What is the formula for 3 phase power?

kW = √3 × V × I × PF ÷ 1000, where V is the line-to-line voltage, I is the line current and PF is the power factor. Apparent power is kVA = √3 × V × I ÷ 1000.

Why is √3 (1.732) used in three-phase calculations?

In a balanced three-phase system the three phase voltages are 120° apart. The line-to-line voltage is √3 times the line-to-neutral voltage, and total power across three phases works out to √3 × V(line-to-line) × I.

Why is 208 V not 240 V?

A 120/208 V wye service has 120 V from each phase to neutral. The voltage between two phases is 120 × 1.732 = 207.8 V, rounded to 208 V.

How do I find amps from kW on a three-phase load?

I = kW × 1000 ÷ (1.732 × V × PF). A 50 kW load at 480 V with a 0.85 power factor draws 50,000 ÷ (1.732 × 480 × 0.85) ≈ 70.8 A.

Should I use line or phase current?

Use line current, the current you measure on each ungrounded conductor with a clamp meter, together with line-to-line voltage. That works for both wye and delta loads.

3 Phase Power Calculator: kW, kVA, Amps

Enter the line-to-line voltage, line current and power factor to get real power (kW) and apparent power (kVA) for a balanced three-phase load.

Three-phase power formulas

kVA = √3 × V_L-L × I ÷ 1000
kW = kVA × PF = √3 × V_L-L × I × PF ÷ 1000
I = kW × 1000 ÷ (√3 × V_L-L × PF)

√3 ≈ 1.732. V_L-L is the voltage measured between any two phases: 208, 240, 480 or 600 V on common North American systems. I is the current in each line. These formulas assume the load is balanced, meaning roughly equal current on all three phases. That is true for motors, most HVAC equipment and properly laid out panels.

Worked examples

1. A 208 V panel at 100 A

kVA = 1.732 × 208 × 100 ÷ 1000 = 36.0 kVA
kW at PF 0.9 = 36.0 × 0.9 = 32.4 kW

That is the most this feeder can deliver at full load. A 100 A, 120/208 V panel serves about 36 kVA.

2. The same current at 480 V

kVA = 1.732 × 480 × 100 ÷ 1000 = 83.1 kVA

The same 100 A carries 2.3 times the power at 480 V. That is why commercial and industrial buildings distribute at 480 V and step down to 208 V only where receptacles and lighting need it.

3. Current for a 50 kW load

A 50 kW process load at 480 V with a power factor of 0.85:

I = 50,000 ÷ (1.732 × 480 × 0.85) = 50,000 ÷ 706.7 ≈ 70.8 A

If the load is continuous, conductors must be rated at least 125% of that, 88.5 A. The wire size calculator gives 3 AWG copper at 75 °C (100 A). For long feeders, check the 3 phase voltage drop too.

Single phase vs three phase

A single-phase load draws power in pulses that drop to zero 120 times a second. Three phases overlap so total power is constant, which lets motors run smoothly and makes three-phase conductors more efficient: three wires carry √3 times the power of two wires at the same voltage and current. For single-phase loads, use the amps to watts calculator.

Common three-phase voltages

System	Line-to-line	Line-to-neutral	Typical use
120/208 V wye	208 V	120 V	Commercial receptacles, lighting, small RTUs
120/240 V high-leg delta	240 V	120 V (208 V high leg)	Older shops and light industrial
277/480 V wye	480 V	277 V	US commercial and industrial
347/600 V wye	600 V	347 V	Canadian commercial and industrial

Power factor

Power factor is the ratio of real power (kW) to apparent power (kVA). Resistive heating has a PF of 1. Induction motors typically run around 0.85 at full load and much lower when lightly loaded. Equipment and conductors must carry the full kVA current, which is why utilities may charge industrial customers for low power factor, and why capacitor banks or drives are used to correct it.

Unbalanced loads

When phase currents differ, the simple formula is only an estimate. Calculate each phase separately with line-to-neutral voltage (kVA per phase = V_L-N × I ÷ 1000) and add the three results. Size the feeder for the most heavily loaded phase.

3 Phase Power Calculator