Electrical Power Systems • NEC 450 & IEEE C57.12 Standard

3-Phase Transformer kVA & Amps Calculator

Calculate 3-phase apparent power (kVA), primary/secondary full-load amperes (FLA), NEC 450 standard rating selection, and core/winding losses.

Governed by NEC (NFPA 70)

Input Parameters

Primary Line-to-Line Voltage (V1) primary_voltage_v

Primary utility or supply voltage

Secondary Line-to-Line Voltage (V2) secondary_voltage_v

Secondary utilization voltage feeding the load panel

Connected Active Load (kW) load_kw

Total real power demand of connected equipment

Load Power Factor (cos θ) power_factor

Inductive motor load typically 0.80 - 0.85; resistive is 1.0

Continuous Duty & Growth Margin safety_margin_pct

NEC Article 215/450 requires 125% factor for continuous duty

Calculated Outputs

Operating Load Demand (kVA) —

Standard NEC Transformer Size —

Primary Full-Load Amperes (FLA) —

Secondary Full-Load Amperes (FLA) —

Full-Load Heat Loss Dissipation —

Verified Mathematical Identity

kVA = kW / PF | FLA = (kVA · 1,000) / (√3 · V_LL) | P_heat ≈ kVA · 0.015

Analytical Derivation & Methodology

1. Apparent Power from Active Load

In AC systems, apparent power S (in kVA) accounts for reactive currents: S_load = P_kW / PowerFactor. Applying the continuous duty safety margin gives design capacity: S_design = S_load × (1 + Margin%).

2. Three-Phase Voltage & Current Relation

For a balanced 3-phase system, apparent power is S = √3 × V_LL × I_line. Inverting for full-load amperes yields: FLA = (kVA × 1,000) / (√3 × V_LL), where √3 ≈ 1.7320508.

3. NEC Standard Rating Selection & Heat Dissipation

Commercial dry-type transformers follow standard NEMA/NEC step ratings: 15, 30, 45, 75, 112.5, 150, 225, 300, 500 kVA. Core hysteresis and I²R winding resistance dissipate approx 1.5% to 2.5% of rated capacity as heat under full load.

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Frequently Asked Questions

To find Amps from 3-phase kVA: Amps = (kVA × 1,000) / (1.732 × Voltage). For example, a 75 kVA transformer at 208V delivers: (75 × 1,000) / (1.732 × 208) = 208.2 Amperes.

In a 3-phase system, the line-to-line voltage is vectorially 120° out of phase with line-to-neutral voltage. The geometric vector difference between any two phases is 2 × sin(60°) = √3 ≈ 1.732.

Assuming an 0.85 power factor, 100 kW equals 117.6 kVA. Adding a 25% continuous duty factor requires 147 kVA. The nearest standard commercial transformer rating is 150 kVA.