Introduction #

Instant answer: For a balanced three-phase unit, kVA = √3 × V_L × I_L ÷ 1000. From a documented diversified load, base kVA = kW ÷ PF. Any growth reserve and catalog selection are separate project decisions. Screen: 200 kW @ 0.88 PF ≈ 227.3 kVA at 480 V before reserve.

Open Transformer Size — 200 kW · 0.88 PF · 480 V →

Decision gate: 3φ transformer kVA #

Decision Prefer Do not
Load given in kW Base kVA = diversified kW ÷ PF Size on kW as if it were kVA
Unbalanced wye load Check each phase winding and total kVA Average the phases or compare the hottest phase directly with total nameplate kVA
Pure “kVA formula 3 phase” school search Point to 3φ power formula guide Compete for generic kVA formula
Boundary Utility interconnection studies This planning formula alone

This guide is for electrical engineers, facility managers, and designers who need to size three-phase transformers (not the generic single-phase formula). For the overall sizing process, see the Transformer Sizing Guide.

Single-Phase vs Three-Phase Transformer Sizing #

Single-phase transformers serve single-phase loads (lighting, small motors, outlets). Three-phase transformers serve three-phase loads (motors, chillers, industrial machinery, distribution boards). Industrial and commercial facilities typically use three-phase transformers for main distribution because most loads are three-phase and three-phase delivery is more efficient. In either case, start from documented demand and apparent power; then evaluate growth, starting duty, harmonics, environment and the manufacturer catalog. The formula from voltage and current differs: single-phase uses V × I; balanced three-phase uses √3 × V_L × I_L (line voltage and line current). For the overall process, see the Transformer Sizing Guide. To convert kW to kVA when you have power factor, use the PF–kW–kVA tool; for a base-load screen use the Transformer Size Calculator.

Three-Phase Transformer kVA Formula #

For balanced three-phase load, apparent power (kVA) is:

Formula:

S (kVA) = (√3 × V_L × I_L) ÷ 1000

Where:

  • V_L = line-to-line voltage (V)
  • I_L = line current (A), same for each phase in a balanced load
  • √3 ≈ 1.732

Why √3: In three-phase, phase voltage V_ph = V_L ÷ √3 (wye) and line current I_L equals phase current I_ph in wye. Power per phase = V_ph × I_ph; total power = 3 × V_ph × I_ph = 3 × (V_L ÷ √3) × I_L = √3 × V_L × I_L. So the √3 relates line quantities to total three-phase apparent power. For delta connection, the same expression holds for total power in terms of line voltage and line current.

When load is given in kW and power factor, kVA = kW ÷ PF; the formula above is used when you have voltage and current (e.g. from measurement or equipment nameplate).

Line Voltage vs Phase Voltage Explained #

  • Line voltage (V_L): Voltage between two line conductors (e.g. L1–L2). This is the voltage normally specified (e.g. 400 V, 415 V, 480 V).
  • Phase voltage (V_ph): In wye, voltage between one line and neutral: V_ph = V_L ÷ √3. In delta there is no neutral; phase voltage equals line voltage (V_ph = V_L).

For transformer sizing, use line voltage and line current in the kVA formula. Equipment nameplates and distribution voltages are usually given as line-to-line. Ensure the transformer’s primary and secondary voltage ratings match the system line voltages.

Example: Three-Phase Transformer Sizing Calculation #

Given: Balanced, diversified three-phase load of 200 kW at 0.88 PF and 480 V line-to-line.

Step 1 – Required kVA:
kVA = 200 ÷ 0.88 ≈ 227.3 kVA.

Step 2 – Define project reserve:
Do not add a universal percentage automatically. Establish reserve from measured peak duration, future load commitments, motor starting, harmonics, ambient/altitude, redundancy and manufacturer loading limits.

Step 3 – Compare catalogs: Select a catalog frame only after the reserve and duty checks are documented.

Check with current (optional):
I_L = (227.3 × 1000) ÷ (√3 × 480) ≈ 273.4 A. This is the balanced load current at the base kVA, not the full-load current of an automatically selected transformer.

Common line voltages and the same base load (200 kW, 0.88 PF → 227.3 kVA):

Line voltage (V) Base kVA Base-load current
400 V 227.3 kVA 328.0 A
415 V 227.3 kVA 316.2 A
480 V 227.3 kVA 273.4 A

The base kVA is set by load and PF; line voltage sets current (I_L = kVA × 1000 ÷ (√3 × V_L)). Lower voltage means higher current for the same kVA. Cable and protection selection still requires the applicable installation and protection rules.

Vendor-neutral workflow (vs OEM size calculators) #

Manufacturer “transformer size calculators” often jump from a few inputs to a catalog SKU. Use this vendor-neutral sequence first, then open the OEM tool only to pick impedance, temperature rise, and enclosure:

  1. Demand kW (diversified) ÷ PF → base kVA
  2. Establish project reserve from load profile, growth, starting duty and environment
  3. Compare the reserve-inclusive requirement with the actual manufacturer catalog
  4. Check unbalance / motor FLA / harmonics before PO
  5. Confirm amps with kVA to amps and run Transformer Size Calculator

Multi-scenario sizing ladder #

Scenario Inputs Planning kVA Typical pick
Balanced plant feed 200 kW @ 0.88 PF 227.3 kVA base Add only documented project reserve, then compare catalogs
Unbalanced 480/277 V wye panel Phase loads 100 / 60 / 60 kVA Total = 220 kVA; hottest winding = 100 kVA At least 300 kVA winding-capacity screen, then verify OEM unbalance limits
Motor-heavy MCC 75 kW motor @ 0.85 PF + auxiliaries 40 kW @ 0.90 P = 115 kW; Q ≈ 65.8 kVAR; S ≈ 132.5 kVA base Run starting-voltage-drop and thermal checks before choosing a frame

These are planning screens—not substitute for OEM thermal curves or stamped drawings.

Load Balance and Its Impact on Sizing #

Balanced load means equal current and apparent power on all three phases. The total-kVA formula above assumes balance. For line-to-neutral loads on a four-wire wye secondary, compare each phase winding with one-third of the transformer's three-phase nameplate rating. If phase A is 100 kVA and phases B and C are 60 kVA each, total load is 220 kVA, but a 150 kVA transformer provides only 50 kVA of nominal capacity per phase and is plainly inadequate. A winding-capacity screen requires at least 3 × 100 = 300 kVA, subject to the transformer's connection, manufacturer unbalance limits, neutral/harmonic loading and load redistribution. Do not apply this shortcut to line-to-line or delta-connected loads without a vector model.

Common Three-Phase Sizing Mistakes #

Mistake 1: Using Phase Voltage Instead of Line Voltage in the Formula #

Error: Using phase voltage (e.g. 277 V on a 480 V wye system) in the kVA formula instead of line-to-line voltage.

Correct approach: The standard three-phase formula uses line voltage V_L: S (kVA) = (sqrt(3) x V_L x I_L) / 1000. Using V_ph understates kVA by a factor of sqrt(3) and leads to undersizing. Always use line-to-line voltage and line current.

Mistake 2: Ignoring Power Factor #

Error: Sizing from kW only (e.g. 200 kW to 200 kVA) when power factor is less than 1.

Correct approach: Always use kVA = kW / PF. A 200 kW load at 0.88 PF requires 227 kVA, not 200 kVA. Use the PF-KW-kVA tool to convert; then document project reserve and compare the result with an actual manufacturer catalog.

Engineering recommendation: For three-phase sizing, start from load kVA (kW / PF) or from measured line voltage and current. Apply only defensible diversity assumptions, document reserve separately, and verify the catalog frame against starting, harmonic and thermal conditions. For unbalanced installations, check both total kVA and individual winding loading.

Frequently Asked Questions #

Q1: What is the three-phase transformer kVA formula? #

A: For balanced three-phase load, S (kVA) = (√3 × V_L × I_L) / 1000, where V_L is line-to-line voltage (V) and I_L is line current (A). When load is given in kW and power factor, use base kVA = diversified kW / PF, then evaluate reserve and catalog availability separately.

Q2: How does unbalanced load affect three-phase transformer sizing? #

A: Check total kVA and each winding. For line-to-neutral loads on a wye secondary, each phase winding nominally represents one-third of total three-phase nameplate kVA; do not compare the hottest phase kVA directly with the total nameplate rating.

Q3: What is the 80% rule for transformer loading? #

A: Many planners keep continuous loading near ≤80% of nameplate kVA for thermal headroom and growth. That is a planning screen, not a universal code mandate—confirm against your standard and OEM temperature-rise rating. Example: a 300 kVA unit → target continuous ≈ 240 kVA.

Q4: How many amps is a 75 kVA three-phase transformer? #

A: I_L = (kVA × 1000) ÷ (√3 × V_L). At 480 V: 75,000 ÷ (1.732 × 480) ≈ 90 A. At 208 V: ≈ 208 A. Verify with the kVA to amps calculator.

Q5: What transformer size for a 200 A service? #

A: At 240 V single-phase, 200 A ≈ 48 kVA; at 208 V three-phase, 200 A ≈ 72 kVA (√3 × 208 × 200 ÷ 1000). That is an amp-to-kVA conversion, not a final transformer selection; check the load study, reserve, duty and catalog before choosing equipment.

Next step #

Open Transformer Size — 200 kW · 0.88 PF · 480 V →

Then confirm the 227.3 kVA base-load current with kVA to amps and browse the Power calculator hub.

Conclusion #

Three-phase transformer sizing uses S = sqrt(3) × V_L × I_L with line voltage and current. Calculate base kVA from diversified kW and PF, then treat reserve and catalog selection as explicit project decisions. For unbalanced loads, check total load, winding loading and connection—not only an average or the hottest phase in isolation.

About the Author: David Kim, P.E. is a senior power systems engineer with 14+ years of experience in transformer design, substation engineering, and industrial power systems. Former ABB application engineer specializing in transformer selection and 3-phase distribution. Has designed distribution systems for manufacturing facilities, data centers, and commercial buildings. All content in this guide has been reviewed and validated by licensed engineers.