What is the wye-delta transformation?

It is a way to replace a three-resistor triangle (delta, Δ) with an equivalent three-resistor star (wye, Y) that behaves identically as seen from the three terminals A, B, C — or to go the other way. The point is that some networks, like a Wheatstone bridge, contain a delta or wye that blocks any series-parallel reduction. Swap it for its equivalent and the rest of the circuit collapses to a single resistance. For example a balanced 9 Ω delta becomes a balanced 3 Ω wye.

What are the delta-to-wye (Δ→Y) formulas?

Each wye arm equals the product of the two delta edges touching that node, divided by the sum of all three deltas. With edges Rab, Rbc, Rca: Ra = Rab·Rca / (Rab+Rbc+Rca), Rb = Rab·Rbc / (Rab+Rbc+Rca), Rc = Rbc·Rca / (Rab+Rbc+Rca). For (10, 20, 30) the sum is 60, so Ra = 10·30/60 = 5 Ω, Rb = 10·20/60 = 3.33 Ω, Rc = 20·30/60 = 10 Ω.

What are the wye-to-delta (Y→Δ) formulas?

Each delta edge equals the sum of the three pairwise products of the wye arms, divided by the arm opposite that edge. With arms Ra, Rb, Rc and P = Ra·Rb + Rb·Rc + Rc·Ra: Rab = P/Rc, Rbc = P/Ra, Rca = P/Rb. For a symmetric wye of 3 Ω, P = 27, so each edge is 27/3 = 9 Ω, which is why a 3 Ω star equals a 9 Ω triangle.

Why does this help simplify a complex resistor network?

Series and parallel rules only work when two resistors share exactly one or exactly two nodes. A bridge has a middle resistor that shares one node with four others, so neither rule applies. Convert the upper (or lower) delta of the bridge into a wye and that middle resistor disappears into the star point, leaving two series-parallel branches you can reduce step by step to one equivalent resistance.

How are the balanced cases related (Δ = 3·Y)?

When all three resistors are equal, the formulas simplify dramatically. A balanced delta of value RΔ transforms to a balanced wye of RΔ/3, and a balanced wye of RY transforms to a balanced delta of 3·RY. So RΔ = 3·RY. A symmetric 9 Ω delta is a 3 Ω wye; a symmetric 5 Ω wye is a 15 Ω delta. This factor of three is the fastest sanity check on any star-delta result.

Where is the Y-Δ transform actually used?

The classic case is the unbalanced Wheatstone bridge, where you cannot find the equivalent resistance by inspection until you convert one delta to a wye. It also appears in three-phase power (star vs delta motor windings and starters), in filter and attenuator design (tee ⇄ pi networks are the same transform under different names), and in any resistive mesh where you need a single equivalent resistance between two terminals.

Solve an unbalanced Wheatstone bridge

You have a four-arm bridge with a galvanometer resistance across the middle and you need the total resistance the source sees. There is no series-parallel path while that middle resistor is in place. Take the three resistors forming the top delta, convert Δ→Y, and the middle arm folds into the new star point. What is left is two parallel branches you can reduce by hand to a single equivalent resistance.

Pick three-phase star vs delta winding values

A motor or heater bank can be wired in star (wye) or delta, and the two give different line behaviour. When you have one configuration's per-phase resistance and need the equivalent in the other connection, enter the three values and read the converted set — the same Δ = 3·Y relation that sets the 1.732 line-voltage ratio shows up directly in the numbers here.

Convert a tee attenuator to its pi equivalent

Resistive tee (T) and pi (π) pads are the wye and delta of signal design under different names. If you laid out a tee attenuator but the board footprint wants a pi, type the three tee resistors as a wye, convert Y→Δ, and you have the pi resistor values that give the same attenuation and impedance match.

Check a homework or exam network reduction

Circuits courses lean on Y-Δ for exactly the meshes that defeat series-parallel rules. Work the transform by hand, then paste your three inputs here to confirm each arm before you carry the equivalent forward. The round-trip property (Δ→Y→Δ returns the original) is a quick way to verify you applied the right direction.

Wye-Delta Resistor Calculator (Y ⇄ Δ Transformation)

Convert a three-terminal resistor network between wye (Y / T) and delta (Δ / π) — Δ→Y and Y→Δ both directions, exact formulas, one-click copy — browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Convert a three-terminal resistor network between its wye (Y / T) and delta (Δ / π) forms. Enter three resistances, pick the direction, read the equivalent network.

Quick examples

Direction

Delta resistances (triangle edges, Ω)

Rab (A–B)

Rbc (B–C)

Rca (C–A)

Equivalent network

Ra (→A)

3 Ω

Rb (→B)

3 Ω

Rc (→C)

3 Ω

Formulas used

Ra = Rab·Rca / (Rab + Rbc + Rca)Rb = Rab·Rbc / (Rab + Rbc + Rca)Rc = Rbc·Rca / (Rab + Rbc + Rca)

Use this to collapse a bridge or ladder that has no plain series-parallel path: swap one Y for a Δ (or back) and the rest reduces.

What this tool does

A free wye-delta (star-delta) resistor transformation calculator. Many bridge and ladder circuits have no plain series-parallel reduction: there is always one stubborn triangle (delta) or star (wye) of three resistors in the way. The Y-Δ transform swaps that triangle for an equivalent star, or the star for an equivalent triangle, and suddenly the rest of the network collapses to a single resistance. Enter three resistances in ohms, pick the direction, and the tool applies the standard equations: Δ→Y takes the product of the two adjacent edges over the sum of all three, while Y→Δ takes the sum of pairwise arm products over the opposite arm. A balanced delta of value R maps to a balanced wye of R divided by 3, so a symmetric 9 Ω triangle becomes a 3 Ω star. Every figure stays on the same three terminals A, B, C, so the equivalence holds for any external load. Results copy with one click and the shareable link reopens the exact transform. 100% client-side, nothing uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Developer; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Wye-Delta Resistor Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Solve an unbalanced Wheatstone bridge
You have a four-arm bridge with a galvanometer resistance across the middle and you need the total resistance the source sees. There is no series-parallel path while that middle resistor is in place. Take the three resistors forming the top delta, convert Δ→Y, and the middle arm folds into the new star point. What is left is two parallel branches you can reduce by hand to a single equivalent resistance.
Pick three-phase star vs delta winding values
A motor or heater bank can be wired in star (wye) or delta, and the two give different line behaviour. When you have one configuration's per-phase resistance and need the equivalent in the other connection, enter the three values and read the converted set — the same Δ = 3·Y relation that sets the 1.732 line-voltage ratio shows up directly in the numbers here.
Convert a tee attenuator to its pi equivalent
Resistive tee (T) and pi (π) pads are the wye and delta of signal design under different names. If you laid out a tee attenuator but the board footprint wants a pi, type the three tee resistors as a wye, convert Y→Δ, and you have the pi resistor values that give the same attenuation and impedance match.
Check a homework or exam network reduction
Circuits courses lean on Y-Δ for exactly the meshes that defeat series-parallel rules. Work the transform by hand, then paste your three inputs here to confirm each arm before you carry the equivalent forward. The round-trip property (Δ→Y→Δ returns the original) is a quick way to verify you applied the right direction.

Common pitfalls

Mixing up which delta edge sits opposite which wye arm. In Δ→Y each arm uses the two edges that touch its node; in Y→Δ each edge is divided by the arm opposite to it, not an adjacent one. Label your nodes A, B, C first and the pairing stops being guesswork.
Forgetting that a balanced delta is three times the wye, not one third. Going Y→Δ the resistance goes up (RΔ = 3·RY); going Δ→Y it goes down (RY = RΔ/3). If a 3 Ω star gave you a 1 Ω triangle you ran the formula backwards — the right answer is 9 Ω.
Feeding a zero or negative resistance. A negative resistor is non-physical, and a zero wye arm in Y→Δ pushes a delta edge to infinity (division by that arm). The tool rejects both with a clear message rather than printing a meaningless number.

Privacy

Every step — the Δ→Y and Y→Δ formulas, the validity checks and the formatting — is plain JavaScript that runs inside your browser tab. The resistor values you type never leave the page and nothing is logged. The one caveat: the shareable link encodes your three resistances and the direction in the query string, so a link pasted into chat records those numbers in the recipient server's access log. For a confidential design, use the copy button and paste the text rather than sharing the URL.

FAQ

Tool combos

Folks in your role tend to reach for these alongside this tool.

Developer

Browse all tools for this role

Wye-Delta Resistor Calculator (Y ⇄ Δ Transformation)

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Wye-Delta Resistor Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Solve an unbalanced Wheatstone bridge

Pick three-phase star vs delta winding values

Convert a tee attenuator to its pi equivalent

Check a homework or exam network reduction

Common pitfalls

Privacy

FAQ

Unit Converter

Percentage Calculator

Ohm's Law Calculator

Parallel & Series Resistor Calculator

Resistor Color Code Calculator

Scientific Calculator

24-Point Solver & Game

555 Timer Calculator

A1C to Blood Glucose Calculator

Add Days to Date Calculator

Age Calculator

Age Difference Calculator