Impedance Calculator

The Impedance Calculator determines the total opposition an AC circuit presents to current when circuit resistance and reactance values are already known. It calculates Net reactance, Impedance magnitude, Phase angle, Power factor magnitude, and Reactance type from the entered Resistance, Inductive reactance, and Capacitive reactance.

The resulting impedance value is used where an AC circuit’s voltage-current relationship must be reviewed. Typical applications include checking current in an AC branch circuit or feeder, evaluating the effect of inductive or capacitive loads, reviewing voltage-drop calculations that use impedance rather than resistance alone, and analyzing motor, transformer, filter, or other alternating-current circuits.

AC Impedance Components

AC impedance combines resistance with reactance.

• Resistance is the real, non-frequency-dependent opposition to current entered in ohms.
• Inductive reactance is the positive reactance caused by inductance at the frequency of interest.
• Capacitive reactance is the opposing reactance caused by capacitance at the frequency of interest.
• Net reactance is the difference between inductive reactance and capacitive reactance.

The calculator uses these input fields:

Input	Electrical meaning
Resistance	Circuit resistance in ohms
Inductive reactance	Inductive reactance XL at the frequency of interest, in ohms
Capacitive reactance	Capacitive reactance XC at the frequency of interest, in ohms

Inductive reactance and capacitive reactance act in opposite directions. A circuit is inductive when Inductive reactance exceeds Capacitive reactance. It is capacitive when Capacitive reactance exceeds Inductive reactance.

Impedance Formula

The calculator first determines net reactance:

\(\displaystyle X = X_L - X_C\)

Where:

• X = net reactance in ohms
• X_L = inductive reactance in ohms
• X_C = capacitive reactance in ohms

It then calculates impedance magnitude:

\(\displaystyle |Z| = \sqrt{R^2 + X^2}\)

Where:

• (|Z|) = impedance magnitude in ohms
• (R) = Resistance in ohms
• (X) = net reactance in ohms

The phase angle is:

\(\displaystyle \theta = \operatorname{atan2}(X,R)\)

Power factor magnitude is:

\(PF = \frac{R}{|Z|}\)

A positive phase angle indicates an inductive circuit. A negative phase angle indicates a capacitive circuit. The calculator displays the power factor as a magnitude, while Reactance type identifies whether the circuit is inductive or capacitive.

Calculation Example

Enter the following known AC circuit values:

Input	Value
Resistance	12 ohm
Inductive reactance	16 ohm
Capacitive reactance	4 ohm

Net Reactance

\(\displaystyle X = 16 - 4 = 12\ \text{ohm}\)

The circuit has 12 ohm of net inductive reactance.

Impedance Magnitude

\(\displaystyle |Z| = \sqrt{12^2 + 12^2}\)

\(\displaystyle |Z| = \sqrt{288} = 16.9706\ \text{ohm}\)

\(\displaystyle \theta = \operatorname{atan2}(12,12) = 45\ \text{deg}\)

\(PF = \frac{12}{16.9706} = 0.7071\)

The calculator returns:

Result	Value
Net reactance	12 ohm
Impedance magnitude	16.9706 ohm
Phase angle	45 deg
Power factor magnitude	0.7071 PF
Reactance type	inductive

The 45-degree positive phase angle shows that voltage leads current in this inductive circuit. The 0.7071 power factor magnitude corresponds to resistance and net reactance having equal 12-ohm values.

Practical Electrical Use

Impedance is used when resistance alone does not describe the circuit. For DC circuits, voltage drop and current calculations commonly use resistance. For AC circuits containing inductive or capacitive elements, total impedance affects both current magnitude and phase relationship.

For a known AC voltage, circuit current can be calculated using impedance magnitude:

\(\displaystyle I = \frac{V}{|Z|}\)

For example, if 120 V is applied across a circuit with an impedance magnitude of 16.9706 ohm:

\(\displaystyle I = \frac{120}{16.9706} = 7.07\ \text{A}\)

That current value can support a broader load review, such as comparing calculated load current with conductor ampacity, overcurrent protection, equipment ratings, or voltage-drop limits. Those installation decisions require the actual circuit conditions, including conductor material, AWG or kcmil size, insulation temperature rating, terminal rating, ambient temperature, adjustment factor, correction factor, and the number of current-carrying conductors.

Field Verification

Use reactance values that apply to the actual frequency and circuit configuration. If those values must be derived from component and frequency data, review the Reactance Calculator first. Inductive reactance and capacitive reactance vary with frequency, so values from a different operating frequency will not represent the installed circuit.

The calculator performs AC impedance arithmetic from known values. It does not determine conductor ampacity, select AWG or kcmil conductors, calculate raceway fill, establish branch-circuit or feeder protection, or replace equipment documentation and AHJ requirements. For installed systems, verify the source voltage, operating frequency, conductor and raceway arrangement, load characteristics, equipment ratings, and applicable code requirements separately.

Related calculations: RLC Resonance Calculator, Power Factor Calculator, Ohm's Law Calculator.