formula.expertYour record

Wye Line and Phase Voltage

VL=3 VφV_{L} = \sqrt{3} \, V_{\varphi}
sig figs

Worked example: 277 V phase → 480 V line. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
3=1.7320508075688772\sqrt{3} = 1.7320508075688772Square Root of Three · exact

Where Wye Line and Phase Voltage fits

Your answer feeds
Three-Phase Real PowerThree-Phase Apparent PowerThree-Phase Motor Full-Load CurrentMotor Locked-Rotor Starting Current

See also

Motor Locked-Rotor Starting Current: Both use line-to-line voltage.Three-Phase Apparent Power: Both use line-to-line voltage.Three-Phase Motor Full-Load Current: Both use line-to-line voltage.Three-Phase Real Power: Both use line-to-line voltage.
Here the solver did the work. Could you?

Wye and delta systems →

UniversityCircuits & Electrical Power

Test your skills in the Exam Room: new numbers every attempt. Free lessons for students, no sign-up, just pure learning.

See your Report Card
Learning zone

Wye Line and Phase Voltage explained

VφVL

Two phases of a wye are not simply additive because they peak 120° apart; the vector difference of two equal phasors 120° apart is √3 times either one. That single fact names every common system: 120/208 V (208 = √3 × 120), 277/480 V (480 = √3 × 277), and 230/400 V across most of the world. In a wye the line current equals the phase current: it is only the voltages that get the √3.

The practical consequence is that one transformer bank feeds two voltages: lighting and receptacles hang line-to-neutral at 120 V or 277 V, while motors and heaters take line-to-line at 208 V or 480 V. The trap is assuming 240 V single-phase equipment will work on a 208 V wye leg: it sees 208 V, and a heater delivers only (208/240)² ≈ 75% of its rated output.

Wye Line and Phase Voltage formula

VL=3 VφV_{L} = \sqrt{3} \, V_{\varphi}
Where
  • VLV_{L}= Line-to-line voltage (V)
  • VφV_{\varphi}= Phase (line-to-neutral) voltage (V)
Revised 16 October 2026
Cite this page

formula.expert. (2026, October 16). Wye Line and Phase Voltage Formula & Calculator. https://formula.expert/solvers/wye-line-phase-voltage

formula.experthttps://formula.expert/solvers/wye-line-phase-voltage