Three-Phase Power Calculator
Calculate power, current, or voltage for 3-phase systems.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any 2 values to solve for the others — or enter 3 for a precise result.
How three-phase power calculation works
Three-phase power is the dominant method of electrical power distribution for industrial, commercial, and large residential applications. Unlike single-phase systems that deliver power in pulses, three-phase systems deliver constant power because the three waveforms are offset by 120 degrees. This makes three-phase systems more efficient for high-power loads and allows smaller conductor sizes for the same power delivery.
For a balanced three-phase system, the relationship between voltage, current, power, and power factor is governed by two key formulas depending on how voltage is measured. If you are working with line-to-line voltage (the voltage between any two phases), the real power in kilowatts is P = √3 × VL-L × I × PF / 1000. If you are working with line-to-neutral voltage (the voltage between one phase and the neutral point, available only in wye configurations), the formula becomes P = 3 × VL-N × I × PF / 1000.
The √3 factor (approximately 1.732) appears because the line-to-line voltage is √3 times larger than the phase voltage in a balanced wye system. This factor adjusts the single-phase power equation to account for the contribution of all three phases. Understanding which voltage configuration your system uses is critical to getting correct results.
Three-phase power formulas
Line-to-Line
P = √3 × VL-L × I × PF
S = √3 × VL-L × I
Q = √3 × VL-L × I × sin(arccos(PF))
Line-to-Neutral (Wye only)
P = 3 × VL-N × I × PF
S = 3 × VL-N × I
Q = 3 × VL-N × I × sin(arccos(PF))
Where P is real power (W), S is apparent power (VA), Q is reactive power (VAR), V is voltage (V), I is current (A), and PF is power factor. Divide by 1000 for kW/kVA/kVAR.
Worked example
Motor Sizing
Determine the required current and power for three-phase induction motors based on voltage and power factor. Essential for selecting motor starters, contactors, and overload protection.
Electrical Load Calculations
Calculate total load current when adding new three-phase equipment to an existing panel or distribution board. Ensures you stay within the rated capacity of breakers, busbars, and feeders.
Generator Sizing
Size backup generators correctly by converting load kW to kVA at the expected power factor. A generator rated 500 kVA at 0.8 PF can supply 400 kW of real power continuously.
Transformer Rating
Transformers are rated in kVA because their thermal limit depends on current (heating), not real power. Use this calculator to verify that a transformer can handle both the kW load and the reactive power.
Tips for using the three-phase power calculator
Balanced load assumption
This calculator assumes a perfectly balanced three-phase system where all three phases carry equal current and have the same power factor. In real-world installations, some imbalance is normal, but large imbalances should be investigated as they indicate wiring issues or uneven load distribution.
Power factor varies by load type
Induction motors typically have a power factor of 0.7 to 0.9 at full load, dropping significantly at partial load. Resistive loads like heaters and lighting have PF near 1.0. Variable frequency drives (VFDs) include built-in PF correction and often achieve 0.95 or higher.
Enter 3 values for complete accuracy
When you enter only voltage and current, the calculator assumes a power factor of 1.0 to compute power. For an accurate result that accounts for reactive power, always enter all three known values: voltage, current, and either power factor or real power.
Know your system configuration
Always verify whether your system uses line-to-line or line-to-neutral voltage. Selecting the wrong configuration will give results that are off by a factor of √3. If you are unsure, check the nameplate of your equipment or consult the system one-line diagram.
Related calculators
Frequently asked questions
What is the difference between line-to-line and line-to-neutral?
Line-to-line voltage is measured between two phases; line-to-neutral is between one phase and neutral. Line-to-line = √3 × line-to-neutral.
What is power factor?
The ratio of real power (kW) to apparent power (kVA). Typical motor loads are 0.8–0.9.
How do I calculate 3-phase power?
P = √3 × V<sub>L-L</sub> × I × PF for line-to-line. P = 3 × V<sub>L-N</sub> × I × PF for line-to-neutral.
What is the √3 (1.732) for?
It is the square root of 3, which relates line-to-line voltage to line-to-neutral voltage in a balanced 3-phase system.
Sources & references
This tool uses standard formulas and reference values from:
- • NFPA 70 — National Electrical Code (NEC), conduit fill, box fill and conductor ampacity. nfpa.org
- • IPC-2221, Generic Standard on Printed Board Design (trace width / current). ipc.org
- • NIST reference constants and unit definitions; IEEE standards where applicable. nist.gov
For educational and preliminary use. Verify against full engineering calculations and the governing standard before any real design.