Per-Unit System Calculator (Base Impedance and Base Change)

How to use the per-unit System calculator

Choose a base power and base voltage, and enter an actual impedance in ohms. You get the base impedance, base current and per-unit impedance. Enter a new base to convert the per-unit value — for example from a transformer’s own rating to a 100 MVA system base.

For more background, read How to Calculate Short Circuit Fault Current.

Per-unit System formulas

Quantity	Formula
Base impedance	Zb = kVb² ÷ MVAb
Base current	Ib = MVAb ÷ (√3 × kVb)
Per-unit	Zpu = ZΩ ÷ Zb
Change of base	Znew = Zold × (Vold/Vnew)² × (Snew/Sold)

Base impedances

Voltage	10 MVA base	100 MVA base
0.415 kV	0.01722 Ω	0.001722 Ω
3.3 kV	1.089 Ω	0.1089 Ω
6.6 kV	4.356 Ω	0.4356 Ω
11 kV	12.1 Ω	1.21 Ω
22 kV	48.4 Ω	4.84 Ω
33 kV	108.9 Ω	10.89 Ω
66 kV	435.6 Ω	43.56 Ω
132 kV	1742 Ω	174.2 Ω
220 kV	4840 Ω	484 Ω

Example: transformer on a system base

A 2.5 MVA transformer with 6.25% impedance on its own base, converted to 100 MVA:

Z = 0.0625 × (100 ÷ 2.5) = 2.5 pu on 100 MVA.

Short-circuit with per-unit

Fault current in pu = 1 ÷ Z_total,pu; multiply by base current for amps. Adding source, transformer and cable impedances in per unit is how quick fault-level studies are done by hand.

Frequently asked questions

What is the per-unit system?

Expressing voltages, currents and impedances as fractions of chosen base values. It removes transformer ratios from calculations and makes equipment of different sizes easy to compare.

How do I calculate base impedance?

Z_base = (kV_base)² ÷ MVA_base. For 11 kV and 10 MVA, Z_base = 12.1 Ω.

How do I change a per-unit value to a new base?

Z_new = Z_old × (V_old ÷ V_new)² × (S_new ÷ S_old).

What is the link between % impedance and per unit?

Percentage impedance is per-unit × 100. A transformer with 6% impedance has 0.06 pu on its own rating.

Related calculators

• Transformer Short-Circuit Current CalculatorEstimate the maximum fault current on a transformer secondary from kVA, voltage and percentage impedance (infinite-bus method).
• Transformer Current Calculator (Full-Load Amps)Calculate primary and secondary full-load current of single-phase and three-phase transformers from kVA and voltages.
• kVA to kW Converter (and kW to kVA)Convert kVA to kW and kW to kVA using power factor — for generators, UPS, transformers and DG set sizing.
• Reactance and Impedance Calculator (XL, XC and Z)Calculate inductive reactance, capacitive reactance and series RLC impedance at any frequency — with phase angle.
• kW to Amps Calculator (Single-Phase, Three-Phase and DC)Convert kilowatts to amps for single-phase, three-phase and DC circuits using voltage and power factor — with charts for 230 V and 415 V.
• Three-Phase Motor Power & Current CalculatorCalculate input power, output power and full-load current of a three-phase motor from voltage, power factor and efficiency.

Embed this calculator