Sizing wire for a transformer requires calculating the full-load ampacity (FLA) and applying the NEC 125% continuous load multiplier. For the most common commercial dry-type transformer—a 112.5 kVA, 3-phase, 480V secondary—the exact calculated minimum ampacity is 169.1A. This dictates a concrete pick of 2/0 AWG copper THHN wire paired with a 175A molded case circuit breaker (MCCB). If you are sizing a 150 kVA 480V 3-phase unit, you need 4/0 AWG copper and a 225A breaker. Below is the exact formula derivation, unit tracking, and decision matrix to size any transformer feeder.
The Core Transformer Wire Sizing Formulas
To use a transformer wire size calculator accurately, you must first derive the Full Load Amps (FLA), then apply the continuous load multiplier to find the minimum wire ampacity. The base equations for single-phase and three-phase systems are:
Single-Phase:
I_FLA = (kVA × 1000) / V
Three-Phase:
I_FLA = (kVA × 1000) / (V × √3)
Minimum Wire Ampacity (Continuous):
A_min = I_FLA × 1.25
| Symbol | Definition | Standard Unit |
|---|---|---|
I_FLA | Full Load Ampacity (current drawn at rated capacity) | Amperes (A) |
kVA | Transformer apparent power rating (kilovolt-amperes) | kilovolt-amperes (kVA) |
V | System voltage (Line-to-Line for 3-phase, Line-to-Line or Line-to-Neutral for 1-phase depending on configuration) | Volts (V) |
√3 | Square root of 3 (constant for 3-phase power geometry) | Dimensionless (~1.732) |
A_min | Minimum required wire ampacity before derating | Amperes (A) |
1.25 | NEC 215.2(A)(1) multiplier for continuous loads (operating 3+ hours) | Dimensionless |
Rearranged Forms
When troubleshooting or verifying an existing installation, you often need to solve for the transformer capacity or the voltage rather than the current. Here are the algebraically rearranged forms:
- Solving for kVA (1-Phase):
kVA = (I_FLA × V) / 1000 - Solving for kVA (3-Phase):
kVA = (I_FLA × V × √3) / 1000 - Solving for V (1-Phase):
V = (kVA × 1000) / I_FLA - Solving for V (3-Phase):
V = (kVA × 1000) / (I_FLA × √3)
Assumptions, Limits, and Unit Traps
The formulas above apply strictly to standard 60Hz (or 50Hz) dry-type and liquid-filled distribution transformers operating at unity or near-unity power factor for sizing purposes. They do not account for inrush current (which is handled by the breaker's magnetic trip curve, not the wire's thermal mass) or harmonic heating from non-linear loads (which requires K-rated transformers and oversized neutrals).
Unit Mistakes That Break the Calculation
- Using kW instead of kVA: Transformers are rated in apparent power (kVA), not real power (kW). If you use a 100 kW load with a 0.8 power factor, the transformer sees 125 kVA. Always use the nameplate kVA.
- Forgetting the × 1000 multiplier: The formula requires Volt-Amperes (VA), not kilovolt-amperes. Dividing 112.5 by 480 yields 0.23A instead of the correct 135.3A.
- Using Line-to-Neutral voltage in 3-Phase: For a 480Y/277V system, the 3-phase formula requires the Line-to-Line voltage (480V). Plugging in 277V will artificially inflate the calculated current by a factor of √3, leading to massively oversized, un-terminable wire.
Realistic Answer Magnitudes
A quick sanity check prevents catastrophic math errors. For a 3-phase 480V system, the rule of thumb is roughly 1.2 amps per kVA. A 75 kVA transformer should yield ~90A. A 300 kVA transformer should yield ~360A. If your calculator outputs 900A for a 75 kVA unit, you have a decimal or voltage error.
Worked Examples with Unit Tracking
Below are two step-by-step derivations tracking units through the math to ensure dimensional consistency.
Problem 1: Single-Phase 50 kVA Step-Down Transformer
Scenario: Sizing the secondary feeder for a 1-phase, 50 kVA transformer with a 240V secondary. Assume continuous load.
- Calculate FLA:
I_FLA = (50 kVA × 1000 [VA/kVA]) / 240 V
I_FLA = 50,000 VA / 240 V = 208.33 A - Apply Continuous Multiplier:
A_min = 208.33 A × 1.25 = 260.41 A - Select Wire (NEC Table 310.16, 75°C column):
250 kcmil copper is rated for 255A (too small). 300 kcmil copper is rated for 285A. Pick 300 kcmil. - Select Breaker (NEC 240.6):
Next standard size above 260.41A is a 300A breaker. (The 300 kcmil wire at 285A is protected by the 300A breaker under the next-size-up rule of NEC 240.4(B) since 285A does not correspond to a standard breaker size).
Problem 2: Three-Phase 112.5 kVA Commercial Dry-Type
Scenario: Sizing the secondary feeder for a 3-phase, 112.5 kVA transformer, 480V secondary. This is the most common size for commercial lighting and receptacle panels.
- Calculate FLA:
I_FLA = (112.5 kVA × 1000 [VA/kVA]) / (480 V × 1.732)
I_FLA = 112,500 VA / 831.36 V = 135.32 A - Apply Continuous Multiplier:
A_min = 135.32 A × 1.25 = 169.15 A - Select Wire (NEC Table 310.16, 75°C column):
1/0 AWG is 150A (too small). 2/0 AWG copper is rated for 175A. Pick 2/0 AWG. - Select Breaker:
169.15A allows a standard 175A breaker. The 2/0 AWG wire (175A) perfectly matches the breaker.
Decision Path: From Calculated Amps to Exact AWG
Use this decision tree table to map your calculated A_min directly to the required copper wire size and standard breaker. This table assumes 75°C terminations and standard THHN/THWN-2 conductors in a raceway with no more than 3 current-carrying conductors.
| Calculated A_min Range | Required Copper AWG/kcmil | 75°C Ampacity | Standard Breaker Size | Common Transformer Match (3-Phase 480V) |
|---|---|---|---|---|
| 0A – 40A | 8 AWG | 50A | 40A or 50A | 15 kVA (18A FLA) |
| 41A – 65A | 6 AWG | 65A | 60A or 70A | 30 kVA (36A FLA) |
| 66A – 85A | 4 AWG | 85A | 80A or 90A | 45 kVA (54A FLA) |
| 86A – 100A | 3 AWG | 100A | 100A | None standard |
| 101A – 115A | 2 AWG | 115A | 110A or 125A | 75 kVA (90A FLA) |
| 116A – 130A | 1 AWG | 130A | 125A | None standard |
| 131A – 150A | 1/0 AWG | 150A | 150A | None standard |
| 151A – 175A | 2/0 AWG | 175A | 175A | 112.5 kVA (135A FLA) |
| 176A – 200A | 3/0 AWG | 200A | 200A | 150 kVA (180A FLA) * |
| 201A – 230A | 4/0 AWG | 230A | 225A | 150 kVA (with 1.25x continuous) |
| 231A – 255A | 250 kcmil | 255A | 250A | 225 kVA (270A FLA) * |
* Note: For 150 kVA and 225 kVA, the FLA multiplied by 1.25 pushes the requirement into the next wire size up. Always size for the 1.25x continuous value, not the raw FLA.
Ambient Derating and Final Default Pick
The decision table above assumes a 30°C (86°F) ambient temperature. If your transformer is located in a boiler room, on a hot roof, or in an unventilated electrical closet where ambient temperatures exceed 30°C, you must apply the correction factors from NEC Table 310.15(B)(1)(1). For example, at 45°C (113°F), the correction factor for 90°C rated THHN is 0.87. You divide the base ampacity by 0.87, which frequently forces you to bump up one full AWG size.
Furthermore, if you are pulling more than three current-carrying conductors in a single conduit (e.g., feeding two transformers from one panel), you must apply the bundling derating factors from NEC Table 310.15(C)(1). Four to six conductors require an 80% derating factor.
For deeper coordination on primary overcurrent protection and transformer inrush trip curves, refer to the NFPA 70 National Electrical Code Article 450 and manufacturer-specific sizing guides like those provided by Eaton Transformers.
