Per Unit Impedance Calculator

Calculator Inputs

System Type

Calculation Mode

Convert to a new base

Primary Base

Base Voltage

Voltage Unit

Base Power

Power Unit

Impedance Input

Resistance R (ohm)

Reactance X (ohm)

Impedance Magnitude |Z| (ohm)

Angle (degrees)

Percent Impedance (%Z)

X/R Ratio

Reactance Sign

New Base for Conversion

New Base Voltage

New Voltage Unit

New Base Power

New Power Unit

Reset

Formula Used

Base impedance
Z_base = V_base² / S_base

Per unit impedance
Z_pu = Z_actual / Z_base

Rectangular form
Z_actual = R + jX

Magnitude and angle
|Z| = √(R² + X²), angle = tan^-1(X / R)

Percent impedance
%Z = 100 × |Z_pu|

Base conversion
Z_pu,new = Z_pu,old × (S_new / S_old) × (V_old / V_new)²

When voltage is entered in kV and power in MVA, the base impedance comes out directly in ohms. This is common in practical building and site power studies.

How to Use This Calculator

Choose whether your study is single-phase or three-phase.
Enter the primary base voltage and base power.
Select your preferred entry mode: rectangular values, polar values, or percent impedance.
Fill in the corresponding impedance inputs.
Enable base conversion if you need the same equipment impedance shown on another study base.
Press Calculate to display the result block above the form.
Review the summary tables, chart, and conversion check.
Use the CSV and PDF buttons to export the calculated values for reports or documentation.

Example Data Table

Case	Base Voltage	Base Power	Input	Base Impedance (ohm)	\|Z\| (ohm)	\|Z\| (p.u.)	%Z
Transformer feeder study	11 kV	5 MVA	R = 0.25, X = 0.75	24.2000	0.7906	0.0327	3.27%
Low-voltage distribution	0.48 kV	0.5 MVA	R = 0.01, X = 0.04	0.4608	0.0412	0.0895	8.95%
Percent impedance entry	13.8 kV	10 MVA	%Z = 6, X/R = 8	19.0440	1.1426	0.0600	6.00%
Equipment catalog conversion	33 kV	25 MVA	\|Z\| = 2.4, angle = 78°	43.5600	2.4000	0.0551	5.51%

These examples help verify your own entries before using the export functions in formal construction power-system documentation.

FAQs

1) What is per unit impedance?

Per unit impedance is actual impedance divided by a chosen base impedance. It expresses electrical values on a normalized scale, making comparisons easier across equipment, feeders, and transformer ratings.

2) Why use per unit values in construction projects?

Large construction sites and buildings often mix generators, transformers, switchgear, and cable runs. Per unit values simplify fault studies, equipment comparison, coordination reviews, and base conversions during design and commissioning.

3) How do I calculate base impedance?

Base impedance equals base voltage squared divided by base power. With voltage in kV and power in MVA, the result is directly in ohms, which is convenient for engineering calculations.

4) Does the formula change for three-phase systems?

When you use line-to-line kV and three-phase MVA, the familiar V²/S relation still works. The key is keeping the voltage and power bases consistent throughout the study.

5) What does percent impedance mean?

Percent impedance is simply the per unit impedance magnitude multiplied by 100. For example, 0.06 p.u. equals 6% impedance. Many transformer nameplates list impedance this way.

6) Can I convert impedance from one base to another?

Yes. The calculator applies the standard base conversion formula using old and new voltage and power bases. This is useful when combining vendor data with project study assumptions.

7) What if my reactance is negative?

Negative reactance can appear in compensated or capacitive conditions. The calculator accepts that sign, preserves the complex form, and still computes magnitude, angle, and converted per unit values.

8) Which input mode should I choose?

Use rectangular mode when R and X are known, polar mode when magnitude and angle are given, and percent mode when equipment data sheets provide %Z and X/R ratio.