AC Impedance Calculator Formula

Understand the math behind the ac impedance calculator. Each variable explained with a worked example.

Use the AC Impedance Calculator

Formulas Used

Impedance (Z)

impedance = sqrt(pow(resistance, 2) + pow(inductive_reactance - capacitive_reactance, 2))

Phase Angle

phase_angle = atan((inductive_reactance - capacitive_reactance) / resistance) * 180 / pi

Variables

VariableDescriptionDefault
resistanceResistance (R)(Ω)100
inductive_reactanceInductive Reactance (XL)(Ω)150
capacitive_reactanceCapacitive Reactance (XC)(Ω)80

How It Works

AC Impedance

Impedance is the total opposition to current flow in an AC circuit, including both resistance and reactance.

Formula

Z = sqrt(R² + (XL - XC)²)

where XL = 2*pi*f*L is inductive reactance and XC = 1/(2*pi*f*C) is capacitive reactance. The phase angle is phi = arctan((XL - XC) / R).

Worked Example

A series RLC circuit with R = 100 Ω, XL = 150 Ω, XC = 80 Ω.

resistance = 100inductive_reactance = 150capacitive_reactance = 80
  1. 01Z = sqrt(R² + (XL - XC)²)
  2. 02Z = sqrt(100² + (150 - 80)²)
  3. 03Z = sqrt(10000 + 4900)
  4. 04Z = sqrt(14900) = 122.07 Ω
  5. 05phi = arctan(70/100) = 34.99°

Ready to run the numbers?

Open AC Impedance Calculator