Three-Phase Power Calculator — The √3 Math
Every three-phase calculation carries a √3 ≈ 1.732, and it is there because the three phases sit 120° apart. The practical consequence is that three-phase moves the same power with about 42% less line current than single-phase at the same voltage. Work from a load in kW, from a measured line current, or from motor horsepower with efficiency.
Solve a three-phase system
Line-to-line
Motor mode only
Line current
Single-phase at the same voltage would draw far more.
Real power
50.00 kW
Apparent power
58.82 kVA
See the breakdown
Assumes a balanced load. Motor branch circuits must be sized from NEC Table 430.250 full-load currents, not from these figures.
The formula, explained in plain English
Use line-to-line voltage
The √3 already handles the phase relationship. Entering 277 V instead of 480 V on a 480 V system will give an answer 42% too low.
Balanced loads only
These formulas assume equal current in all three lines. Unbalanced panels need per-phase analysis, and high-leg delta systems have a 208 V leg that can't serve 120 V loads.
Worked examples
A load, a measurement, and a motor.
50 kW at 480 V, PF 0.85
The defaults above.
kVA = 50 ÷ 0.85 = 58.82 kVA · kVAR = 30.99 kVAR
single-phase at 480 V would be 122.5 A — 42% more
Result: 70.75 A lands on 4 AWG copper; the single-phase equivalent would need 1/0. Across a whole building that difference is the commercial case for three-phase service.
Measured 85 A at 208 V, PF 0.9
A clamp-meter reading on a commercial panel feeder.
kVA = 1.732 × 208 × 85 ÷ 1,000 = 30.62 kVA
kVAR = √(30.62² − 27.56²) = 13.35 kVAR
Result: a 30.6 kVA existing load. Compare this against the panel's rating to find real spare capacity — measured demand beats an estimated calculation every time.
25 hp motor at 480 V, 92% efficient, PF 0.87
Motor output mode.
I = 20,264 ÷ (1.732 × 480 × 0.87) = 28.02 A
NEC Table 430.250 for 25 hp at 460 V: 34 A ← use this
Result: the calculation gives 28 A but the Code table says 34 A, and the table governs per NEC 430.6(A)(1). This is exactly why motor circuits are never sized from arithmetic — the tables carry deliberate margin, and an inspector will check against them.
Line amps per kW, three-phase
Multiply your load in kW by the figure below to get line current. A quick field shortcut that replaces the √3 arithmetic.
| Line voltage | PF 0.80 | PF 0.85 | PF 0.90 | PF 1.00 |
|---|---|---|---|---|
| 208 V | 3.470 A/kW | 3.266 A/kW | 3.084 A/kW | 2.776 A/kW |
| 240 V | 3.007 A/kW | 2.830 A/kW | 2.673 A/kW | 2.406 A/kW |
| 480 V | 1.504 A/kW | 1.415 A/kW | 1.336 A/kW | 1.203 A/kW |
| 600 V | 1.203 A/kW | 1.132 A/kW | 1.069 A/kW | 0.962 A/kW |
Sources & standards: √3 = 1.7321; 1 hp = 745.7 W. NEC (NFPA 70) 2023 — 430.6(A)(1) and Table 430.250 for three-phase motor full-load currents, Article 430 motor circuits, Table 310.16 conductor ampacities, 220.61 neutral load. Formulas assume a balanced three-phase load. Local amendments override the model code.
Frequently asked questions
Common questions about three-phase power, √3, and motor circuits.
What is the three-phase power formula?
P = √3 × V × I × PF for real power, and rearranged, I = P ÷ (√3 × V × PF) for line current. V is the line-to-line voltage. So a 50 kW load at 480 V with 0.85 power factor draws 50,000 ÷ (1.732 × 480 × 0.85) = 70.75 amps per line.
Why is there a √3 in three-phase calculations?
Because the three phase voltages are 120° apart. The line-to-line voltage is √3 times the line-to-neutral voltage — 480 V line-to-line corresponds to 277 V to neutral, and 208 V corresponds to 120 V. When you express power in terms of line-to-line voltage and line current, that geometric relationship shows up as the √3 ≈ 1.732 factor.
How much current does three-phase save?
About 42% compared with single-phase at the same voltage and power. A 50 kW load at 480 V draws 70.75 A three-phase but would draw 122.5 A single-phase. Less current means smaller conductors, less voltage drop, and less I²R heat — which is why every commercial and industrial building of any size is three-phase.
Do I use line voltage or phase voltage?
Line-to-line voltage — the value the system is named for: 208 V, 240 V, 480 V, 600 V. The √3 in the formula already accounts for the relationship to phase voltage. Using 277 V (the line-to-neutral value of a 480 V system) with the √3 formula will give an answer about 42% too low.
How do I calculate current from motor horsepower?
Set the mode above to motor output and enter the horsepower plus efficiency. Horsepower is shaft output, so input power is higher: kW = hp × 0.7457 ÷ efficiency. But for actual circuit design, NEC 430.6(A)(1) requires you to use the full-load current from Table 430.250 instead of any calculation — the table values are deliberately conservative and are what an inspector will check against.
Does this work for unbalanced or wild-leg systems?
No. These formulas assume a balanced three-phase load — equal current in all three lines. Unbalanced loads need per-phase analysis, and a 240/120 V high-leg delta ("wild leg") system has one phase at 208 V to neutral that cannot serve 120 V loads at all. For unbalanced panels, calculate each phase separately and size for the worst one.
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