Impedance Magnitude Calculator

The Impedance Magnitude Calculator finds the magnitude of a single-frequency AC impedance when the circuit’s resistance and net reactance are already known. It produces the impedance magnitude in ohms, along with phase angle, power-factor magnitude, and whether the net reactance is inductive or capacitive.

Impedance magnitude is used when reviewing an AC circuit’s opposition to current as a combined resistance-and-reactance value. It can support voltage-drop analysis, motor and transformer circuit review, branch-circuit or feeder troubleshooting, and comparison of calculated AC circuit behavior with measured values. It does not establish conductor ampacity, select AWG or kcmil conductors, determine overcurrent protection, or verify equipment ratings.

Resistance and Signed Net Reactance

AC impedance has two perpendicular components:

• Resistance is the real component of impedance. It dissipates power as heat and is entered in ohms.
• Signed net reactance is the imaginary component. It represents energy storage in magnetic or electric fields rather than continuous real-power dissipation.
• Positive reactance is inductive.
• Negative reactance is capacitive.

The calculator uses these interface fields:

Input	Unit	Electrical meaning
Resistance	ohm	Nonnegative AC resistance value
Signed net reactance	ohm	Net circuit reactance; positive for inductive and negative for capacitive behavior

The result is based on an impedance expressed as:

[ Z = R + jX ]

Where:

\(\displaystyle R = \text{Resistance}\)

\(\displaystyle X = \text{Signed net reactance}\)

The sign of (X) affects phase angle and reactance type. It does not change the positive impedance magnitude because magnitude uses the squared values of resistance and reactance.

Impedance Magnitude and Phase Angle

The calculator’s primary output is Impedance magnitude:

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

This is the vector magnitude of resistance and signed net reactance. It is not the arithmetic sum of the two values.

The calculator also determines the impedance phase angle with:

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

The atan2 function preserves the direction of the reactance component:

• A positive phase angle indicates inductive impedance.
• A negative phase angle indicates capacitive impedance.
• A zero phase angle indicates purely resistive impedance when net reactance is zero.

For a circuit analyzed at a known RMS voltage, impedance magnitude may be used with Ohm’s law to determine current magnitude:

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

That calculation requires a compatible single-frequency sinusoidal voltage and an impedance value representing the actual circuit condition being evaluated.

Power Factor Magnitude

The Power-factor magnitude result is calculated from the resistance portion of the impedance triangle:

\(\displaystyle \text{PF magnitude} = \frac{R}{|Z|}\)

Power-factor magnitude is shown as a positive number from 0 to 1. The phase angle and Reactance type indicate whether the associated power factor is lagging or leading:

Reactance type	Signed net reactance	Phase relationship
inductive	Positive	Current lags voltage
capacitive	Negative	Current leads voltage
resistive	Zero	Current and voltage are in phase

A power-factor magnitude alone does not identify leading or lagging behavior. The sign of Signed net reactance, the displayed phase angle, and the Reactance type output provide that direction.

Calculation Example

Enter the following known AC impedance components:

Field	Entered value
Resistance	3 ohm
Signed net reactance	4 ohm

The impedance magnitude is:

\(\displaystyle |Z| = \sqrt{3^2 + 4^2}\)

\(\displaystyle |Z| = \sqrt{9 + 16} = \sqrt{25}\)

[ boxed{|Z| = 5 text{ohm}} ]

The phase angle is:

\(\displaystyle \theta = \operatorname{atan2}(4,3)\)

[ boxed{theta = 53.1301 text{deg}} ]

The power-factor magnitude is:

\(\displaystyle \text{PF magnitude} = \frac{3}{5}\)

[ boxed{text{PF magnitude} = 0.6 text{PF}} ]

Because Signed net reactance is positive, the result identifies the circuit as:

[ boxed{text{Reactance type: inductive}} ]

The displayed results are therefore:

Result	Value
Resistance used	3 ohm
Reactance used	4 ohm
Impedance magnitude	5 ohm
Phase angle	53.1301 deg
Power-factor magnitude	0.6 PF
Reactance type	inductive

Electrical Use and Limits

Apply this calculation after resistance and net reactance have already been determined for the same frequency and circuit condition. In practical electrical work, those values may come from a design calculation, manufacturer data, circuit model, or properly interpreted test data.

For voltage-drop review, conductor impedance is frequency-dependent and may include resistance and inductive reactance. The impedance magnitude can help describe the AC opposition to current, but a complete voltage-drop calculation also depends on system voltage, circuit length, conductor arrangement, current, power factor, and the applicable circuit model.

For motor, transformer, and other AC load calculations, the displayed phase angle and power-factor magnitude describe the relationship between resistance and net reactance in the entered impedance. They do not replace a full equipment analysis, starting-current calculation, fault-current study, or manufacturer operating data.

This worksheet performs single-frequency sinusoidal impedance arithmetic only. It does not calculate reactance from component values, model harmonics, verify conductor or equipment ratings, determine ampacity, evaluate terminal rating or insulation temperature rating, account for adjustment factors or correction factors, calculate raceway fill, or approve an installation. Final conductor, branch-circuit, feeder, equipment, and installation decisions must be evaluated against the actual design conditions and the requirements enforced by the AHJ.