Three-phase circuit tool
Three-phase delta–wye calculator
Convert balanced three-phase line and phase voltage or current for wye and delta connections. The calculator also reports total and per-phase apparent power using the same electrical quantities.
Wye values
Line voltage
400 V
Measured line to line
Phase voltage
230.9401 V
Line to neutral
Line current
10 A
Phase current
10 A
Current through one load branch
Total apparent power
6.9282 kVA
√3 × VL × IL
Per-phase apparent power
2.3094 kVA
Vφ × Iφ
Balanced-system result
These relationships assume three equal phase magnitudes separated by 120°. They do not model an unbalanced load or neutral current.
Wye (Y) relationship
Balanced three-phase reference; phasors are separated by 120°.
VL = √3 × Vφ · IL = Iφ
How to use the delta–wye calculator
Identify the actual load connection and whether your known values are measured at the line terminals or across one phase branch.
- 01
Choose the winding connection
Select wye when three branches meet at a common star point, or delta when the three branches form a closed loop.
- 02
Choose line or phase values
Line voltage is measured between line conductors. Phase voltage is measured across one load branch; line and phase currents are defined in the same way.
- 03
Review all four electrical quantities
Compare the converted line and phase values with the connection diagram, then verify the nameplate and actual wiring before applying the result.
Balanced delta and wye relationships
These equations apply to symmetrical three-phase voltages and equal phase loads separated by 120 electrical degrees.
Wye voltage
VL = √3 × Vφ
Wye current
IL = Iφ
Delta voltage
VL = Vφ
Delta current
IL = √3 × Iφ
Total apparent power
S = √3 × VL × IL = 3 × Vφ × Iφ
In a balanced wye connection, each phase branch is connected from a line conductor to the common star point, so line voltage is the vector difference between two phase voltages. In a balanced delta connection, each branch is directly across two line conductors, while line current is the vector difference between two branch currents.
Do not use the ideal square-root-of-three relationships to diagnose an unbalanced, open-phase, high-leg, grounded-corner or distorted system. Confirm the actual transformer and load connection, phase sequence, grounding arrangement and measurement reference. De-energize equipment and follow applicable electrical safety procedures before inspecting or changing wiring.
Checks before using the converted values
The calculator describes an ideal balanced connection; field systems may require additional measurements and protection checks.
Confirm the system is balanced
Unequal phase impedances or source voltages produce different branch currents and invalidate a single-value balanced conversion.
Confirm the measurement reference
Do not treat line-to-line voltage as line-to-neutral voltage. Confirm where the meter probes and current sensor are connected.
Identify the neutral arrangement
A wye point may be grounded, isolated or not brought out. Delta systems can also have special grounded or center-tapped arrangements.
Check the equipment nameplate
Motor and transformer nameplates may specify allowable delta or wye voltages and connection links. A mathematical conversion does not authorize rewiring.
Verify protection and conductor ratings
Current, grounding, fault protection, insulation and conductor sizing must be checked against the governing code and manufacturer data.
Delta–wye calculator questions
What is the difference between line and phase values?
Line values are measured at the external line conductors. Phase values apply across or through one winding or load branch inside the wye or delta connection.
Why is wye line voltage √3 times phase voltage?
The line voltage is the vector difference between two equal phase-to-neutral voltages separated by 120 degrees, which gives a magnitude of √3 times one phase voltage.
Why is delta line current √3 times phase current?
At each delta corner, line current is the vector difference between two equal branch currents separated by 120 degrees, producing a magnitude of √3 times one branch current.
Can this calculator tell me how to reconnect a motor?
No. Motor lead arrangements, permitted voltages and starting methods depend on the exact motor. Follow its nameplate and manufacturer connection diagram.
Can I use this result for an unbalanced load?
No. An unbalanced system requires phase-by-phase complex analysis or direct measurement; the simple √3 relationships assume equal phase magnitudes and 120-degree separation.
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