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Series RLC Resonance and Quality

Find ideal series-circuit resonant frequency and quality factor, with editable capacitance, inductance, resistance and inverse relationships.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For L = 0.004 H, C = 0.000002 F and R = 0.2 Ω, resonance is approximately 1,779.406359 Hz and the quality factor is 223.606798.

f₀ = 1/(2π√(LC)); Q = √(L/C)/R = 2πf₀L/R.

Worked example

Enter these known values and leave the other values blank.

Series inductance
0.004 H
Series capacitance
0.000002 F
Total series resistance
0.2 Ω
Driven current resonance frequency
1779.4 Hz
Series circuit quality factor
223.6

Assumptions and limitations

  • This model is an ideal linear series RLC circuit. It uses total series resistance, including any losses represented by a lumped resistor.
  • The reported frequency is the driven current resonance, where inductive and capacitive reactance cancel. It is not the damped free-oscillation frequency of an unforced circuit.
  • Q is dimensionless and uses the series-circuit formula. A parallel circuit generally requires a different expression.
  • All five quantities must be strictly positive. A zero-resistance idealization has unbounded Q and is outside the finite-output domain.
  • Frequency is cycles per second. The retained RPM choice expresses cycles per minute and does not assert mechanical rotation.
  • All captured unit choices and inverse branches remain available. Supplying too many locked contradictory quantities reports an inconsistency.
  • Component tolerance, frequency-dependent losses and parasitic elements can shift measured circuit behavior; the arithmetic does not simulate these effects.

Common questions

Does resistance change this resonance frequency?

Within the ideal series model, f₀ depends on L and C. Resistance changes Q and the resonance width.

Can I use Q for a parallel RLC circuit?

No. This page uses the series form Q = √(L/C)/R.

What happens when capacitance is quadrupled?

With L fixed, the resonance frequency halves because frequency varies as 1/√C.

References

Use mathematical 2π in resonance and both inverses, replacing the captured rounded 6.28319 coefficient. Preserve the separate series quality-factor relation. Inductance, capacitance, series resistance, resonant frequency and finite Q must be strictly positive, using exact-sign comparisons.

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