Three Phase Power Calculator
The √3 arithmetic — line volts × line amps × √3 is the kVA, and the power factor splits it into work and burden.
Three Phase Power Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Balanced system — no unbalance or harmonics modeled
- Line quantities only; delta/wye internal details folded into √3
In short: 480 V line-to-line at 20 A three-phase carries 16.627688 kVA; at an 0.85 power factor that is 14.133535 kW of real work. √3 is the whole trick: three phases 120° apart share one magnetic cycle, and the line quantities multiply by 1.732 instead of 3. Each leg sits at 277.128129 V to neutral — the 277 V lighting voltage hiding inside every 480 V system.
Formula
S = √3 × V_LL × I; P = S × PF; V_leg = V_LL ÷ √3
Three balanced phases deliver √3 times the product of line voltage and line current in apparent power: S = √3 · V · I. The power factor splits S into real work P and reactive burden Q = √(S²−P²). Each leg sees the line voltage over √3 to neutral — which is why a 480 V system powers 277 V lighting and a 208 V system powers 120 V receptacles from the same transformer.
Worked Example
- Enter the line-to-line voltage and the per-line current.
- Enter the load's power factor.
- Read the kVA, the real kW, and the leg voltage to neutral.
Defaults: 14.133535 kW at 0.85. Drive the power factor to 95% and the SAME 20 A delivers 15.796303 kW — 1.66 kW of extra work for no extra copper, which is the power factor page's whole sales pitch.
Strengths & Limits Of This Model
Where this engine is strong
- kVA, kW and kvar all named — the triangle complete
- The leg voltage printed — the hidden 277 V, surfaced
Where it stops
- Unbalanced or harmonic loads need per-phase measurement
Practical Use Cases
Panel schedules
kVA per breaker, √3 style
Motor feeds
the amps a motor really draws
Service sizing
the demand the utility sees
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Three Phase Power Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does √3 appear?
Because power in a balanced three-phase system is three times one phase's power, and the line quantities relate to phase quantities by √3. The two √3's fold into one factor: S = √3 · V_line · I_line. It is geometry, not a fudge — 120° of separation, phasor-summed.
What is 277 V doing inside a 480 V system?
Each leg sits at the line voltage divided by √3 from neutral: 480 ÷ 1.732 = 277.128129 V. Ballast and LED drivers ride that leg voltage; it is the same transformer serving both numbers.
How do I get kW from kVA?
Multiply by the power factor: 16.627688 kVA at 0.85 is 14.133535 kW. The missing share — 8.759178 kvar here — sloshes in and out of the magnetic fields every half cycle, doing no work but heating the copper all the same.
Does three phase save copper?
Yes — that is its founding reason. Three phases deliver √3 times the power of a single phase on the same conductor metal (and the same voltage drop discipline), plus motors get a self-starting rotating field for free.
What if the phases are unbalanced?
This arithmetic assumes balance. Unbalance means each leg needs its own current math, motors heat from negative-sequence components, and the neutral starts carrying current it was promised it never would.
Why do motors prefer three phase?
Because the three legs already make a rotating magnetic field — the motor's stator just follows it. Single-phase motors must manufacture the rotation with start capacitors and switch tricks; the three-phase motor has no such parts.
Is 208 V the same math?
Identical: √3 × 208 × I. The leg voltage reads 120.088856 V — which is why a 208 V panel powers ordinary 120 V receptacles leg-to-neutral. Change the numbers, never the formula.
How does this page differ from the transformer page?
That page trades volts for amps across a ratio; this one prices what a service carries at a given voltage and current. They meet at the kVA — the transformer's copper knows no other unit.