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Physics

Series RLC Impedance

|Z| = √(R² + (XL − XC)²). Free online Series RLC Impedance. Calculate series rlc impedance online — fast, accurate, mobile-friendly, no signup needed.

|Z| (Ω)
101.98039

Derivation

  1. ├── 01GivenR = 100, XL = 50, XC = 30
  2. ├── 02Formula√(t²+(a-n)^(2))
  3. └── 03Compute |Z| (Ω)101.98039
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§01What is

Understanding the Series RLC Impedance

The Series RLC Impedance computes |Z| (Ω) from 3 inputs: r (ω), xl (ω), xc (ω). |Z| = √(R² + (XL − XC)²).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Series RLC Impedance sits in that toolkit — it |Z| = √(R² + (XL − XC)²). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

√(t²+(a-n)^(2))

Where

R
R (Ω)
XL
XL (Ω)
XC
XC (Ω)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: R (Ω) = 100, XL (Ω) = 50, XC (Ω) = 30.

  1. 01Start by noting the input — R (Ω): 100.
  2. 02Start by noting the input — XL (Ω): 50.
  3. 03Start by noting the input — XC (Ω): 30.
  4. 04Substitute these values into the formula: √(t²+(a-n)^(2))
  5. 05Compute |Z| (Ω): the calculator returns 101.98.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Series RLC Impedance Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

R (Ω) halved

R = 50 (from 100)

Keep every other input at its default and halve the r (ω). See how |z| (ω) responds.

  1. 01New R (Ω): 50
  2. 02Baseline |Z| (Ω): 101.98
  3. 03New |Z| (Ω): 53.8516
  4. 04|Z| (Ω) decreases by 47.2% → use this sensitivity to plan for real-world variation.
02 · PATTERN

R (Ω) doubled

R = 200 (from 100)

Keep every other input at its default and double the r (ω). See how |z| (ω) responds.

  1. 01New R (Ω): 200
  2. 02Baseline |Z| (Ω): 101.98
  3. 03New |Z| (Ω): 200.998
  4. 04|Z| (Ω) increases by 97.1% → use this sensitivity to plan for real-world variation.
03 · PATTERN

XL (Ω) halved

XL = 25 (from 50)

Keep every other input at its default and halve the xl (ω). See how |z| (ω) responds.

  1. 01New XL (Ω): 25
  2. 02Baseline |Z| (Ω): 101.98
  3. 03New |Z| (Ω): 100.125
  4. 04|Z| (Ω) decreases by 1.8% → use this sensitivity to plan for real-world variation.
04 · PATTERN

XL (Ω) doubled

XL = 100 (from 50)

Keep every other input at its default and double the xl (ω). See how |z| (ω) responds.

  1. 01New XL (Ω): 100
  2. 02Baseline |Z| (Ω): 101.98
  3. 03New |Z| (Ω): 122.066
  4. 04|Z| (Ω) increases by 19.7% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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