Power Systems Fundamentals
Per-Unit Conversion Calculator
Convert impedance between per-unit bases, or between ohms and per-unit.
About this calculator
The per-unit system expresses impedances, voltages, and currents as a fraction of a chosen base quantity, which lets equipment rated at different voltage levels be compared and combined on one common base — the backbone of every fault-current and load-flow study. The base impedance on a three-phase system is Z_base = kV_base² / MVA_base, using the line-to-line kV base and three-phase MVA base.
This calculator handles the two conversions engineers do constantly: changing a per-unit impedance from the base it was given on (commonly a transformer nameplate base) to the study's system base, using the change-of-base formula; and converting between an actual ohmic impedance and its per-unit equivalent on a stated base.
Common pitfall: the change-of-base formula shown here converts a scalar magnitude. If your impedance has a meaningful X/R ratio you care about, apply the same base-change scalar to the resistance and reactance components separately rather than converting only the magnitude and losing the angle. Also confirm whether nameplate %Z is quoted on the equipment's own base or an already-converted system base before using it here — mixing the two is one of the most common per-unit errors in practice.
Assumptions
- Three-phase MVA base and line-to-line kV base assumed throughout.
- Change-of-base converts a scalar magnitude; to preserve X/R ratio, apply the same base-change factor to R and X separately rather than to the magnitude alone.
- No off-nominal transformer turns-ratio correction is applied when crossing a transformer boundary.
When to use this calculator
Appropriate for
- Converting an impedance or per-unit quantity from one MVA/kV base to another
- Preparing device impedances for a common-base fault or load-flow hand calculation
- Checking a per-unit value someone else supplied against your chosen system base
Not suitable for
- Running the actual fault or load-flow study — this only rebases quantities, it does not solve the network
- Systems where the nameplate base voltages differ from the nominal system voltages by more than a few percent without accounting for the off-nominal turns ratio
- Final study documentation without independent verification of every base and nameplate value used
What this calculator does not cover
- Converts impedance magnitudes — it does not track resistance and reactance (X/R) separately or carry complex angles through the change of base.
- Assumes transformers on nominal taps; off-nominal tap ratios introduce additional per-unit adjustments this calculator does not model.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the change-of-base formula?
Z_pu,new = Z_pu,old × (kV_base,old / kV_base,new)² × (MVA_base,new / MVA_base,old). It rescales a per-unit impedance from the base it was specified on to a new common base.
Why do fault studies use per-unit values instead of ohms?
Per-unit values let equipment at different voltage levels — generators, transformers, cables — be combined on one impedance diagram without manually referring every impedance across each transformer's turns ratio.
What base does transformer nameplate %Z use?
Nameplate impedance is on the transformer's own self-cooled kVA/kV rating. Convert it to your system's MVA/kV base with the change-of-base formula before combining it with other per-unit impedances.
References
- Glover, Sarma, Overbye, Power System Analysis and Design, 6th ed., Ch. 3
- IEEE Std 141 (Red Book), Ch. 2 — Per-Unit System
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Download the Per-Unit Conversion Reference Card
A free quick-reference for practicing electrical engineers — base quantities, change of base, a worked example, and common base values. You'll also hear when new calculators are added: one or two emails a month, nothing else.