Delta to Wye Calculator - Y-Delta Resistor Network Transform

A delta to wye calculator converts a three-resistor delta (also called pi) network into the equivalent three-resistor wye (also called star) network. You enter the three delta resistor values Ra, Rb, and Rc, and the page returns the three wye resistor values R1, R2, and R3 that keep the resistance between every pair of external terminals unchanged. Use it when a circuit-analysis problem, lab worksheet, or three-phase power question gives you a delta arrangement but is easier to solve once it is rewritten as a wye arrangement.

• • Resistor network simplification: Replace a delta resistor triangle with a wye resistor star so bridge, divider, or series-parallel reduction becomes a single equivalent resistance.
• • Three-phase power analysis: Convert a delta-connected source or load into its wye equivalent for balanced line-current or line-to-line voltage work.
• • Lab worksheet checks: Verify hand-computed wye resistor values during an AC circuits or electronics lab exercise.
• • Bridge circuit design: Estimate wye resistors that can replace a delta section when prototyping a sensor or measurement bridge.

The delta and wye forms are interchangeable at the terminals but not element-by-element. A 10-ohm balanced delta becomes a 3.333-ohm balanced wye because the same terminal resistance is now shared across three series legs. The result panel names each wye output by its terminal so it maps back to the original drawing.

When you also need V = I * R or I = V / R alongside the transform, Ohm's Law Calculator provides the underlying single-component equations that often appear beside network work.

The calculator applies the standard Y-Delta transform in reverse. It computes a single divisor from the sum of all three delta resistors, then forms each wye resistor as the product of the two delta resistors that share the matching terminal, divided by that sum.

• Ra: Delta resistor between terminals A and B. Forms the numerator of R1 (with Rc) and R2 (with Rb).
• Rb: Delta resistor between terminals B and C. Forms the numerator of R2 (with Ra) and R3 (with Rc).
• Rc: Delta resistor between terminals C and A. Forms the numerator of R1 (with Ra) and R3 (with Rb).
• Ra + Rb + Rc: Common divisor used by every wye resistor. The calculator displays this value so you can verify the hand calculation.

The three wye outputs preserve the resistance seen between every pair of external terminals, which is why one network can replace the other in a larger diagram without disturbing the rest of the analysis. The common divisor row sits beside the results so you can verify each numerator-over-denominator step by hand.

According to All About Circuits, the wye-delta transformation rewrites three resistors in a Y configuration as three resistors in a delta configuration, with each wye resistor given by the product of the two adjacent delta resistors divided by the sum of all three

When the surrounding circuit is a four-arm bridge rather than a simple triangle, Wheatstone Bridge Calculator covers the ratio-based detector voltage and balance condition used with a delta section.

These four concepts explain why the delta to wye calculator works the way it does and where the product-over-sum rule comes from.

Keeping these concepts visible makes the rest of the page easier to follow. The worked example uses the symmetric simplification, the limitations section explains when the simple divisor model needs adjustment, and the benefits section shows how this transform simplifies a typical network reduction.

When the network you are simplifying includes capacitors in addition to resistors, Capacitor Calculator covers the Q = C * V relationship and component decoding that complement a Y-Delta reduction.

Enter the three delta resistor values, then read the equivalent wye resistors and the divisor used in the transform.

1. 1 Identify the delta arrangement: Confirm that the three resistors form a closed triangle with three external nodes A, B, and C, and pick Ra, Rb, Rc to match the terminals.
2. 2 Enter Ra, Rb, and Rc: Type each delta resistor value in ohms. Use a consistent unit across all three inputs and avoid zero or negative entries because the divisor would collapse to zero.
3. 3 Read the divisor: The result panel shows Ra + Rb + Rc first. Use this value to confirm the denominator before reading each wye resistor.
4. 4 Read R1, R2, and R3: Each wye output is the product of the two delta resistors that share its terminal, divided by the divisor shown above.
5. 5 Transfer values to your circuit: Replace the delta triangle with a wye star in your schematic. The terminals stay in the same places; only the internal layout and resistor values change.

For a 12 / 24 / 36 ohm delta the divisor row shows 72 ohms, R1 = 6 ohms, R2 = 4 ohms, R3 = 12 ohms. Drawing the equivalent wye with R1 on terminal A, R2 on terminal B, and R3 on terminal C keeps the original network analysis valid.

When the wye network feeds an AC load and you also need real, reactive, and apparent power, Power Factor Calculator completes the analysis after the delta-to-wye step.

These benefits describe how the page fits into a real circuit-analysis workflow rather than a generic pitch.

• • Fast Y-Delta transform results: Three inputs become three outputs without writing the product-over-sum expression by hand for each leg.
• • Transparent divisor display: The Ra + Rb + Rc row makes it easy to check the denominator while you are learning the formula or grading a worksheet.
• • Consistent terminal labeling: Each output is named R1, R2, or R3 with its terminal, so the result maps directly onto a wye diagram with A, B, and C nodes.
• • Useful for three-phase work: Convert a delta source or load to its wye equivalent before computing balanced line currents and line-to-line voltages.
• • Supports homework and lab work: Use the calculator to verify hand-calculated wye values during circuits or electronics assignments.

The tool is most useful when you already know the formula but want to skip the arithmetic, or when you are still learning the formula and want to see each intermediate value. The divisor row is the main aid for the second case because the same denominator reappears in every wye resistor.

When the circuit after the transform is a four-diode bridge fed from the wye nodes, Bridge Rectifier Calculator covers the DC output, ripple factor, and PIV that follow the network conversion.

These factors change how the output should be read and where the product-over-sum rule starts to lose accuracy.

• • The calculator assumes ideal passive resistors with no reactance, lead resistance, or contact resistance; those effects can shift the bench result even when the paper result is correct.
• • The result is exact only for the chosen node labeling. Swapping two delta resistor values without relabeling the terminals gives a different equivalent wye and is not a numerical error.
• • Very large or very small delta values can still be entered, but the calculator displays precision and does not warn about measurement uncertainty or component availability.

Treat the calculator as a fast algebraic aid, not as a measurement instrument. If the network is reactive, evaluate the transform at the operating frequency and use impedance in place of resistance.

As published by Wikipedia, the Y-delta transform formulas relate the three resistors of the wye to the three resistors of the delta network so that the equivalent resistance between any two terminals is preserved

As published by MIT OpenCourseWare, network equivalence shows that a delta or pi network of three resistors can be replaced by a wye or star network as long as the terminal resistances match

When the surrounding circuit also contains series capacitors whose combined value changes the impedance seen at the wye terminals, Capacitors in Series Calculator computes the equivalent series capacitance.