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Three-Phase Calculator (Star/Delta)

Quick answer

Solve star and delta circuits: P = root3 VL IL cos phi, phase vs line voltage (root3), currents, and reactive power for industrial loads.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the Three-Phase Calculator Works

P = √3 × VL × IL × cos(φ)

Calculates power relationships in three-phase systems, which are more efficient than single-phase for high-power applications. Supports both star (Y) and delta (Δ) configurations. Worked example: star-connected load, 400 V line, 10 A line current, PF 0.85: phase voltage = 400/1.732 = 231 V, P = 1.732 x 400 x 10 x 0.85 = 5.9 kW, Q = 3.66 kVAR. Line and phase quantities trade by root3: in star a 400 V line means 231 V per phase winding, while delta puts the full 400 V across each element - the same load, different currents per connection.

  1. 1

    Step 1

    Select the connection type (Star or Delta)

  2. 2

    Step 2

    Enter line voltage and line current

  3. 3

    Step 3

    Enter the power factor

  4. 4

    Step 4

    View active, reactive, and apparent power

Use Cases

Industrial motor power calculations

Commercial electrical system design

Generator sizing and selection

Power distribution network planning

Tips

  • 1

    Star connection: VL = √3 × Vph, IL = Iph

  • 2

    Delta connection: VL = Vph, IL = √3 × Iph

  • 3

    Three-phase delivers constant power (no pulsation)

  • 4

    More efficient transmission than single-phase

Common Mistakes

  • Confusing line and phase values

  • Using wrong √3 factor for star vs. delta

  • Forgetting power factor in power calculations

  • Assuming unbalanced loads follow balanced formulas

FAQs

What is the difference between star and delta connections?

In star (Y), each phase connects to a common neutral point. In delta (Δ), phases connect end-to-end forming a triangle. Star provides neutral access; delta provides higher current capacity.

Why is three-phase more efficient than single-phase?

Three-phase delivers constant power (no zero crossings), uses less copper for the same power, and produces rotating magnetic fields directly for motors.

When should I use star vs. delta?

Star is common for distribution with neutral access and lower phase voltage. Delta is used for high-current loads and motors that need to start with reduced voltage (star-delta starter).

What is the three-phase power formula?

P = root3 x VL x IL x cos phi. With 400 V, 25 A, PF 0.9: P = 1.732 x 400 x 25 x 0.9 = 15.6 kW. Apparent power S = root3 x VL x IL = 17.3 kVA.

Star or delta - which draws more current?

Same load impedance in delta draws 3x the line power vs star: phase voltage is full VL in delta but VL/root3 in star. That is why motors start in star then switch to delta to cut starting current to a third.

Why root3 and not 3?

Phase powers add as 3 x VP x IP x cos phi, but line measurements are what you read on meters. Since VL = root3 x VP in star and IP = IL, the substitution gives root3 x VL x IL - the 3 and root3 partly cancel.