LumaQuote Electrical calculators 3 phase power

3 Phase Power Calculator

Calculate three-phase power from line voltage, current and power factor: real power in kW, apparent power in kVA and reactive power in kVAR. Or work back from kW to the line current.

3 phase power formula

For a balanced three-phase load, power is 1.732 times the line-to-line voltage times the line current, times the power factor for real power.

kW = 1.732 × volts × amps × power factor ÷ 1,000

kVA = 1.732 × volts × amps ÷ 1,000

kVAR = kVA × √(1 − power factor²)

amps = kW × 1,000 ÷ (1.732 × volts × power factor)

Examples

100 A at 480 V, power factor 0.9: 1.732 × 480 × 100 × 0.9 = 74.8 kW. At power factor 1.0 it is 83.1 kW.
50 kW at 208 V, power factor 0.9: 50,000 ÷ (1.732 × 208 × 0.9) = 154.2 A per line.

Why 1.732?

The three phases peak a third of a cycle apart, so the voltage between two phases is the square root of 3 times the voltage from a phase to neutral. That is why 120 V to neutral gives 208 V between phases (120 × 1.732), 277 V gives 480 V, and 347 V gives 600 V.

Line and phase values in wye and delta

Wye (star): line current equals phase current, and line voltage is 1.732 × phase voltage. 208Y/120, 480Y/277 and 600Y/347 V are wye systems.
Delta: line voltage equals phase voltage, and line current is 1.732 × the current in each winding. 240 V and 480 V delta services are common in older industrial buildings.

Either way, the power formula is the same when you use line voltage and line current.

Three-phase kVA by current

Apparent power at common line-to-line voltages. Multiply by the power factor for kW.

Line current	208 V	240 V	480 V	600 V
10 A	3.60 kVA	4.16 kVA	8.31 kVA	10.39 kVA
20 A	7.21 kVA	8.31 kVA	16.63 kVA	20.78 kVA
30 A	10.81 kVA	12.47 kVA	24.94 kVA	31.18 kVA
50 A	18.01 kVA	20.78 kVA	41.57 kVA	51.96 kVA
100 A	36.03 kVA	41.57 kVA	83.14 kVA	103.9 kVA
200 A	72.05 kVA	83.14 kVA	166.3 kVA	207.8 kVA
400 A	144.1 kVA	166.3 kVA	332.6 kVA	415.7 kVA

Unbalanced loads

The formula assumes the three phases carry the same current. Lighting and receptacle panels are rarely perfectly balanced. For an unbalanced panel, work out each phase on its own (line-to-neutral volts × that phase's amps × power factor) and add them up.

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3 phase power FAQ

How do you calculate 3 phase power?

Multiply 1.732 × line-to-line voltage × line current × power factor, then divide by 1,000 for kW. Leave out the power factor to get kVA.

What is 1.732 in three-phase calculations?

The square root of 3. It is the ratio between line-to-line and line-to-neutral voltage in a three-phase system, for example 208 ÷ 120.

How many kW is 100 amps three-phase at 480 V?

83.1 kW at power factor 1.0, or 74.8 kW at power factor 0.9.

How many amps is 50 kW three-phase at 208 V?

138.8 A at power factor 1.0, or 154.2 A at power factor 0.9.

Is the voltage in the formula line-to-line or line-to-neutral?

Line-to-line. A 480 V motor nameplate means 480 V between phases. If you only know the line-to-neutral voltage, multiply it by 1.732.

What is kVAR?

Reactive power, the part of the apparent power that flows back and forth without doing work. It comes mostly from motors and transformers, and capacitors are used to cancel it and raise the power factor.