Star-Delta Conversion Calculator

Star-Delta Conversion Formula

Worked Example

A delta of R_ab = 30 Ω, R_bc = 60 Ω and R_ca = 90 Ω:

1. ΣR = R_ab + R_bc + R_ca = 180 Ω
2. R_a = R_ab R_ca ÷ ΣR = 30 × 90 ÷ 180 = 15 Ω
3. R_b = R_ab R_bc ÷ ΣR = 10 Ω; R_c = R_bc R_ca ÷ ΣR = 30 Ω

R_c: 30 Ω

GATE tip

Each star resistor is the product of the two delta resistors touching that node, divided by the sum of all three. Each delta resistor is the sum of pairwise star products divided by the opposite star resistor.

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Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.