Use matching phase data
This model is for three-phase, four-wire wye with an intact neutral. Supply phase-current magnitudes and displacement angles for one simultaneous steady operating condition, using balanced line-neutral voltage references 120° apart. Phase sequence defines their order. Each PF is relative to its own phase voltage; leading current is ahead of that voltage and lagging current is behind it.
A zero-current phase contributes no vector and has no defined current angle, so its PF and direction are unused. For a nonzero phase at PF 1, either displacement choice gives zero displacement. PF 0 represents a purely reactive sinusoidal current; it does not mean zero current.
The PF 0–1 input model represents non-negative real power into loads. Export and regenerative current require reverse-power phasors and are outside this tool. Verify the meter's PF and sign convention before interpreting its values.
Do not combine unrelated clamp readings, nameplate maxima or different operating times as simultaneous phasors. For distorted current, a meter's total RMS and true PF are insufficient to establish the fundamental current vector. Harmonic spectra or suitable power-quality analysis are a different model.
Sum current vectors, not their magnitudes
Set phase A voltage to 0°. For A–B–C, B and C voltages are −120° and +120°; for C–B–A they are +120° and −120°. Each current angle is its voltage angle plus acos(PF) for leading current, or minus acos(PF) for lagging current.
Convert each phase current into rectangular components: I × cos(angle) and I × sin(angle). Add the three real components and the three imaginary components. Neutral magnitude is √(real sum² + imaginary sum²). Reversing the neutral return reference reverses its vector direction but leaves this magnitude unchanged. The preview shows the phase-current sum from a common origin.
The mean magnitude is (IA + IB + IC) / 3. Maximum magnitude deviation is 100 × max(|IA − mean|, |IB − mean|, |IC − mean|) / mean. This describes the entered magnitudes only. It is undefined when all currents are zero and supplies no code or equipment tolerance.
The calculation normalizes magnitudes and groups equivalent component differences to retain precision and exact cancellation for identical phase data. It does not clamp small unequal residuals to zero. Outputs use unrounded arithmetic, with three decimals or scientific notation for display.
Worked examples
With A–B–C, phase currents of 12 A, 10 A and 6 A at unity PF sum to 4 − j3.464101615 A. Neutral magnitude is √28 = 5.291502622 A, displayed as 5.292 A. The mean is 9.333 A and maximum magnitude deviation is 35.714%. The BC training guide prints a rounded 5.3 A; this tool retains intermediate precision.
Equal 10 A magnitudes can give another result: A at PF 1, B at PF 0.5 leading and C at PF 0.5 lagging. With A–B–C, current angles are 0°, −60° and +60°, whose sum is 20 A. Magnitude deviation is still 0%. With the reversed sequence, the same local displacements produce a 10 A neutral magnitude. These are hypothetical sinusoidal examples, not equipment readings.
Two loaded phases of a wye supply are also different from a split-phase circuit. At unity PF, 10 A on A, 10 A on B and 0 A on C give a 10 A neutral magnitude. Subtracting the two equal scalar readings would give the wrong result.
What the result cannot establish
Electronic loads can create harmonic currents. The CEATI power-quality guide explains that third-harmonic components from different phases can add in the neutral. The present sine-wave calculation does not estimate those components, so it cannot establish actual total neutral RMS or heating for a nonlinear load.
Open or floating neutrals, unequal voltage phase displacement, delta systems, 180° split-phase systems, earth/bonding paths, faults and transients are outside this model. No neutral/conductor size, protection, phase reassignment plan, motor limit or jurisdictional acceptance is calculated.
For power/current conversion under its separate balanced assumptions, use the AC electrical calculator. The connected load calculator totals a common-PF load group; it does not determine unbalanced phase angles.
Common questions
Do three equal current readings guarantee zero neutral current?
No. This model also needs the current angles. Equal magnitudes with unequal displacement can produce a nonzero sum. Harmonics require additional waveform information.
Can I enter 80 for an 80% power factor?
No. Enter 0.8. The leading/lagging choice defines the angle's direction relative to that phase's own voltage.
Is a 0% magnitude deviation a pass?
No. It states only that the entered phase-current magnitudes are equal. It does not establish neutral current, equipment suitability or compliance.
Related tools
Sources and scope
BC Industry Training Authority, Level 3, D-5: Analyze Three-Phase Circuits, version 1, new October 2012, corrected June 2016: printed/PDF page 13 for phase sequence, pages 53–57 for neutral phasor addition and page 73 for sinusoidal PF. The general unequal-PF method combines that per-phase relationship with vector addition; it does not apply the resistive example's magnitude-only shortcut to arbitrary angles.
CEA Technologies Inc. (CEATI), Power Quality Reference Guide, copyright 2007, hosted by Hydro One, printed/PDF page 50: third-harmonic addition in the neutral. Both originals checked November 10, 2026. These dated physical references are not a current Canadian wiring-code approval.
Inputs and results stay in this page and are not saved or transmitted. Report a problem or suggest a source; values are not attached automatically.