What a Transformer Actually Does
A transformer moves power from one AC voltage to another using two coils sharing a magnetic core. It does not create power — it trades voltage for current so the product (volt-amps) stays essentially constant. Step a voltage down and the current on that side goes up by the same ratio. That single idea is the key to every sizing calculation.
- Power is conserved: V × I is nearly equal on both sides.
- Step down voltage → current goes up; step up voltage → current goes down.
- Sizing is about apparent power (kVA), not just watts.
The kVA Sizing Formulas
Transformers are rated in kVA (kilo-volt-amperes) of apparent power, because the load's power factor is the customer's concern, not the transformer's.
Single-phase: kVA = V × I ÷ 1,000.
Three-phase: kVA = √3 × V_line × I ÷ 1,000. The √3 appears because the three phases are 120° apart.
Always size to the apparent power of the load, not its real power in watts, unless the power factor is 1.
Misapplying the √3 factor on a single-phase load over- or under-sizes the unit by about 73%. Confirm the supply and load are genuinely three-phase before using it.
Turns Ratio and Current
The turns ratio a = N_primary ÷ N_secondary equals the voltage ratio V_primary ÷ V_secondary. By power conservation, the current ratio is the inverse: I_primary ÷ I_secondary = N_secondary ÷ N_primary. So a 240 V-to-24 V control transformer (10:1 ratio) that feeds a 10 A, 24 V load draws only 1 A on the 240 V primary — the 240 VA is identical on both sides.
- Turns ratio = voltage ratio.
- Current ratio is the inverse of the turns ratio.
- Thin primary, thick secondary is normal on a step-down unit.
Losses and Efficiency
Two losses dominate. Core (iron) losses come from magnetizing the core and occur whenever the transformer is energized, even at no load. Copper (I²R) losses come from winding resistance and scale with the load current squared. Small dry-type transformers typically run 95–98% efficient at full load, but because core loss is fixed, efficiency falls at light load — the losses become a larger share of a smaller power flow.
At light loads, fixed core loss drags efficiency down. Oversizing a transformer for a tiny always-on load can waste more than it saves.
Don't Forget Motor Inrush
Motors draw 5–10 times their running current for a fraction of a second at startup. A transformer sized exactly to the running load will sag or trip on every start. Size with headroom — typically round up to the next standard kVA and add margin for inrush, especially for compressor, pump, and conveyor loads.
- Motor starting current can be 5–10x running current.
- Round up to the next standard kVA rating.
- Add inrush margin for motors and transformers feeding them.
Worked Example: A 480 V, 30 A Three-Phase Load
A three-phase load draws 30 A at 480 V line-to-line.
kVA = √3 × 480 × 30 ÷ 1000 = 24.94 kVA.
The next standard dry-type rating is 25 kVA — but if the load includes a motor with 7x inrush, a 25 kVA unit may dip hard at startup. A 30 kVA or 37.5 kVA unit gives the needed margin. If the same 24.94 kVA were mistakenly computed with the single-phase formula (480 × 30 ÷ 1000 = 14.4 kVA), the unit would be undersized by 73% — a classic and costly error.
Frequently Asked Questions
Why is a transformer rated in kVA and not kW?
Because the transformer does not care about the load's power factor. Its windings heat based on current (apparent power, kVA). The same 25 kVA transformer serves a 20 kW resistive load or a 18 kW motor at 0.9 pf equally.
Single-phase or three-phase formula — which do I use?
Use three-phase only when both supply and load are three-phase. Most residential and control transformers are single-phase, where kVA = V × I ÷ 1,000. Applying √3 to a single-phase load mis-sizes by ~73%.
What causes transformer overheating?
Overload (current beyond rating), harmonic distortion from nonlinear loads, poor ventilation, and sustained motor inrush beyond the design margin. Core and copper losses both turn into heat inside the enclosure.
How much headroom should I add?
At minimum round up to the next standard kVA. For motor or variable loads, add 25–50% for inrush and future growth; a transformer running near 100% continuously runs hotter and lives shorter.