For 3-phase power at 480V with power factor 0.85: 10 kW = 14.2 amps, and 50 amps = 35.3 kW. The formulas differ from single-phase because 3-phase power uses three conductors carrying current 120° out of phase with each other, resulting in the √3 (1.732) factor that appears in all 3-phase calculations.
Use the calculator below for instant conversions, then review the formulas and reference tables for common 3-phase HVAC and commercial equipment.
3-Phase Power Formulas
kW to Amps (3-Phase)
Amps = (kW × 1,000) ÷ (Volts × √3 × Power Factor)
For 480V at PF 0.85: Amps = kW × 1,000 ÷ (480 × 1.732 × 0.85) = kW × 1.415
Amps to kW (3-Phase)
kW = (Amps × Volts × √3 × Power Factor) ÷ 1,000
For 480V at PF 0.85: kW = Amps × 480 × 1.732 × 0.85 ÷ 1,000 = Amps × 0.707
kVA to Amps (3-Phase)
Amps = (kVA × 1,000) ÷ (Volts × √3)
For 480V: Amps = kVA × 1,000 ÷ (480 × 1.732) = kVA × 1.203
Amps to kVA (3-Phase)
kVA = (Amps × Volts × √3) ÷ 1,000
For 480V: kVA = Amps × 480 × 1.732 ÷ 1,000 = Amps × 0.831
Power Factor (PF) is crucial for kW calculations. kVA is "apparent power" (volts × amps). kW is "real power" (what actually does work). The relationship: kW = kVA × PF. Motors typically have PF of 0.80–0.90. Resistive loads (heaters) have PF of 1.0. Always check equipment nameplates for actual PF.
Quick Reference Tables
kW to Amps Conversion (Various Voltages, PF = 0.85)
| kW | 208V | 240V | 380V | 480V | 600V |
|---|---|---|---|---|---|
| 1 | 3.27A | 2.83A | 1.79A | 1.42A | 1.13A |
| 2 | 6.53A | 5.66A | 3.58A | 2.84A | 2.27A |
| 3 | 9.80A | 8.49A | 5.37A | 4.25A | 3.40A |
| 5 | 16.3A | 14.2A | 8.94A | 7.09A | 5.67A |
| 7.5 | 24.5A | 21.2A | 13.4A | 10.6A | 8.51A |
| 10 | 32.7A | 28.3A | 17.9A | 14.2A | 11.3A |
| 15 | 49.0A | 42.5A | 26.9A | 21.3A | 17.0A |
| 20 | 65.3A | 56.6A | 35.8A | 28.4A | 22.7A |
| 25 | 81.7A | 70.7A | 44.7A | 35.5A | 28.4A |
| 30 | 98.0A | 84.9A | 53.7A | 42.5A | 34.0A |
| 40 | 131A | 113A | 71.6A | 56.7A | 45.4A |
| 50 | 163A | 142A | 89.4A | 70.9A | 56.7A |
| 75 | 245A | 212A | 134A | 106A | 85.1A |
| 100 | 327A | 283A | 179A | 142A | 113A |
Motor HP to Amps (3-Phase, Full Load)
| HP | 208V | 230V | 460V | 575V |
|---|---|---|---|---|
| 1 | 4.6A | 4.2A | 2.1A | 1.7A |
| 1.5 | 6.6A | 6.0A | 3.0A | 2.4A |
| 2 | 7.5A | 6.8A | 3.4A | 2.7A |
| 3 | 10.6A | 9.6A | 4.8A | 3.9A |
| 5 | 17.5A | 15.2A | 7.6A | 6.1A |
| 7.5 | 25.3A | 22.0A | 11.0A | 9.0A |
| 10 | 32.2A | 28.0A | 14.0A | 11.0A |
| 15 | 48.3A | 42.0A | 21.0A | 17.0A |
| 20 | 62.1A | 54.0A | 27.0A | 22.0A |
| 25 | 78.2A | 68.0A | 34.0A | 27.0A |
| 30 | 92.0A | 80.0A | 40.0A | 32.0A |
| 40 | 120A | 104A | 52.0A | 41.0A |
| 50 | 150A | 130A | 65.0A | 52.0A |
| 60 | 177A | 154A | 77.0A | 62.0A |
| 75 | 221A | 192A | 96.0A | 77.0A |
| 100 | 285A | 248A | 124A | 99.0A |
Values from NEC Table 430.250 (Induction motors, Design B)
Amps to kW Conversion (480V, Various Power Factors)
| Amps | PF 0.80 | PF 0.85 | PF 0.90 | PF 1.00 |
|---|---|---|---|---|
| 10 | 6.65 kW | 7.07 kW | 7.49 kW | 8.31 kW |
| 20 | 13.3 kW | 14.1 kW | 15.0 kW | 16.6 kW |
| 30 | 19.9 kW | 21.2 kW | 22.5 kW | 24.9 kW |
| 50 | 33.2 kW | 35.3 kW | 37.4 kW | 41.6 kW |
| 75 | 49.8 kW | 53.0 kW | 56.1 kW | 62.4 kW |
| 100 | 66.5 kW | 70.7 kW | 74.9 kW | 83.1 kW |
| 150 | 99.7 kW | 106 kW | 112 kW | 125 kW |
| 200 | 133 kW | 141 kW | 150 kW | 166 kW |
| 300 | 199 kW | 212 kW | 225 kW | 249 kW |
| 400 | 266 kW | 283 kW | 299 kW | 333 kW |
Understanding 3-Phase Power
What Is 3-Phase Power?
3-phase power uses three conductors, each carrying alternating current that peaks at different times (120° apart). This provides:
- More efficient power delivery: ~1.73× the power of single-phase with only 1.5× the conductors
- Smoother motor operation: Constant power delivery (no pulsing like single-phase)
- Smaller equipment: Motors, generators, and transformers are physically smaller for the same power rating
3-Phase vs. Single-Phase Comparison
| Property | Single-Phase | 3-Phase |
|---|---|---|
| Conductors | 2 (hot + neutral) or 2 hots | 3 hots (+ neutral for 4-wire) |
| Power formula | V × I × PF | V × I × √3 × PF |
| 10kW at 240V | 41.7A (PF 1.0) | 24.1A (PF 1.0) |
| Motor smoothness | Pulsating torque | Constant torque |
| Residential use | Standard | Rare (large homes) |
| Commercial use | Small loads | Standard |
| Wire sizing (10kW) | Larger | Smaller |
Common 3-Phase Voltages
| Voltage | Configuration | Common Use |
|---|---|---|
| 208V | 3-phase wye | Small commercial HVAC, motors |
| 240V | 3-phase delta | Motor loads, welders |
| 380V | 3-phase wye (European) | International equipment |
| 480V | 3-phase wye | Large commercial/industrial HVAC |
| 600V | 3-phase wye (Canada) | Industrial in Canada |
208V 3-phase is NOT the same as 240V single-phase. In a 208V 3-phase wye system, 208V is the line-to-line voltage (120V line-to-neutral × √3 = 208V). Equipment rated for 240V single-phase may not work correctly on 208V 3-phase — the voltage is 13% lower, which affects motor performance and heater output.
3-Phase HVAC Equipment Sizing
Commercial Air Conditioners and Chillers
| Cooling Capacity | Typical kW | 208V Amps | 480V Amps | Wire (480V) |
|---|---|---|---|---|
| 5 tons | 6–8 kW | 20–26A | 8–11A | 14 AWG |
| 7.5 tons | 9–12 kW | 29–39A | 13–17A | 14–12 AWG |
| 10 tons | 12–16 kW | 39–52A | 17–23A | 12–10 AWG |
| 15 tons | 18–24 kW | 59–78A | 25–34A | 10–8 AWG |
| 20 tons | 24–32 kW | 78–104A | 34–45A | 8–6 AWG |
| 25 tons | 30–40 kW | 98–131A | 42–57A | 6–4 AWG |
| 30 tons | 36–48 kW | 117–157A | 51–68A | 4–3 AWG |
| 40 tons | 48–64 kW | 157–209A | 68–90A | 3–1 AWG |
| 50 tons | 60–80 kW | 196–261A | 85–113A | 1–1/0 AWG |
Rooftop Units (Packaged HVAC)
| Unit Size | Compressor HP | Fan HP | Total kW | 480V Amps |
|---|---|---|---|---|
| 3 ton | 3 HP | 0.5 HP | 3.5–4.5 kW | 5–7A |
| 5 ton | 5 HP | 1 HP | 5.5–7 kW | 8–10A |
| 7.5 ton | 7.5 HP | 1.5 HP | 8–10 kW | 11–14A |
| 10 ton | 10 HP | 2 HP | 10–13 kW | 14–18A |
| 15 ton | 15 HP | 3 HP | 15–20 kW | 21–28A |
| 20 ton | 20 HP | 5 HP | 20–27 kW | 28–38A |
| 25 ton | 25 HP | 7.5 HP | 27–35 kW | 38–50A |
Electric Heating (3-Phase)
| Heating Element | kW | 208V Amps | 240V Amps | 480V Amps |
|---|---|---|---|---|
| 5 kW | 5 | 13.9A | 12.0A | 6.0A |
| 10 kW | 10 | 27.8A | 24.1A | 12.0A |
| 15 kW | 15 | 41.7A | 36.1A | 18.0A |
| 20 kW | 20 | 55.6A | 48.1A | 24.1A |
| 25 kW | 25 | 69.4A | 60.1A | 30.1A |
| 30 kW | 30 | 83.3A | 72.2A | 36.1A |
| 40 kW | 40 | 111A | 96.2A | 48.1A |
| 50 kW | 50 | 139A | 120A | 60.2A |
Electric heating has PF = 1.0, so kW = kVA
Wire Sizing for 3-Phase Circuits
NEC Table 310.16 Ampacity (3-Phase, Copper, 75°C)
| Wire Gauge | Ampacity | Typical Use |
|---|---|---|
| 14 AWG | 20A | Small motors, controls |
| 12 AWG | 25A | 5 HP motors at 480V |
| 10 AWG | 35A | 7.5 HP motors at 480V |
| 8 AWG | 50A | 15 HP motors at 480V |
| 6 AWG | 65A | 20 HP motors at 480V |
| 4 AWG | 85A | 25–30 HP motors at 480V |
| 3 AWG | 100A | 40 HP motors at 480V |
| 2 AWG | 115A | 50 HP motors at 480V |
| 1 AWG | 130A | Sub-feeders |
| 1/0 AWG | 150A | 75 HP motors at 480V |
| 2/0 AWG | 175A | 100 HP motors at 480V |
| 3/0 AWG | 200A | Service entrance |
| 4/0 AWG | 230A | Service entrance |
| 250 kcmil | 255A | Large feeders |
| 300 kcmil | 285A | Large feeders |
| 350 kcmil | 310A | Large feeders |
| 500 kcmil | 380A | Main service |
Motor circuits have special sizing rules. NEC Article 430 requires conductors sized at 125% of motor full-load current, and overcurrent protection sized up to 250% for standard motors (to handle starting current). Always reference NEC Tables 430.248–430.250 for motor FLA values rather than nameplate data.
Power Factor Correction
Why Power Factor Matters
Low power factor means:
- Higher current for the same real power
- Larger wire sizes needed
- Utility penalties (commercial accounts)
- Reduced transformer capacity
| Load Type | Typical Power Factor |
|---|---|
| Incandescent lighting | 1.00 |
| Resistive heating | 1.00 |
| LED lighting (good ballast) | 0.90–0.98 |
| Fluorescent lighting | 0.85–0.95 |
| AC motors (full load) | 0.85–0.90 |
| AC motors (partial load) | 0.50–0.80 |
| VFD-driven motors | 0.95–0.99 |
| Welders | 0.50–0.70 |
Calculating Capacitor kVAR for Correction
kVAR needed = kW × (tan(cos⁻¹(PF₁)) - tan(cos⁻¹(PF₂)))
To correct 100 kW load from PF 0.75 to PF 0.95:
- tan(cos⁻¹(0.75)) = 0.882
- tan(cos⁻¹(0.95)) = 0.329
- kVAR = 100 × (0.882 - 0.329) = 55.3 kVAR
Real-World Examples
Example 1: Sizing Wire for 3-Phase RTU
Scenario: 20-ton rooftop unit, 480V 3-phase. Nameplate: 30 kW, PF 0.85.
Calculation:
- Amps = 30,000 ÷ (480 × 1.732 × 0.85) = 42.5A
- 125% for continuous load = 53.1A
- Wire: 6 AWG copper (65A ampacity)
- Breaker: Per NEC 440, up to 175% of 42.5A = 74.4A → 70A or 80A
Example 2: Converting HP to kW
Scenario: 25 HP motor, 480V, 3-phase. What's the power draw?
From NEC Table 430.250: 25 HP at 460V = 34A FLA
Power calculation:
- kVA = 34 × 480 × 1.732 ÷ 1000 = 28.3 kVA
- Assuming PF 0.87: kW = 28.3 × 0.87 = 24.6 kW
Verification: 25 HP × 0.746 kW/HP = 18.65 kW mechanical output. At ~75% motor efficiency: 18.65 ÷ 0.75 = 24.9 kW input. ✓
Example 3: Panel Load Calculation
Scenario: New commercial HVAC installation with:
- (2) 10-ton AC units at 14 kW each
- (1) 30 kW electric heater
- (4) 2 HP exhaust fans at 2.5 kW each
Total load:
- AC units: 2 × 14 = 28 kW
- Heater: 30 kW
- Fans: 4 × 2.5 = 10 kW
- Total: 68 kW
Current at 480V, PF 0.85:
- Amps = 68,000 ÷ (480 × 1.732 × 0.85) = 96.3A
- With demand factors, likely ~80A effective
Service: 200A, 3-phase, 480V service with room for growth
Example 4: Comparing 208V vs. 480V Wiring Cost
Scenario: 50 kW load requires wiring. Compare 208V and 480V options.
| Voltage | Amps (PF 0.85) | Wire Size | Approx. Cost (100 ft, 3 conductors) |
|---|---|---|---|
| 208V | 163A | 2/0 AWG | $800–$1,200 |
| 480V | 70.9A | 4 AWG | $200–$350 |
Savings at 480V: ~$500–$850 in wire costs alone, plus smaller conduit, easier installation.
Key Takeaways
- 3-phase formula: Amps = kW × 1000 ÷ (V × √3 × PF) — the √3 factor (1.732) is essential
- Power factor matters: PF 0.85 is typical for motors; PF 1.0 for resistive heating
- 480V uses ~2.3× less current than 208V for the same power — smaller wire, lower cost
- Motor FLA from NEC tables, not nameplates — use Tables 430.248–430.250
- kVA ≠ kW — kW = kVA × Power Factor (real power vs. apparent power)
- Motor circuits: Wire at 125% of FLA, breakers up to 175–250% of FLA
- Always verify voltage configuration: 208V 3-phase ≠ 240V single-phase
Frequently Asked Questions
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