Three-Phase Power Formulas

Three-phase power is the standard way electricity is distributed to commercial and industrial equipment because it delivers more usable power per amp of wire than single-phase. The math uses either line-to-line voltage with a √3 factor or line-to-neutral voltage with a factor of 3, and both forms give the same answer because V_LL = √3 × V_LN. This page covers both formulas and shows how the same load looks on 208V, 240V, 480V, and 120V legs.

Formulas

P = √3 × V_L-L × I × PF

P = 3 × V_L-N × I × PF

V_L-L = √3 × V_L-N

Three-phase power uses three AC waveforms offset by 120 degrees. The √3 factor (1.732) appears because of the geometric relationship between line-to-line and line-to-neutral voltages. Three-phase delivers more power per amp than single-phase, meaning smaller wire and lower losses for the same power output.

Worked Examples

Example 1: 10kW motor at 208V (3-phase, PF 0.85)

I = 10000 / (1.732 × 0.85 × 208) = 10000 / 306.3 = 32.65A per line

Example 2: Same 10kW at 480V (3-phase, PF 0.85)

I = 10000 / (1.732 × 0.85 × 480) = 10000 / 706.9 = 14.15A per line

Example 3: 208V line-to-line to line-to-neutral

V_L-N = 208 / 1.732 = 120V (this is why 208/120V panels exist)

Common Mistakes

Using single-phase formula for three-phase circuits. Current is 1.732x lower than single-phase at the same power.
Confusing line-to-line and line-to-neutral voltage. Using the wrong one changes the result by √3.
Assuming 240V three-phase is the same as 240V single-phase. Three-phase 240V has different current draw.

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This is a formula reference page for educational use. Always consult a licensed electrician and verify compliance with the National Electrical Code (NEC) and local electrical codes before applying any of these formulas to real installations.

Standards & References

This page cites the following electrical codes and standards. Always consult the current edition of your local adopted standard for authoritative requirements.

IEC 60038. IEC standard voltages. Defines 230/400V as the nominal low-voltage supply for 50Hz systems, which harmonized European residential supply in 1995.
International Electrotechnical Commission. Reference →
ANSI C84.1. American National Standard for Electric Power Systems and Equipment: Voltage Ratings (60 Hz). Defines the nominal system voltages (120, 208, 240, 277, 480V) and their allowable ranges at the service entrance and utilization point.
American National Standards Institute / NEMA. Reference →
NEC Table 310.16. Allowable ampacities of insulated conductors rated up to 2000V, 60°C through 90°C, not more than three current-carrying conductors in raceway or cable.
National Electrical Code (NFPA 70), Article 310, Conductors for General Wiring. Reference →

Disclaimer: The information on this page is provided for reference. Always consult a licensed electrician and the current edition of your local adopted electrical code before performing electrical work.