Why √3 instead of 3?

Three-phase voltages are 120° apart in time, so adding three sinusoids does not just multiply by 3. The vector sum of three balanced sinusoids 120° apart works out to √3 (about 1.732) times one of them. This factor shows up in every balanced three-phase power equation.

Is that V_LL or V_LN?

The equation above uses line-to-line voltage (V_LL). On a 480V three-phase system, V_LL = 480 V and V_LN = 277 V. If you have only line-to-neutral, multiply by √3 to get line-to-line.

Does this work for unbalanced systems?

No. The √3 formula assumes balanced loads on all three phases. For unbalanced systems (uneven phase loading), you have to calculate each phase independently and sum the results.

3-Phase Power Calculator

Calculate three-phase power, current, and voltage. Free calculator for 3-phase electrical systems with power factor.

Inputs

Direction

Amps → WattsWatts → Amps

Current

Line-to-Line Voltage

Power Factor

Result

Power

8,313.8W

Power (kW)

8.314kW

P = I × V × √3 × PF = 10 × 480 × 1.732 × 1

About this calculator

Three-phase power is the workhorse of commercial and industrial electrical systems. Most motors over a few horsepower are three-phase, as are most large HVAC, pumping, and process loads. Calculating three-phase power, current, or voltage from any two of the three values plus power factor is a recurring task on the job and on the journeyman exam.

Formula

In a balanced three-phase system, real power equals √3 times line-to-line voltage times line current times power factor. Apparent power drops the power factor. Solving for current rearranges the same equation.

P (watts) = √3 × V_LL × I_L × PF
S (VA) = √3 × V_LL × I_L
I_L = P ÷ (√3 × V_LL × PF)

How to use

Pick which value you want to solve for: power, current, or voltage.
Enter the two known values - typically voltage and current, or power and voltage.
Set power factor (1.0 for resistive, 0.85-0.9 for typical motor loads).
The calculator solves the equation and shows the result with units.
Switch between watts/kW and amps/milliamps as needed.

Worked example

Setup

A 480 V three-phase motor draws 18 A at a power factor of 0.88. What is the real power consumption?

Calculation

P = √3 × 480 × 18 × 0.88 = 1.732 × 480 × 18 × 0.88 = 13,168 W ≈ 13.2 kW.

Answer

The motor consumes 13.2 kW of real power. Apparent power (kVA) is 14.97, so the motor draws about 1.8 kVAR of reactive power - typical for an inductive load.

Frequently asked questions

Why √3 instead of 3?: Three-phase voltages are 120° apart in time, so adding three sinusoids does not just multiply by 3. The vector sum of three balanced sinusoids 120° apart works out to √3 (about 1.732) times one of them. This factor shows up in every balanced three-phase power equation.
Is that V_LL or V_LN?: The equation above uses line-to-line voltage (V_LL). On a 480V three-phase system, V_LL = 480 V and V_LN = 277 V. If you have only line-to-neutral, multiply by √3 to get line-to-line.
Does this work for unbalanced systems?: No. The √3 formula assumes balanced loads on all three phases. For unbalanced systems (uneven phase loading), you have to calculate each phase independently and sum the results.