factor, and bandwidth
    Supports: f₀, Q, and bandwidth definitions for resonant circuits
  • Horowitz & Hill — The Art of Electronics — RLC resonance, Q, and bandwidth
    Supports: f₀=1/(2π√(LC)); series vs parallel Q
  • NIST Guide to the SI (SP 811) — SI units for inductance, capacitance, and frequency
    Supports: H, F, Hz relationships
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Calculate RLC resonant frequency, Q, and bandwidth for ideal series or parallel tanks from L, C, and R.

Default example (series): 1 mH · 1 µF · 10 Ω → f₀ ≈ 5.033 kHz, Q ≈ 3.162.

Supported and not supported

Supported

  • Ideal series RLC and ideal parallel RLC
  • f₀, ω₀, Q, BW = f₀/Q, X₀ = ω₀ L
  • API result via electrical.rlc_resonance

Not supported

  • Coupled coils / transformers
  • Crystal / ceramic resonators
  • Lossy tanks with separate ESR/ESL
  • Transient step response (use RC tool for first-order τ)

Agent / API notes

Capability id: electrical.rlc_resonance · tool id: rlc-resonance · pin calculation_version: 1.0.0.

Stable error codes: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, INVALID_MODE.

Inputs are SI: L in henries, C in farads, R in ohms.

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Frequently asked questions

Key distinctions behind the calculation.

What is RLC resonance?

It is the frequency where XL = XC, so the reactive parts cancel. For ideal series or parallel LC, f₀ = 1/(2π√(LC)).

How do series and parallel Q differ?

Series: Qₛ = (1/R)√(L/C) — smaller R means higher Q. Parallel (ideal): Qₚ = R√(C/L) — larger R means higher Q.

What is bandwidth BW?

BW = f₀/Q is the approximate −3 dB bandwidth of the resonance peak (or notch for series impedance magnitude).

What units should I use?

API inputs are SI: L in henries, C in farads, R in ohms. The page UI converts mH/µH, µF/nF, etc.

What if L, C, or R is missing or zero?

The calculator and API reject the request with MISSING_REQUIRED_INPUT or VALUE_MUST_BE_POSITIVE.

Is this a full SPICE model?

No. It is an ideal lumped RLC estimate — not coupled inductors, crystal resonators, or lossy tank models with ESR/ESL.