Quick answer
Impedance of a series RLC circuit is Z = √(R² + (X_L − X_C)²), with X_L = 2πfL and X_C = 1 ÷ (2πfC). For 100 Ω, 50 mH and 10 µF at 60 Hz, Z = 265.93 Ω, with X_L = 18.85 Ω, X_C = 265.26 Ω and a phase angle of −67.9°.
Enter resistance, inductance, capacitance and frequency. The calculator returns impedance, reactances and the phase angle.
Related tools: Voltage Divider Calculator: Output voltage of a two-resistor divider. RMS Voltage Calculator: Convert between RMS, peak and peak-to-peak voltage of a sine wave. Parallel Plate Capacitor Calculator: Capacitance of two parallel plates.
How to use the RLC Impedance Calculator
- Enter resistance (Ω) (above 0).
- Enter inductance (mH) (above 0).
- Enter capacitance (µF) (above 0).
- Enter frequency (Hz) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Resistance | A number, in Ω | > 0 |
| Inductance | A number, in mH | > 0 |
| Capacitance | A number, in µF | > 0 |
| Frequency | A number, in Hz | > 0 |
Formula and method
Formula
X_L = 2πfL, X_C = 1 ÷ (2πfC), Z = √(R² + (X_L − X_C)²), φ = arctan((X_L − X_C) ÷ R)
IEEE-754 double precision; shown to the decimals indicated.
Series circuit driven by a sinusoidal source.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Resistance = 100; Inductance = 50; Capacitance = 10; Frequency = 60.
| Result | Value |
|---|---|
| Impedance | 265.9271 Ω |
| Inductive reactance | 18.8496 Ω |
| Capacitive reactance | 265.2582 Ω |
| Phase angle | -67.911° |
Example 2
Inputs: Resistance = 22; Inductance = 10; Capacitance = 100; Frequency = 1000.
| Result | Value |
|---|---|
| Impedance | 65.0721 Ω |
| Inductive reactance | 62.8319 Ω |
| Capacitive reactance | 1.5915 Ω |
| Phase angle | 70.24° |
Example 3
Inputs: Resistance = 470; Inductance = 1; Capacitance = 1; Frequency = 5000.
| Result | Value |
|---|---|
| Impedance | 470.0002 Ω |
| Inductive reactance | 31.4159 Ω |
| Capacitive reactance | 31.831 Ω |
| Phase angle | -0.051° |
The first line is the headline result (impedance). Below it the rLC Impedance Calculator lists inductive reactance, capacitive reactance and phase angle, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Capacitive or inductive
At 60 Hz the capacitive reactance exceeds the inductive reactance, so the circuit is capacitive and current leads voltage by 67.9° (negative phase). A positive angle means an inductive circuit.
Resonance
The reactances cancel at f₀ = 1 ÷ (2π√(LC)) ≈ 225 Hz for these values, where impedance falls to R. Away from resonance the reactive part dominates.
How the result changes with resistance
Holding every other input at the first worked example, this table changes only resistance. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Resistance | Impedance | Inductive reactance | Capacitive reactance |
|---|---|---|---|
| 50 | 251.4304 Ω | 18.8496 Ω | 265.2582 Ω |
| 100 | 265.9271 Ω | 18.8496 Ω | 265.2582 Ω |
| 200 | 317.3598 Ω | 18.8496 Ω | 265.2582 Ω |
| 400 | 469.8055 Ω | 18.8496 Ω | 265.2582 Ω |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Resistance: entering "0" shows "Resistance must be greater than 0." beside that field and no result.
- Frequency: entering "0" shows "Frequency must be greater than 0." beside that field and no result.
Choosing between the RLC Impedance Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Voltage Divider Calculator](/engineering/voltage-divider-calculator/) | input voltage, r1 and r2 | Output voltage |
| [RMS Voltage Calculator](/engineering/rms-voltage-calculator/) | i know the and voltage | RMS voltage |
| [Parallel Plate Capacitor Calculator](/engineering/parallel-plate-capacitance-calculator/) | plate area, plate separation and relative permittivity εr | Capacitance |
| [Current Divider Calculator](/engineering/current-divider-calculator/) | total current, r1 and r2 | Current through R1 |
| [Inductive Reactance Calculator](/engineering/inductor-reactance-calculator/) | inductance and frequency | Inductive reactance |
Background: electrical circuits
Ohm's law links voltage, current and resistance: V = I × R, so I = V ÷ R and R = V ÷ I. Power is P = V × I, which also equals I² × R and V² ÷ R.
These relations hold for ohmic components, where resistance is constant. Diodes and transistors are non-linear, and in AC circuits with reactive parts impedance (Z) takes the place of resistance. Check component ratings and local electrical code before relying on any calculation.
Assumptions and limitations
- Positive phase means the circuit is inductive
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for resistance and frequency to confirm this.
Frequently asked questions
What is impedance?
The total opposition to alternating current, in ohms.
What does the phase angle mean?
The shift between voltage and current.
Does it work for parallel RLC?
No, this is the series form.
What does the RLC Impedance Calculator calculate?
Impedance and phase angle of a series RLC circuit. It returns Impedance, Inductive reactance, Capacitive reactance and Phase angle.
What formula does the RLC Impedance Calculator use?
X_L = 2πfL, X_C = 1 ÷ (2πfC), Z = √(R² + (X_L − X_C)²), φ = arctan((X_L − X_C) ÷ R). Series circuit driven by a sinusoidal source.
What do I need to enter in the rLC Impedance Calculator?
You enter Resistance (Ω), Inductance (mH), Capacitance (µF) and Frequency (Hz).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Positive phase means the circuit is inductive.
What is an example of a rLC Impedance result?
With resistance 100, inductance 50, capacitance 10 and frequency 60, the impedance is 265.9271 Ω.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Positive phase means the circuit is inductive.
Related calculators
- Voltage Divider Calculator — Output voltage of a two-resistor divider.
- RMS Voltage Calculator — Convert between RMS, peak and peak-to-peak voltage of a sine wave.
- Parallel Plate Capacitor Calculator — Capacitance of two parallel plates.
- Current Divider Calculator — Current through each of two parallel resistors.
- Inductive Reactance Calculator — Reactance of an inductor at a frequency.
- RC Circuit Calculator — Time constant, cutoff frequency and charge level of an RC circuit.
Sources
- OpenStax, University Physics Volume 2 (Rice University): electricity, circuits and thermodynamics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.