Transformer Sizing Calculator

Transformer Basics A transformer transfers electrical energy between circuits using electromagnetic induction. Ideal transformer equations: V₁/V₂ = N₁/N₂ = I₂/I₁ (voltage, turns, and current ratios) S = V × I (apparent power in VA or kVA, conserved in an ideal transformer)

Turns Ratio a = N₁/N₂ = V₁/V₂ Step-up: V₂ > V₁ → a < 1 (more secondary turns) Step-down: V₂ < V₁ → a > 1 (fewer secondary turns) Isolation transformer: a = 1 (same voltage, galvanic isolation)

kVA Rating Single-phase: S = V × I (kVA) Three-phase: S = √3 × V_line × I_line = 3 × V_phase × I_phase Power factor: P (kW) = S (kVA) × pf Rule of thumb: add 20 to 25% margin to load kVA when sizing.

Voltage Regulation VR% = (V_no-load − V_full-load) / V_full-load × 100% Low VR (< 5%) is desirable for stable voltage supply. VR depends on transformer impedance: Z% = (Z_pu) × 100

Efficiency η = P_out / P_in = P_out / (P_out + P_core + P_copper) P_core = constant iron/eddy current losses (load-independent) P_copper = I²R = varies with load (zero at no load, max at full load) Max efficiency when P_core = P_copper, which for distribution transformers lands at 50 to 75% of rated load

Transformer Impedance Z% = 4 to 8% typical for power transformers Fault current (secondary short circuit): I_fault = I_rated / Z_pu

Impedance cuts both ways, and it is worth being clear about the direction. A lower Z% gives better voltage regulation, meaning the secondary sags less under load, but it also lets far more current flow into a fault. Halve the impedance and you double the prospective short circuit current, which is why a low-impedance transformer needs switchgear with a higher breaking capacity. Utilities pick the number deliberately rather than always minimizing it.