3-Phase Resistance Calculator

The 3-Phase Resistance Calculator computes phase and line resistances using voltage, current, connection type, conductor length, cross-section, and temperature.

3-Phase Resistance Calculator Explained

Three-phase resistance describes the real, energy-dissipating part of a load in a three-phase system. In balanced systems, each phase has the same resistance. Two common connections are wye (also called star) and delta, and each maps line measurements to phase resistance differently.

This Calculator supports two practical modes. The first mode starts from operating data: line-to-line voltage, line current, and optional power factor. It returns the per-phase resistance using standard relationships. The second mode starts from terminal ohmmeter readings. It infers per-phase resistance from how the winding is wired internally.

The math is straightforward, yet paying attention to connection type is vital. Our derivation uses basic circuit rules and three-phase identities. The result, R_phase, is stated clearly, and key variables are defined as you go.

How to Use 3-Phase Resistance (Step by Step)

Decide whether you have live operating data or offline terminal measurements. Then pick the mode that fits. The steps below outline a typical workflow from inputs to a reliable result.

• Select connection type: Wye (Star) or Delta.
• Choose mode: Operating Data (voltage/current/power factor) or Ohmmeter (line-to-line resistance at terminals).
• Enter known variables: V_line, I_line, and power factor if using operating data; or R_line-line if using an ohmmeter.
• Optionally set temperature to correct resistances to a reference, especially for copper windings.
• Review the calculated per-phase resistance and any derived totals, such as three-phase power.

When in doubt, run both modes if you have both kinds of measurements. The comparison is a strong validity check and often catches wiring issues or bad probes.

Formulas for 3-Phase Resistance

These formulas come from ohm’s law, power relations, and how phases map to line quantities in balanced systems. We show the minimal derivation ideas and variables so you can follow the logic and trust the result.

• General: P_total = √3 × V_line × I_line × cos(θ). For a purely resistive load, cos(θ) = 1.
• Wye (Star), operating data:
  – V_phase = V_line / √3
  – I_phase = I_line
  – R_phase = V_phase / I_phase = (V_line / √3) / I_line
  – From power: R_phase = V_phase² / (P_total / 3)
• Delta, operating data:
  – V_phase = V_line
  – I_phase = I_line / √3
  – R_phase = V_phase / I_phase = V_line / (I_line / √3) = √3 × V_line / I_line
  – From power: R_phase = V_phase² / (P_total / 3)
• Wye, ohmmeter at terminals (balanced, isolated neutral):
  – Measured between any two lines: R_line-line = 2 × R_phase
  – So R_phase = R_line-line / 2
• Delta, ohmmeter at terminals (balanced):
  – Two paths between any pair of lines: one branch R_phase and another of 2 × R_phase in series
  – In parallel: R_line-line = (R_phase ∥ 2R_phase) = (2/3) × R_phase
  – So R_phase = (3/2) × R_line-line
• Temperature correction (linear model for copper):
  – R_T2 = R_T1 × [1 + α × (T2 − T1)], with α ≈ 0.00393 per °C for copper.

When loads are not purely resistive, resistance is the real part of impedance: R = |Z| × cos(θ). The Calculator lets you input power factor if known, which refines the result.

What You Need to Use the 3-Phase Resistance Calculator

Gather a few measured values and choose the connection. For best accuracy, confirm whether the load is balanced and whether the neutral (in wye) is isolated.

• Connection type: Wye (Star) or Delta
• Mode: Operating data or Ohmmeter data
• V_line (line-to-line voltage), in volts
• I_line (line current), in amperes
• Power factor cos(θ), if not purely resistive
• R_line-line (ohmmeter between any two lines), in ohms

Check ranges. Very small resistances need a four-wire meter. Very large resistances can be skewed by lead leakage. If your variables are inconsistent, the Calculator will warn you to recheck inputs.

Using the 3-Phase Resistance Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

1. Open the Calculator and pick Wye or Delta.
2. Select the calculation mode: Operating Data or Ohmmeter.
3. Enter V_line and I_line, and cos(θ) if applicable; or enter R_line-line if using an ohmmeter.
4. Set the reference temperature and material if you want temperature-corrected values.
5. Click Calculate to get R_phase and any derived quantities.
6. Review the result and compare across phases if you entered multiple measurements.

These points provide quick orientation—use them alongside the full explanations in this page.

Worked Examples

Example 1: A balanced wye-connected heater bank runs at V_line = 400 V and I_line = 10 A. Assume purely resistive behavior, so cos(θ) = 1. V_phase = 400/√3 ≈ 231 V. R_phase = V_phase / I_phase = 231 / 10 = 23.1 Ω. Total three-phase power is P_total = √3 × 400 × 10 ≈ 6.93 kW. This matches a resistive load profile and is within wiring limits. What this means

Example 2: A delta-connected motor is isolated and measured with a DC ohmmeter. Between any two terminals, R_line-line = 6.0 Ω. For a balanced delta, R_phase = (3/2) × R_line-line = 9.0 Ω at the measured temperature, say 20 °C. Correcting to 75 °C for copper: R_75 = 9.0 × [1 + 0.00393 × (75 − 20)] ≈ 9.0 × 1.216 ≈ 10.94 Ω. The increase reflects the higher winding temperature in service. What this means

Assumptions, Caveats & Edge Cases

These computations assume a balanced three-phase system unless stated otherwise. That means equal phase resistances and symmetrical voltages. Real systems may deviate, so interpret small differences with judgment.

• Unbalanced loads: If per-phase currents or voltages differ, compute each phase separately rather than using one averaged result.
• Non-resistive loads: With motors or reactors, include power factor. Resistance equals the real part of impedance, not the magnitude.
• Ohmmeter method: For wye with an isolated neutral, R_line-line doubles R_phase. If the neutral is bonded, this relation changes.
• Contact and lead resistance: Use four-wire measurement for low ohms to avoid lead error.
• Temperature: Resistance rises with temperature. If comparing to nameplate or spec, correct to the reference temperature.

If results look implausible, check wiring (mis-strapped delta/wye), meter range, and whether other equipment is still connected. Small wiring mistakes can dominate low-ohm readings.

Units Reference

Using correct units keeps the derivation tight and the result correct. The table below lists the core quantities and how they are typically expressed for three-phase resistance work.

Read the table left to right. Identify the quantity, then find its symbol and unit. Use consistent units throughout the calculation to avoid scaling errors.

Troubleshooting

If your numbers do not make sense, the issue is often with inputs or connection assumptions. Walk through the common checks below before re-measuring.

• Result too low in ohms: Suspect meter lead resistance or a parallel path still connected.
• Result too high in ohms: Look for an open phase, poor contact, or wrong connection selection.
• Mismatch between operating and ohmmeter modes: Reconfirm wye/delta and neutral status.
• Inconsistent phases: A damaged winding or loose terminal can unbalance readings.

If problems persist, measure each phase-to-neutral (wye) or each branch in isolation (delta), and compare the three results. Large spread suggests a genuine fault.

FAQ about 3-Phase Resistance Calculator

Does the Calculator work for non-resistive loads?

Yes. Enter the power factor to compute the real part of impedance (resistance). If power factor is unknown, the result assumes a resistive load.

How do I know if my load is wye or delta?

Check the wiring diagram or nameplate. Many motors show a terminal map indicating star (Y) or delta (Δ), along with voltage options.

Can I use DC ohmmeter readings on motors?

Yes, for winding checks when the motor is de-energized and isolated. Compare the three line-to-line readings; they should be very similar if balanced.

Why do my resistance values change with temperature?

Conductor resistance rises with temperature. Use the temperature correction formula to compare measurements to specifications at a defined reference.

Key Terms in 3-Phase Resistance

Wye (Star) Connection

A three-phase configuration where each phase connects to a common neutral point. Line voltage equals √3 times phase voltage in a balanced system.

Delta Connection

A closed-loop configuration connecting the three phases in a triangle. Line voltage equals phase voltage, and line current is √3 times phase current.

Per-Phase Resistance

The resistance of a single phase branch. In balanced systems, all three phases share this value and it defines real power dissipation.

Line-to-Line Resistance

The resistance measured between any two line terminals with an ohmmeter. Its relation to per-phase resistance depends on connection type.

Power Factor

The ratio of real power to apparent power, equal to cos(θ). It captures how far a load deviates from purely resistive behavior.

Balanced Load

A three-phase load with equal phase impedances and symmetrical voltage supply. It simplifies analysis and improves power quality.

Temperature Coefficient

A constant that quantifies how resistance changes with temperature. For copper, α is about 0.00393 per °C near room temperature.

Impedance

The generalized opposition to AC, combining resistance and reactance. Its real part is resistance, which sets real power dissipation.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• Three-phase electric power overview (Wikipedia)
• Wye–Delta relationships and transformations (All About Circuits)
• Electrical resistance and temperature effects in conductors (NREL)
• Power, voltage, current relations in three-phase systems (IEEE)
• Four-wire ohms for accurate low-resistance measurement (Fluke)

These points provide quick orientation—use them alongside the full explanations in this page.