Calculate 3 phase resistance per branch for a balanced wye or delta resistive load from line voltage and current or kW, or find line current.

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3-Phase Resistance Formula

The following equation gives resistance per equal branch for a balanced wye (star) purely resistive load, using RMS line quantities at unity PF.

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

For wye, R = V / (√3 × I) and I = V / (√3 × R). For delta, R = √3 × V / I and I = √3 × V / R. Select the connection and solve mode, complete the visible fields, choose units and select Calculate. Total resistive watts = √3 × line-to-line volts × line amps. An equivalent balanced delta needs three times the wye branch resistance to preserve line voltage, current and power; this is a network equivalence, not rewiring the same resistors. These relationships follow the balanced line/phase equations in the DOE Electrical Science handbook, volume 3.

What is a 3-Phase Resistance Calculator?

Definition:

This calculator solves resistance per equal branch from line-to-line voltage and line current, or line current from voltage and branch resistance. It supports balanced purely resistive wye and delta loads, unit conversion and phase/power details. It does not model AC reactance, imbalance or connected measurement paths, and it does not select protection.

How to Calculate 3-Phase Resistance?

Example Problem:

The following example outlines the steps and information needed to calculate the phase resistance when the line-to-line voltage and line current are known.

Choose Phase resistance from current and Wye (star). Enter line-to-line RMS voltage 400 V.

Next, determine the line current. In this example, the current is 10 A.

Finally, calculate the phase resistance using the formula above:

R = V / (√3 × I)

Substitute the values to obtain R = 400 / (√3 × 10)

Thus, R ≈ 23.094 Ω per wye branch. For an equivalent balanced delta at the same line voltage and current, resistance is approximately 69.282 Ω per branch.

FAQ

What factors can affect the accuracy of three-phase resistance calculations?

Voltage/current measurement uncertainty, unequal branches, temperature-dependent resistance and non-resistive loads can affect the result. A resistance measurement between connected terminals is not necessarily the resistance of one branch.

Can this calculator be used for both star and delta configurations?

Yes. Select Wye (star) or Delta. Each uses its own line/phase relationship; the result displays phase voltage, phase current, total resistive power and equivalent resistance in the other topology.

How do I select the value to calculate?

Use the Solve for menu: Phase resistance from current, Phase resistance from power, or Line current. Complete every visible numeric input. In current mode, choose A or kA for the result; changing an input unit converts its magnitude.