Delta to Wye (Δ-Y) Conversion Calculator

For a balanced three-phase network, Z_Y = Z_Δ / 3 — divide each delta branch impedance by 3 to get the equivalent wye impedance. Reversing it, Z_Δ = 3 × Z_Y. So a 60 Ω balanced delta becomes a 20 Ω wye, and a 10 Ω wye becomes a 30 Ω delta. These are the delta to wye conversion formula and the wye to delta conversion formula for balanced systems.

If the network is balanced (all three delta branches identical), divide one branch value by 3 — done. If it is unbalanced, use the general delta-wye transformation: Z_a = Z_ab × Z_ca / (Z_ab + Z_bc + Z_ca), Z_b = Z_ab × Z_bc / (sum), Z_c = Z_bc × Z_ca / (sum). Tab 1 of the calculator above handles the balanced delta to wye conversion; tab 2 handles the unbalanced case with every step shown.

With delta branches Z_ab, Z_bc, Z_ca and their sum S = Z_ab + Z_bc + Z_ca: Z_a = Z_ab × Z_ca / S, Z_b = Z_ab × Z_bc / S, Z_c = Z_bc × Z_ca / S. Each wye arm equals the product of the two adjacent delta branches divided by the sum of all three. Example: 30, 60, 90 Ω delta (S = 180) gives Z_a = 15, Z_b = 10, Z_c = 30 Ω.

Balanced: multiply each wye impedance by 3 (Z_Δ = 3 × Z_Y). Unbalanced: with N = Z_a×Z_b + Z_b×Z_c + Z_c×Z_a, compute Z_ab = N / Z_c, Z_bc = N / Z_a, Z_ca = N / Z_b. Each delta branch equals the sum of pairwise wye products divided by the opposite wye arm. Example: 15, 10, 30 Ω wye gives N = 900, so Z_ab = 30, Z_bc = 60, Z_ca = 90 Ω.

It follows from equating terminal resistances. In a balanced delta, the resistance between any two terminals is one branch in parallel with the series pair of the other two: Z_Δ || 2Z_Δ = (2/3)Z_Δ. In a balanced wye, the resistance between two terminals is 2Z_Y. Equating them gives 2Z_Y = (2/3)Z_Δ, so Z_Y = Z_Δ / 3. The derivation works for any linear impedance (resistance, reactance), not just resistors.

A delta (Δ) connection wires three branches into a closed triangle with no neutral — each branch sits directly across line-to-line voltage, and line current is √3 times branch current. A wye (Y, star) connection ties one end of each branch to a common neutral node — each branch sees line-to-neutral voltage (V_L/√3), and line current equals branch current. Delta is common in motors and heavy loads; wye is standard for distribution because it provides a neutral.

Use wye when you need a neutral point for single-phase loads or grounding (typical distribution: 400 V line-to-line / 230 V line-to-neutral in wye). Use delta when the load is purely three-phase with no neutral needed, or when you want a winding to circulate third-harmonic currents (transformer delta tertiaries). For analysis, convert whichever one you have into the one that matches the rest of your circuit model.

Wye: V_line = √3 × V_phase and I_line = I_phase. Delta: V_line = V_phase and I_line = √3 × I_phase. So on a 400 V three-phase wye supply, each phase sees 400/√3 ≈ 230.9 V; on a 400 V delta supply, each branch sees the full 400 V but carries only I_line/√3. Tab 4 of this calculator computes all of these plus three-phase apparent, real, and reactive power (S, P, Q).

Yes — resistor networks are the classic case. Enter the three delta resistor values in tab 2 (or a single value in tab 1 for a balanced resistor network) and it returns the equivalent wye resistors. This is the same transformation used in circuit analysis to simplify bridge-like three-phase and mesh networks, where the delta wye resistor network conversion reduces a loop into a star that is easier to solve.

The same scaling rules apply, because a balanced branch impedance scales as a whole: a delta inductor becomes L_Y = L_Δ / 3 (reactance X_L = 2πfL drops by 3×), and a delta capacitor becomes C_Y = 3 × C_Δ (capacitance triples because X_C = 1/(2πfC) must drop by 3×). In tab 1, pick Inductor or Capacitor, enter the component value and frequency, and the calculator shows both the reactance and the equivalent component value.

It is exact for linear lumped impedances at a given frequency — the two networks present identical impedance between every pair of external terminals, so the rest of the circuit cannot tell them apart. It is not exact if the branches are nonlinear (diodes, saturating inductors) or if frequency-dependent parasitics differ between the branches, because then the branch impedances are not the single values you entered.

A star-delta (wye-delta) starter is a motor control method that starts a three-phase induction motor with its windings in wye and then switches to delta for running. In wye, each winding sees 1/√3 of line voltage, so starting current and torque drop to about 1/3 of the delta values — a gentler start. Once up to speed, the contactors switch to delta for full torque. The voltage ratios come from exactly the wye vs delta relationships computed in tab 4.

Common examples: (1) motor winding analysis — three-phase motor impedances are often delta-connected but easier to analyze per-phase in wye; (2) power transformers — converting between Dy and Yy vector groups during short-circuit studies; (3) simplifying PCB or filter networks with delta resistor loops into equivalent wye networks; (4) fault analysis — unbalanced wye loads (e.g. 15/10/30 Ω) are often converted to delta to compute line currents.

Use the Balanced tab when all three branches are identical — it needs just one value and also supports inductor/capacitor networks with frequency. Use the Unbalanced Δ→Y tab when the three delta branches differ (three inputs), and the Unbalanced Y→Δ tab for the reverse direction. Use the Line/Phase tab when you do not need impedance conversion at all, just V_line vs V_phase, I_line vs I_phase, and three-phase power.

Yes. Tab 4 takes line voltage, line current, and power factor and computes phase voltage, phase current (for wye or delta), apparent power S = √3 × V_L × I_L, real power P = S × cos φ, and reactive power Q = S × sin φ. Example: 400 V, 10 A, 0.8 pf gives S ≈ 6.93 kVA, P ≈ 5.54 kW, Q ≈ 4.16 kVAR — identical total power in either connection, since power is connection-independent.

Yes. This tool is 100% client-side: every calculation runs in your browser with plain JavaScript, and nothing you type is sent anywhere — there is no server, no tracking request, and no data leaves the page. You can verify this in your browser's network panel or disconnect from the internet and keep calculating.