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Delta To Star Conversion Calculator

Work out delta to star conversion instantly with clear inputs, formula shown and shareable results.

About Delta To Star Conversion Calculator

The delta-to-star transform replaces a triangle of resistors with an equivalent star: each star arm is the product of the two delta resistors touching that node divided by the sum of all three. It is the standard trick for reducing bridge networks that have no series or parallel pairs.

Formula

Delta to star

Ra = Rab x Rca / (Rab + Rbc + Rca), and similarly for Rb and Rc

Worked example

With the default values below, Delta To Star Conversion Calculator returns Star resistance at A of 568.42. Change any input above and every figure here is recalculated in your browser.

Inputs used

R between A and B
1,200 Ω
R between B and C
1,800 Ω
R between C and A
2,700 Ω

Results

Star resistance at A
568.42 Ω
Star resistance at B
378.95 Ω
Star resistance at C
852.63 Ω
Sum of delta resistances
5,700.00 Ω

Step by step

  1. 1Values used
  2. 2Delta to star
  3. 3Star resistance at A= 568.42 Ω
  4. 4Star resistance at B= 378.95 Ω
  5. 5Star resistance at C= 852.63 Ω
  6. 6Sum of delta resistances= 5,700.00 Ω

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Electrical results are planning estimates only. Verify against the applicable wiring rules (IEC 60364, BS 7671, NEC or local code) and have all installation work designed and checked by a qualified electrician.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Electrical results are planning estimates only. Verify against the applicable wiring rules (IEC 60364, BS 7671, NEC or local code) and have all installation work designed and checked by a qualified electrician.

Frequently Asked Questions

When do I need this?

When a network cannot be reduced by series and parallel combination alone — a Wheatstone bridge with a load across the middle is the classic case.

What is the reverse transform?

Star to delta: Rab = (Ra Rb + Rb Rc + Rc Ra) / Rc, and similarly for the other two.

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