Star-Delta (Y-Δ) Transformation Calculator

How to use the star-delta transformation calculator

Enter the three delta resistances between terminals a–b, b–c and c–a. The calculator gives the equivalent star resistances connected from each terminal to a common centre point. To go from star to delta, enter the star values and solve for the delta fields with the × buttons.

For more background, read DOL vs Star-Delta Starter: Which to Use.

Delta to star

R_a = R_abR_ca ÷ ΣR  ·  R_b = R_abR_bc ÷ ΣR  ·  R_c = R_bcR_ca ÷ ΣR

Star to delta

R_ab = (R_aR_b + R_bR_c + R_cR_a) ÷ R_c

and similarly for R_bc (÷ R_a) and R_ca (÷ R_b).

Example

Delta 30, 60 and 90 Ω (sum 180 Ω):

• R_a = 30 × 90 ÷ 180 = 15 Ω
• R_b = 30 × 60 ÷ 180 = 10 Ω
• R_c = 60 × 90 ÷ 180 = 30 Ω

When to use it

• Simplifying bridge networks that cannot be reduced with series and parallel rules alone.
• Converting delta-connected loads to star for per-phase calculations in three-phase systems.
• Analysing the Wheatstone bridge when it is unbalanced.

Star-delta motor starting

A motor started in star sees 1/√3 of line voltage, so starting current and torque fall to one third of their direct-on-line values. After a few seconds, the starter switches to delta for full voltage.

Frequently asked questions

How do I convert delta to star?

Each star resistance equals the product of the two delta resistances touching that node, divided by the sum of all three. R_a = R_ab × R_ca ÷ (R_ab + R_bc + R_ca).

How do I convert star to delta?

Each delta resistance equals the sum of the pairwise products of the star resistances divided by the opposite star resistance. Enter the star values here and press × on the delta fields to solve backwards.

What about balanced loads?

For three equal resistances, R_star = R_delta ÷ 3, and R_delta = 3 × R_star.

Does this work for AC impedances?

Yes, with complex impedances. This calculator handles resistances (or magnitudes of identical-angle impedances).

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