Series RLC Impedance Calculator
Impedance, phase angle and power factor of a series R-L-C circuit. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates impedance |Z|, phase angle and power factor from resistance, inductance, capacitance and frequency. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
A negative angle means the circuit is capacitive.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Textbook circuit identity (Ohm's law, power, series/parallel, AC circuit theory); no governing standard |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Resistance | 10 Ω |
| Inductance | 100 mH |
| Capacitance | 100 µF |
| Frequency | 50 Hz |
- XL = 31.4159 Ω, XC = 31.831 Ω, X = -0.4151 Ω
- |Z| = √(10² + -0.4151²) = 10.0086 Ω
- φ = atan(X / R) = -2.377°
Assumptions
- Series connection
- Sinusoidal, single frequency
A negative angle means the circuit is capacitive.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Resistance | Ω | greater than 0 Ω | |
| Inductance | mH | greater than 0 mH | |
| Capacitance | µF | greater than 0 µF | |
| Frequency | Hz | greater than 0 Hz |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Impedance |Z| | Ω | Shown to 3 decimal places | |
| Phase angle (degrees, + inductive) | (number) | Shown to 2 decimal places | |
| Power factor | (number) | Shown to 4 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with resistance
| Resistance (Ω) | Impedance |Z| (Ω) | Phase angle | Power factor |
|---|---|---|---|
| 1 | 1.083 | -22.54 | 0.9236 |
| 2.5 | 2.534 | -9.43 | 0.9865 |
| 5 | 5.017 | -4.75 | 0.9966 |
| 10 | 10.009 | -2.38 | 0.9991 |
| 20 | 20.004 | -1.19 | 0.9998 |
| 40 | 40.002 | -0.59 | 0.9999 |
| 100 | 100.001 | -0.24 | 1 |
Other inputs are the same as in the worked example above.
Standards and further reading
These are textbook relationships (Ohm's law, series and parallel networks, AC phasors, three-phase quantities). No standard sets the method; standards apply when the result feeds a design, for example cable or protection selection.
Frequently asked questions
What do I need to enter?
Enter resistance, inductance, capacitance and frequency. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Series connection. Sinusoidal, single frequency.
Which calculators should I use next?
Common next steps are Inductive and Capacitive Reactance and Power Factor. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- AC Circuit Formulas: Reactance and Impedance: AC circuit formulas: RMS and peak, frequency and period, inductive and capacitive reactance
- Resonance Formulas: Frequency, Q, Bandwidth: Resonance formulas for a series or parallel LC circuit: resonant frequency, reactance at resonance
More Electrical Fundamentals calculatorsAll engineering calculatorsSeries RLC Impedance in Elecmetric