Star and Delta Connection Calculator

Find the line and phase voltage, current and power for a load connected in star or in delta, and see what star-delta starting does.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

In star each winding sees the line voltage divided by root three and the line current equals the phase current. In delta each winding sees the full line voltage and the line current is root three times the phase current.

The same winding connected in star takes one third of the line current and gives one third of the power and torque that it does in delta. That is why a star-delta starter reduces the start current.

Formulas used

  • V_{ph} = V_L/\sqrt{3},\ I_L = I_{ph}\ \text{(star)}
  • V_{ph} = V_L,\ I_L = \sqrt{3}\,I_{ph}\ \text{(delta)}
  • P = \sqrt{3}\,V_L I_L \cos\varphi

Worked example

With the default numbers in the calculator above:

  1. Star: voltage across each phase: 239.60 V
  2. Star: line current (the same as the phase current): 7.99 A
  3. Delta: voltage across each phase: 415.00 V
  4. Delta: phase current: 13.83 A
  5. Delta: line current: 23.96 A
  6. Power in delta: 13.78 kW
  7. Power in star: 4.59 kW
  8. Star line current as a share of delta line current: 33.33 %

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Does star-delta starting suit every load?

No. The starting torque falls to a third as well, so it only suits loads that start light, such as fans and centrifugal pumps.

Which connection is the motor wound for?

The nameplate shows the voltage for star and for delta. For star-delta starting the motor must be wound for the full line voltage in delta.

Related calculators

Further reading: Standard electrical engineering texts (three-phase circuits). Motor wiring must be done by a licensed person.

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