The formulas
A transformer is rated in kilovolt-amperes (kVA), and one kVA is 1,000 volt-amperes. Power in equals power out, ignoring losses, so the current on each side comes from that rating and that side's voltage.
- Single-phase: I = kVA × 1,000 ÷ V.
- Three-phase: I = kVA × 1,000 ÷ (1.732 × V). V is the line-to-line voltage, and 1.732 is the square root of 3.
- kVA from volts and amps: V × I ÷ 1,000 for single-phase, and 1.732 × V × I ÷ 1,000 for three-phase.
- Single-phase turns ratio: Np ÷ Ns = Vp ÷ Vs = Is ÷ Ip. Secondary voltage is Vs = Vp ÷ ratio.
For a three-phase transformer, Vp ÷ Vs of the line-to-line voltages is the line-to-line voltage ratio, and Is ÷ Ip equals it for line currents. The turns ratio itself depends on the winding connection: a delta-wye bank, for example, has a larger turns ratio than its line-to-line voltage ratio.
The same kVA is used on both sides. Only the voltage changes, so the primary and secondary currents are different numbers.
Worked example 1: three-phase, 75 kVA
480 V primary, 208 V secondary. Primary = 75,000 ÷ (1.732 × 480) = 75,000 ÷ 831.4 = 90.2 A. Secondary = 75,000 ÷ (1.732 × 208) = 75,000 ÷ 360.3 = 208.2 A.
Worked example 2: single-phase, 25 kVA
480 V primary, 240 V secondary. Primary = 25,000 ÷ 480 = 52.1 A. Secondary = 25,000 ÷ 240 = 104.2 A. The ratio is 480 ÷ 240 = 2 : 1, and the secondary current is twice the primary current, which is a quick check on the arithmetic.
Worked example 3: kVA from a nameplate current
A three-phase 480 V side is marked 90.2 A. kVA = 1.732 × 480 × 90.2 ÷ 1,000 = 75.0 kVA.
These are original arithmetic examples, not exam questions.
Where the code starts
The currents above are the first step. Overcurrent protection for a transformer is in Article 450, and standard device ratings are in 240.6(A). Read the conditions in your own NEC and apply them only as the question directs. The transformer calculations post walks through the order of the steps, and the Calculations portion guide shows where transformers sit in the whole portion. For three-phase power with a power factor, use the Ohm's law calculator.
For resistors in series and parallel and the voltage across each one, use the series and parallel resistance calculator.
Transformer calculator questions
How do I convert kVA to amps?
Multiply kVA by 1,000 and divide by the voltage. For three-phase, divide by 1.732 times the line-to-line voltage instead. Do it once for the primary voltage and once for the secondary voltage.
Why is the secondary current larger on a step-down transformer?
Power in is about equal to power out, so the side with the lower voltage carries the higher current. The current ratio is the inverse of the voltage ratio.
Does this tell me the breaker or fuse size?
No. Overcurrent protection for transformers is in Article 450 of the NEC. Read the section and its conditions in your own code book, then round to a standard rating the way the question directs.