Line Current vs Phase Current in Star and Delta Connections

Two currents, two locations

In a balanced star connection, line current equals phase current. In a balanced delta connection, line current is √3 times phase current. The distinction is where the current is measured: line current flows in a supply conductor; phase current flows through one load winding or branch.

Using the word “current” without stating the location is an invitation to mix them up.

Balanced connection	Line current from phase current	Phase current from line current
Star (wye)	IL = Iph	Iph = IL
Delta	IL = √3 × Iph	Iph = IL / √3

That is the quick answer. The equations apply to balanced sinusoidal phase currents; they do not choose a motor’s terminal links or describe its starting transient. Check a 20 A delta-branch example in the line/phase converter. For the related voltage definitions, see line-to-line versus phase voltage.

Balanced star connection

In star, each load phase connects from a line to the common star point. For a balanced load:

IL = Iph

Each phase sees phase-to-neutral voltage, while line-to-line voltage is √3 times larger:

VLL = √3 × Vph

If a star-connected winding carries 20 A, the corresponding line conductor carries IL = Iph = 20 A under the balanced assumption. The current does not acquire a √3 factor in star.

Balanced delta connection

In delta, each phase branch connects between two lines. Each branch therefore sees line-to-line voltage:

Vph = VLL

The line current is the vector difference of two branch currents. For a balanced load:

IL = √3 × Iph

If each delta branch carries 20 A, line current is √3 × 20 = 34.64 A. Conversely, a measured 34.64 A line current would imply approximately 34.64 / √3 = 20 A in each balanced delta branch. The line conductor carries the vector difference of two branch currents; this is why the result is not simply 2 × 20 A.

Why motor labels can be confusing

A dual-voltage motor nameplate may show different connection diagrams and current ratings. The links in the terminal box determine the voltage applied to each winding. A current calculated from total three-phase power is line current; it should not automatically be compared with an assumed winding current without checking the connection and nameplate.

Star-delta starting introduces another operating state. Starting connections, transition and running connections have different current relationships. A steady-state power calculator does not reproduce the transient behavior.

A useful identification habit

Label measurements and calculations explicitly:

• IL1, IL2, IL3 for line currents;
• Iph for current in one load phase;
• VLL for line-to-line voltage;
• Vph for voltage across one phase.

Then draw or confirm the connection. This small discipline prevents a √3 error from passing through load schedules, cable checks and protection calculations.

When the balanced relationship is insufficient

Unequal impedances, open phases, supply unbalance and harmonic currents require more detailed analysis. Measure all line currents and relevant voltages, and use manufacturer information for equipment connections. The star/delta relationships are a foundation, not a substitute for inspecting the actual circuit.

For a three-phase four-wire feeder, a separate fundamental neutral-current calculation can illustrate what unequal phase currents leave in the neutral. It does not represent harmonics. If a measured harmonic spectrum is available, the third-harmonic worksheet addresses one different, tightly limited component.

Where measurements can mislead

A clamp around a supply conductor measures line current. Accessing a winding current may require internal conductors or drive data and should not be attempted without appropriate procedures. If a variable-speed drive sits between the supply and motor, its input line current and motor-side phase current are different quantities with different waveforms.

Record the measurement location: upstream of a drive, downstream of a drive, in a line conductor, or in an accessible winding lead. Also record whether the equipment was starting, accelerating or at steady load. Without that context, two valid readings may appear to contradict each other.

Use the balanced formulas as a model check

For a balanced 15 kW load at 415 V and PF 0.85, the three-phase current calculation estimates about 24.55 A of line current. Converting it to a winding current requires the actual star or delta connection.

If the three measured line currents differ, avoid averaging them merely to make the balanced formula fit. Phase imbalance can affect heating and equipment performance. Preserve the individual readings and move to a phase-by-phase assessment.

Convert a line or phase quantity. The diagram changes with the selected connection. Phase refers to one load winding or branch, not automatically to neutral.