Skip to main content

AC Circuit Calculator (RLC Impedance)

Quick answer

Analyze series RLC circuits on AC: Z = root(R2 + (XL-XC)2), current I = V/Z, phase angle, and real P = VI cos phi.

  • Works at any frequency.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the AC Circuit Calculator Works

Z = √(R² + (XL - XC)²)

Calculates impedance, phase angle, and power for AC circuits containing resistance, inductance, and capacitance. AC circuits behave differently from DC due to reactive components. Worked example: R = 100 ohm, XL = 80 ohm, XC = 140 ohm at 230 V: net reactance -60 ohm (capacitive), Z = root(1002 + 602) = 116.6 ohm, I = 1.97 A, phi = -31 degrees, P = 230 x 1.97 x cos(31) = 388 W. Below resonance the same RLC looks capacitive and above it inductive: sweep the frequency and the phase angle swings from about -60 degrees through zero to +60 degrees at the boundaries.

  1. 1

    Step 1

    Enter resistance (R), inductance (L), and capacitance (C)

  2. 2

    Step 2

    Enter the AC voltage and frequency

  3. 3

    Step 3

    View impedance, phase angle, and power factor

  4. 4

    Step 4

    Calculate active, reactive, and apparent power

Use Cases

Analyzing RLC filter circuits

Designing AC power systems

Calculating resonance in tuned circuits

Power factor analysis and correction

Tips

  • 1

    Phase angle positive: inductive (current lags voltage)

  • 2

    Phase angle negative: capacitive (current leads voltage)

  • 3

    At resonance: XL = XC, impedance = R only

  • 4

    Power factor = cos(φ), ranges from 0 to 1

Common Mistakes

  • Forgetting reactances subtract (XL - XC) not add

  • Using DC resistance values at high frequencies

  • Confusing apparent power (VA) with active power (W)

  • Not considering frequency dependence of reactances

FAQs

What is power factor?

Power factor (PF = cos φ) is the ratio of active power to apparent power. PF = 1 means all power is useful; lower PF means reactive power is wasted in the system.

What is the difference between XL and XC?

XL (inductive reactance) increases with frequency, while XC (capacitive reactance) decreases. They have opposite phase effects, so they partially cancel in series circuits.

What happens at resonance in an RLC circuit?

At resonance, XL = XC so they cancel. Total impedance equals R only (minimum for series, maximum for parallel). Current is maximum and in phase with voltage.

How do I calculate impedance of a series RLC circuit?

Z = root(R2 + (XL - XC)2). With R = 50, XL = 120, XC = 40: Z = root(2500 + 6400) = 92.2 ohm, angle = arctan(80/50) = 58 degrees inductive. Below resonance the circuit looks capacitive.

What is the phase angle in an AC circuit?

phi = arctan((XL - XC)/R). Positive angle means current lags voltage (inductive); negative means it leads (capacitive). At resonance XL = XC, phi = 0, and power factor is unity.

How is real AC power calculated?

P = V x I x cos phi. A circuit drawing 2 A at 230 V with phi = 40 degrees transfers 230 x 2 x 0.766 = 352 W of real power even though the apparent flow is 460 VA.

Related tools

Pick another tool to continue your calculation.

Z

Impedance Calculator (Z=R+jX)

Calculate total impedance from resistance and reactance in AC circuits (Z = √(R²+X²))

⚡

Reactance Calculator (XL, XC)

Calculate capacitive and inductive reactance for capacitors and inductors (Xc, Xl)

🔴

Circuit Breaker Size Calculator (125%)

Calculate appropriate circuit breaker size.

⚡

RL Circuit Calculator

Calculate RL circuit time constant.

🔋

RC Circuit Calculator

Calculate RC circuit time constant.

🔄

RC Circuit Time Constant Calculator

Calculate time constant of an RC circuit.