3-Phase Power Calculator — Free Online Calculator
Calculate three-phase power, line voltage, phase voltage, and current for wye and delta configurations.
How to Use This Calculator
Select wye or delta configuration, enter line voltage and line current, and power factor.
The Formula Explained
Three-phase total power: P = √3 × V_L × I_L × PF. In wye: V_phase = V_line/√3, I_phase = I_line. In delta: V_phase = V_line, I_phase = I_line/√3.
Three-Phase Power: The Workhorse of Industry
Three-phase power is the dominant electrical distribution method for anything beyond small residential loads. The magic of three-phase is that three sinusoidal currents 120 degrees out of phase combine to deliver nearly constant instantaneous power — unlike single-phase which pulses at twice the line frequency. This makes three-phase ideal for motors (smooth torque, no pulsation) and efficient for distribution (smaller wires for the same power). Commercial buildings, industrial plants, and utility distribution all use three-phase.
The math requires understanding the relationship between single-phase and three-phase quantities. For the same power delivery, three-phase current per phase is 1/sqrt(3) = 57.7% of the equivalent single-phase current. A 60 kW load at 240V draws 250A single-phase but only 144A per phase on three-phase — much smaller wire for the same delivered power. This is why utilities distribute at three-phase medium voltage even though residential loads typically use just one phase. Three-phase transformers split into single-phase services at the neighborhood level.
Worked Example: Commercial HVAC Load
A commercial building has a 20-ton rooftop HVAC unit rated 25 kW at 480V three-phase, power factor 0.88. Calculate current draw and wire/breaker sizing.
Apparent power: kVA = kW / PF = 25 / 0.88 = 28.4 kVA. Current: I = kVA × 1000 / (sqrt(3) × V_LL) = 28,400 / (1.732 × 480) = 34.2 amps per phase.
Circuit sizing (continuous load per NEC 215.2(A)(1) — HVAC operates more than 3 hours, so 125% applies): 34.2 × 1.25 = 42.75 amps. Conductor: 8 AWG copper (50A at 75°C). Breaker: 45A or 50A (next standard size per NEC 240.6).
For comparison, the same 25 kW at 208V three-phase: current = 25,000 / 0.88 / (1.732 × 208) = 79 amps per phase. Requires 3 AWG copper and 100A breaker. The 480V version uses much smaller wire — 8 AWG vs 3 AWG — cutting conduit and conductor costs by about 60% for the same power delivery.
Worked Example: Three-Phase Motor Starting
A 50 HP three-phase 460V motor has FLA 65A (NEC Table 430.250), efficiency 93%, PF 0.87 at full load. Starting current (code letter G) is about 6x FLA = 390A for 1-3 seconds.
Running power: P = sqrt(3) × 460 × 65 × 0.87 / 1000 = 45.1 kW real, 51.8 kVA apparent. Mechanical output: 50 HP × 0.746 = 37.3 kW. Efficiency check: 37.3 / 45.1 = 82.7% — below the 93% nameplate, suggesting the motor might be operating at partial load or the efficiency spec is for a different condition.
Starting kVA: sqrt(3) × 460 × 390 / 1000 = 310 kVA. This is far above the running 52 kVA — the starting surge lasts only a few seconds but stresses the distribution system. Upstream transformer must handle 310 kVA instantaneous without excessive voltage sag. Typical: the service transformer should be at least 3x the motor starting kVA for well-behaved starting, or 1,000 kVA transformer for this 50 HP motor. Smaller transformers cause voltage sag affecting other loads during motor start.
Three-Phase Calculation Mistakes
1. Forgetting the sqrt(3) factor. The single most common error. Three-phase power formula requires 1.732, missing it gives 73% low results.
2. Using wrong voltage. Three-phase formulas use line-to-line voltage (V_LL). On a 480Y/277V system, use 480V not 277V. On 208Y/120V, use 208V not 120V.
3. Mixing delta and wye formulas. In delta, line current = sqrt(3) × phase current, and phase voltage = line voltage. In wye, line current = phase current, and line voltage = sqrt(3) × phase voltage. The power formula is the same, but phase quantities differ.
4. Unbalanced loads. The sqrt(3) formula assumes balanced three-phase. If one phase carries significantly more current than others, calculations must be done per-phase. Neutral current in unbalanced wye systems can approach line current — sometimes exceeding it with harmonic loads.
5. Ignoring zero sequence on harmonics. Non-linear loads (LED drivers, VFDs) produce triplen harmonics (3rd, 9th, 15th...) that add in the neutral rather than canceling. Three-phase neutrals on computer loads can carry 173% of phase current due to triplen harmonic accumulation.
Three-Phase Formula Quick Reference
Balanced three-phase power:
P (kW) = sqrt(3) × V_LL × I × PF / 1000.
S (kVA) = sqrt(3) × V_LL × I / 1000.
Q (kVAR) = sqrt(3) × V_LL × I × sin(phi) / 1000.
Current from power:
I (amps) = kW × 1000 / (sqrt(3) × V_LL × PF).
I (amps) = kVA × 1000 / (sqrt(3) × V_LL).
Common voltage systems:
208Y/120V: Small commercial, 208V line-to-line, 120V line-to-neutral.
480Y/277V: Commercial/industrial, 480V line-to-line, 277V for lighting.
600V: Canadian commercial standard.
240V delta: Older industrial, some residential well pumps.
480V delta: Pure motor loads, rarely in new construction.
4,160V: Medium voltage for large motors and industrial distribution.
13,800V: Utility primary distribution, very large facilities.
NEC and Standards
NEC 430 — Motor circuits including three-phase motor sizing and protection. NEC 220 — Load calculations with three-phase formulas. NEC 450 — Transformer installation with phase configuration requirements. ANSI C84.1 — Voltage standards including nominal voltages and tolerance ranges for three-phase systems.
Three-phase power: P = sqrt(3) x V x I x PF explained
Three-phase power is the standard for industrial and commercial distribution because it delivers more power per conductor than single-phase, runs motors more smoothly, and balances loads across three lines. The calculator handles both line-to-line voltage (the standard way 3-phase is described) and computes apparent power (kVA), real power (kW), and line current.
The formula and what it does
V_LL is line-to-line voltage (208, 240, 480, 600). I_line is the current measured on any one of the three phase conductors. sqrt(3) is approximately 1.732 and accounts for the geometric relationship of three voltage phases offset by 120 degrees. PF is the power factor of the load.
Worked example
Scenario: 50 hp motor on 480 V 3-phase, FLA = 65 A from NEC 430.250, PF 0.88 at full load.
Apparent power: S = 1.732 x 480 x 65 = 54,019 VA = 54 kVA. Real power: P = 54 x 0.88 = 47.5 kW. Mechanical output at 91 percent motor efficiency: 47.5 x 0.91 = 43.2 kW = 57.9 hp shaft. That is higher than 50 hp nameplate, suggesting the motor is rated 50 hp at lower-than-FLA operating point, or service factor allows brief overrun. NEC Table 430.250 is conservative; actual motor draw varies by load.
Common mistakes to avoid
undefinedFrequently asked questions
Why does three-phase need three wires instead of six?
Each phase shares a common return through the other two phases (or a neutral on wye systems). Total current sums geometrically to zero with balanced load, so no return conductor needed in balanced 3-phase delta systems.
What is the difference between delta and wye?
Delta connects three phases in a triangle (no neutral). Wye connects three phases to a common center point (neutral available). Delta is common for high-voltage distribution and motors; wye for distribution to mixed 3-phase and single-phase loads.
Can I get single-phase from three-phase?
Yes, any two phases gives single-phase. From wye-connected system you can also get phase-to-neutral. Common configuration: 208Y/120 gives 208 3-phase to motors and 120 V single-phase to outlets.
Why does my residential service look different?
Residential US service is single-phase three-wire (two hots and a neutral, 240 V between hots and 120 V each to neutral). This is single-phase split-phase, not three-phase. Commercial buildings typically have 208Y/120 V or 480Y/277 V 3-phase service.
What is high-leg delta?
240 V three-phase delta with a center-tapped phase that gives 120 V to neutral. The third phase ("wild leg" or "high leg") sits 208 V from neutral. Legacy systems mostly. Modern installs use 208Y/120 wye instead.
How is power factor measured on 3-phase?
PF analyzer measures phase relationship between voltage and current. Total system PF is sum of per-phase real power divided by sum of per-phase apparent power. Balanced 3-phase systems: PF is the same on each phase.