Use 3 phase Ohm’s law to find line voltage, line current or per-phase impedance for a balanced wye or delta load, plus kVA, kW and kVAR.

Impedance of one load branch, not resistance measured line to line.

Typical value 0.9. PF only affects the kW and kVAR results, not voltage or current.

Optional settings

3 Phase Ohm’s Law Formula

The following equation applies to balanced wye loads using RMS line-to-line voltage, RMS line current and per-phase impedance magnitude.

V = √(3) × I × Z
  • Where V is line-to-line RMS voltage (V)
  • I is RMS line current (A)
  • Z is impedance magnitude of each equal load branch (Ω), not resistance measured between supply lines

Choose a solve mode and connection, then complete its visible fields. For wye, V = √3 × I × Z, I = V / (√3 × Z), and Z = V / (√3 × I). For delta, V = I × Z / √3, I = √3 × V / Z, and Z = √3 × V / I. The branch relationship is phase voltage = phase current × impedance magnitude. The DOE Electrical Science handbook, volume 3, AC Power module explains these balanced line/phase relationships.

What is 3 Phase Ohm’s Law?

Definition:

Per-phase Ohm’s law relates voltage and current magnitudes through impedance magnitude. Balanced wye and delta connections require different conversions between line and phase quantities. For sinusoidal loads, total apparent kVA = √3 × line-to-line volts × line amps / 1000; real kW = kVA × PF and reactive magnitude = kVA × √(1 − PF²). PF is used for this power breakdown and does not change the impedance-magnitude solve.

How to Use the 3 Phase Ohm’s Law Calculator?

Example Problem:

The following example outlines the steps and information needed to calculate the missing parameter in a three‐phase system.

Choose Line-to-line voltage and Wye (star).

Enter RMS line current 15 A and per-phase impedance magnitude 10 Ω. Use the applicable PF for the power breakdown (default 0.9), then select Calculate.

Finally, calculate the missing line voltage using the formula above:

V = √3 × I × Z

V = √3 × 15 × 10

V ≈ 259.8076 V (about 259.8 V). This example is wye; the same line current and branch impedance in delta give approximately 86.6025 V.

FAQ

What does the 3 Phase Ohm’s Law Calculator compute?

Select line-to-line voltage, line current or per-phase impedance magnitude for a balanced wye or delta load. The result includes phase values and total/per-phase apparent power, real power and reactive magnitude.

How is the solve target selected?

Use the Solve for menu. Only relevant inputs are displayed; leaving a visible required input blank produces a linked error. Impedance magnitude is not necessarily resistance, and no leading/lagging sign is inferred.

Can this calculator be used for single‐phase systems?

No. It models balanced sinusoidal three-phase loads with the selected wye or delta line/phase relationship. It does not model imbalance or harmonics, and it does not select conductors or protection.