Star Delta Calculator - Wye Delta Resistance Conversion

Agarapu Ramesh — Editor and content reviewer
Editorially reviewed Reviewed by Agarapu Ramesh, science educator (chemistry). LinkedIn
Last reviewed: May 2026 | Standard electrical engineering formulas

Star-delta conversion is a network trick for circuits that do not reduce cleanly by plain series or parallel math. For balanced networks it is easy: delta resistance is three times the star resistance. Unbalanced networks need the full formulas.

Formula at a glance

  • balanced: Rdelta = 3 x Rstar
  • balanced: Rstar = Rdelta / 3
  • unbalanced formulas use products and sums of the three resistors

Field note: The math is not hard, but the diagram matters. A swapped label gives a perfectly calculated wrong answer.

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Star-Delta Starter Calculator

Calculate reduced starting current

A
Result
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How It Works

Star (Y) Start:
• Winding voltage = VL/√3
• Current ≈ 1/3 of DOL
• Torque ≈ 1/3 of DOL

Delta (Δ) Run:
• Full voltage applied
• Full current & torque
• Normal operation

Comparison

ParameterStarDelta
Current33%100%
Torque33%100%
Voltage/winding58%100%

Related

Motor CurrentTransformerkVA to Amps

How to use the Star Delta Calculator

Use this as a bench check, then compare it with the part marking, tolerance and a meter reading when the circuit matters. Small components are cheap. Bad assumptions are not.

Worked example

Example: a balanced 10 ohm star converts to a balanced 30 ohm delta. A balanced 30 ohm delta converts back to 10 ohm star.

Practical checks before you trust the number

  • This calculator is for equivalent resistance networks.
  • Motor star-delta starters are related in name, but the design rules are different.
  • Label the three terminals before converting or the result is easy to misread.

Common mistake

The math is not hard, but the diagram matters. A swapped label gives a perfectly calculated wrong answer.

Sources and references

Related calculators

Frequently Asked Questions

In star, line current = phase current = V_phase ÷ Z = V_line ÷ (√3 × Z). In delta, line current = √3 × phase current = √3 × V_line ÷ Z. So star draws 1/3 of delta starting current for the same voltage. Example: a motor that draws 60 A in delta start draws 20 A in star.

Star starting reduces inrush current to 1/3 of delta direct-online (DOL) starting. Same reduction for starting torque. So a motor with 600% DOL inrush draws 200% in star. Acceptable for low-inertia loads; for high-inertia, star may not develop enough torque to start.

Star (Y) connection puts each winding across √3 less voltage than delta. With voltage reduced to V_line ÷ √3, the current per winding (and thus the line current) drops to 1/3. This sharply cuts inrush, breaker stress, and voltage dip during starting.

Use star-delta on motors above 7.5 kW where DOL inrush would dip the supply voltage too much. The motor must be designed for delta running at the supply voltage. Avoid star-delta for high-starting-torque loads (compressors, conveyors with high static load) — the reduced starting torque may stall the motor in star.

Star: line current = phase current = V_line ÷ (√3 × Z). Delta: line current = √3 × phase current = √3 × V_line ÷ Z. So for the same Z, delta draws 3× the line current of star. That 3:1 ratio is the basis of star-delta starting reduction.

Yes, indirectly. Starting torque also reduces to 1/3 of DOL torque in star. So if DOL torque is 200% of full-load torque (FLT), star torque is about 67% FLT. Check if this is enough to overcome load inertia — many compressors and conveyors won't start in star and need DOL or soft-start instead.

Yes. Lower inrush means less voltage dip, less mechanical shock, and less thermal stress on the motor. But the transition from star to delta itself causes a current spike (closed transition is gentler than open transition). For modern installations, soft-starters and VFDs are usually preferred over star-delta.