Three-Phase kW Calculator
Three-phase real-power calculator using the √3 formula. Supports line-to-line voltages (208 V, 400 V, 480 V) and power factor.
Common conversions
| Input | Result |
|---|---|
| 20 A @ 208 V (PF 0.9) small pump | 6.48 kW |
| 50 A @ 400 V (PF 0.88) European motor | 30.48 kW |
| 124 A @ 460 V (PF 0.87) 100 HP motor | 85.95 kW |
| 60 A @ 480 V (PF 0.9) rooftop HVAC unit | 44.89 kW |
| 80 A @ 600 V (PF 0.85) industrial feeder | 70.67 kW |
| 150 A @ 480 V (PF 0.92) standby generator | 114.73 kW |
| 35 A @ 208 V (PF 0.98) data centre PDU | 12.36 kW |
| 10 A @ 400 V (PF 0.95) small compressor | 6.58 kW |
The math behind it
- kW = (√3 × V × A × PF) / 1000
- kW = (1.7321 × 460 × 124 × 0.87) / 1000
- kW = 85,953 / 1000
Everything you need to know
Three-phase power runs nearly every motor, chiller, and large panel in commercial and industrial buildings. This page covers the full picture: how the windings that generate three-phase power are wired, why the √3 factor appears in the math at all, and how the formula plays out on real equipment.
How delta and wye windings produce three-phase power
A three-phase source, whether a generator or a transformer secondary, has three windings. In a wye (star) connection, one end of each winding joins at a common center point, which becomes the system neutral, and the other end of each winding runs out as a line conductor. Line-to-line voltage is √3 times the winding (phase) voltage, while line current equals winding current. This is how 208Y/120 V, 480Y/277 V, and 600Y/347 V services get their dual voltage labels, both a phase and a line voltage from the same source. In a delta connection, the three windings are joined end-to-end in a closed triangle, with a line conductor tapped from each junction. Here line-to-line voltage equals the winding voltage directly, while line current is √3 times the winding current. Delta sources have no natural center point, so standard delta service has no usable line-to-neutral voltage. Utility primary distribution is frequently delta, then stepped down through a delta-to-wye transformer bank to create the wye service most commercial buildings receive.
Deriving the √3 factor from three sinusoidal phases
Three-phase generation produces three voltage waveforms of equal magnitude, each shifted 120° from the next: Va, Vb, and Vc. The line-to-line voltage between any two phases, say Vab, is the vector difference Va minus Vb. Because the two phase voltages are equal in length and 120° apart, that difference forms an isosceles triangle, and the law of cosines reduces it to |Vab| = 2 × Vphase × sin(60°), which simplifies to √3 × Vphase. That single geometric fact, two equal vectors 120° apart subtracting to √3 times their length, is where every √3 in three-phase math comes from. Total power delivered by all three phases together is always 3 × Vphase × Iphase × PF, regardless of whether the source is wye or delta. Substituting each connection's own relationship between phase and line quantities, both wye and delta reduce that same expression down to the identical line-based formula: kW = √3 × Vline × Iline × PF / 1000. That's why one formula and one calculator handle both winding types as long as you enter line-to-line voltage and line current.
Sizing real three-phase equipment
A 100 HP, 460 V wye-connected induction motor with a nameplate full-load current of 124 A and PF 0.87 draws about 85.95 kW of real input power, of which roughly 74.6 kW (100 HP) becomes usable shaft output after motor losses. A rooftop HVAC unit pulling 60 A per line at 480 V and PF 0.9 draws about 44.89 kW, a number facility engineers use directly against the building's electrical service capacity. A balanced data-center power distribution unit on a 208Y/120 V panel carrying 35 A per phase at PF 0.98 delivers about 12.36 kW to the racks it feeds, and comparing that figure against the panel's rated capacity is standard practice before adding another rack. In every case the same √3 × V × A × PF formula applies; only the nameplate current, voltage, and power factor change.
Common applications
Most motors above 10 HP are three-phase. Convert nameplate kW or FLA to per-phase current to choose overload protection and conductor sizes.
Rooftop units, chillers, and elevator drives almost always run from 208 V or 480 V three-phase. The √3 formula sets feeder ampacity.
Modern racks balance phases across A/B/C. Sum kW per phase, multiply by √3 × V × PF to confirm the upstream breaker has headroom.
Utility-scale inverters are three-phase at 480 V. Tracking kW per phase is the standard way to catch unbalance before it trips a string.
Common mistakes
Use √3 (≈1.732) with line-to-line voltage. Use 3 only with line-to-neutral (phase) voltage. Swapping them gives a 73% error.
The √3 formula assumes a balanced load. With imbalance, compute each phase separately or you'll undersize the most-loaded conductor.
208 V wye-derived circuits look like residential 240 V but deliver 13% less power for the same current, so heater wattage and motor torque both drop.
Wye panels have a true neutral; delta panels generally don't. Trying to pull a 120 V circuit from a standard delta panel without a center-tapped winding simply won't work.
Background and theory
In a balanced three-phase system the instantaneous power is constant (not pulsating as in single-phase), which is why motors run smoother and conductors carry less copper for the same delivered power. That constant-power property comes from the geometric sum: three sinusoids 120° apart, each multiplied by a current 120° apart, sum to a DC value. The √3 factor (and its inverse 1/√3 ≈ 0.577) appears throughout three-phase math, in delta-to-wye transformer ratios, in symmetrical-component analysis, and in fault-current calculations.
When you compare a 1-phase 240 V circuit to a 3-phase 208 V circuit at the same current, three-phase delivers √3 × 208 / 240 ≈ 1.50× the power. That's why commercial buildings prefer 208/480 V three-phase even though the line-to-neutral voltage is lower than residential.
Frequently asked questions
Why does three-phase math use √3 instead of 3?+
Because line-to-line voltage is the vector difference of two phase voltages 120° apart, not their simple sum. That geometric subtraction reduces to √3 (about 1.732) times the phase voltage, not 3 times it.
What's the difference between wye and delta three-phase wiring?+
Wye connects all three windings to a common neutral point, giving both a line and a phase voltage. Delta joins the windings in a closed loop with no neutral point, so only one voltage is available.
Is three-phase power available in ordinary homes?+
No, most residential services are single-phase. Three-phase is typically reserved for commercial, industrial, and agricultural sites with large motor or HVAC loads.
Why do industrial facilities prefer three-phase over single-phase?+
Three-phase delivers constant instantaneous power instead of a pulsing waveform, lets motors self-start without extra circuitry, and carries the same power with less conductor copper than an equivalent single-phase run.
How many amps does a 100 kW three-phase load draw at 480 V?+
About 130.7 A per line at PF 0.92, from A = (100,000) / (√3 × 480 × 0.92).
Do I use a motor's nameplate kW or its electrical input kW for sizing?+
Use input kW, not shaft output kW. Divide the nameplate (shaft output) kW by the motor's efficiency, typically 0.88 to 0.96, to get the actual three-phase electrical draw.
Which voltage do I use on a 208Y/120 V panel?+
Use 208 V with the √3 formula for three-phase loads connected across all three lines, and 120 V with the single-phase formula for branch circuits tapped from one line to neutral.
Can three-phase power be created from a single-phase supply?+
Yes, a rotary phase converter or a variable frequency drive can generate three-phase output from single-phase input, a common fix for shops without three-phase utility service.
Does three-phase wiring really save copper compared to single-phase?+
Yes, roughly 25% less. Delivering the same power over three smaller conductors uses less conductor material than the two larger conductors a single-phase circuit would need at the same voltage class.
Is a generator's three-phase kW rating based on line-to-line or line-to-neutral values?+
The nameplate kW is the total real power across all three phases combined. This calculator gets you there directly from line-to-line voltage and per-line current.