Three-Phase Power Calculator
Three-phase power uses a √3 (1.732) multiplier: P = 1.732 × V × I × PF
Enter line-to-line voltage, current per phase, and power factor to calculate three-phase real power (kW) and apparent power (kVA). Three-phase power is used in commercial buildings, industrial facilities, and large HVAC equipment. For single-phase circuits, use the single-phase power calculator.
Real power: 14.12 kW
Apparent power: 16.62 kVA
What is three-phase power?
Three-phase power delivers electricity through three conductors, each carrying an alternating current 120° out of phase with the others. Commercial and industrial facilities use three-phase systems because they deliver more power with less conductor material and provide smoother torque for large motors compared to single-phase.
The √3 constant (approximately 1.732) appears in every three-phase power formula. It accounts for the vector relationship between the three phase voltages and is the key difference from single-phase math. You cannot simply multiply single-phase power by 3, the correct multiplier is √3 ≈ 1.732.
Common three-phase voltages in North America are 208V (120/208V wye system), 480V (277/480V wye for industrial), and 240V (delta systems). In Europe and the UK, 400V (230/400V wye) is standard. Always enter the line-to-line (phase-to-phase) voltage in this calculator.
- Line-to-line voltage (V): voltage measured between any two of the three phase conductors
- Phase current (A): current flowing through each phase conductor under load
- Power factor (PF): ratio of real to apparent power, typically 0.80–0.95 for industrial motors
- The √3 constant (≈ 1.732): always used in balanced three-phase power calculations
For motors and industrial equipment, use the nameplate PF or default to 0.85. Verify all final designs with a licensed electrical engineer.
How to convert
Real power (kW)
Real power is the actual work done, what motors convert to mechanical output and heaters convert to heat.
P (W) = √3 × V_L × I × PF
P (kW) = (1.732 × V_L × I × PF) / 1000
Apparent power (kVA)
Apparent power is what the utility and transformers must supply. Use it to size transformers, generators, and conductors.
S (VA) = √3 × V_L × I
S (kVA) = (1.732 × V_L × I) / 1000
Rearranged, current from known power
To find current when real power (kW) and voltage are known, rearrange the formula.
I = P / (√3 × V_L × PF)
I = (kW × 1000) / (1.732 × V_L × PF)
Worked examples
Question: What is the real power of a 30A load at 480V three-phase with PF = 0.85?
Solution: P = 1.732 × 480 × 30 × 0.85 = 21,183 W ≈ 21.2 kW
Question: A 208V three-phase panel feeds a 25A balanced load at PF = 0.90. What is apparent power?
Solution: S = 1.732 × 208 × 25 = 9,006 VA ≈ 9.0 kVA
Question: A 15 kW three-phase load runs on 480V at PF = 0.88. What current does it draw?
Solution: I = 15,000 / (1.732 × 480 × 0.88) = 15,000 / 731 ≈ 20.5 A
Common mistakes and notes
- Always enter line-to-line voltage, not line-to-neutral (phase) voltage.
- This calculator assumes a balanced load. For unbalanced three-phase loads, calculate each phase separately.
- Motor nameplate kW or HP ratings are output ratings, input power is higher due to motor efficiency losses.
- NEC continuous load rule: conductors and breakers must be sized at 125% of continuous current.
Assumptions
- Balanced three-phase load assumed, all three phases carry equal current.
- Line-to-line voltage is used (not line-to-neutral).
- Results are planning estimates only, verify against nameplate ratings and applicable code.
Worked example
Example: 1.732 × 480 V × 20 A × 0.85 PF = 14,123 W ≈ 14.1 kW real power.
FAQ
Why does three-phase use √3 (1.732) in the formula?
In a balanced three-phase system the three voltages are 120° apart. The √3 factor comes from the vector sum of the phase voltages and represents the mathematical relationship between line voltage and phase voltage in a wye (star) system. It is a fixed constant, always approximately 1.732.
What voltage do I enter, line or phase voltage?
Enter the line-to-line (line) voltage. For a 120/208V wye system, use 208V. For a 277/480V system, use 480V. The line-to-neutral (phase) voltage is lower by a factor of √3 (so 480 ÷ 1.732 ≈ 277V).
What power factor should I use for three-phase loads?
Use 0.85 for general commercial and industrial planning. Induction motors typically run at 0.80–0.92 depending on load level. Resistive heating elements use PF = 1.0. Variable frequency drives (VFDs) often have a high PF because they include built-in power factor correction.
How does three-phase power compare to single-phase?
Three-phase delivers √3 (≈ 1.732) times more power than single-phase at the same line voltage and current. This is why large motors and industrial equipment use three-phase, significantly more power without proportionally more conductor material.
Can I use this to size a transformer?
Use the apparent power (kVA) result as your starting point for transformer sizing, transformers are rated in kVA. Add a safety margin of 20–25% above the calculated load and verify the final selection with a licensed electrical engineer.
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⚠️ Sanity Check Only
This tool provides informational estimates only. It is not professional engineering advice. Electrical work is dangerous and governed by strict local codes.
Before you start:
- Verify these results with a licensed electrician.
- Cross-reference with the latest Electrical Code (NEC/CEC).
- Never work on live circuits.