How line voltage is calculated

To see this, draw an equilateral triangle. Label each vertex A, B, and C. These represent the three phases A, B, and C. The phase voltages are AB, BC, and CA, when connected delta. The triangle shows that the three phases are 120 degrees apart. More importantly, the vectors AB, BC, and CA show how the three phases, added up together, come back to the starting point.

Now, lets draw a point in the center of the triangle and label that point N. N is neutral. Draw three lines from A, B, and C to N. These represent the three phases A, B, and C also, called AN, BN, and CN, when connected star. These are also 120 degrees apart, but the reference point is N, not each of A, B, and C. (This is the fundamental difference between delta and star.)

Now, draw a dotted line from N to the halfway point of AB. You could also pick BC, or CA - the results will be the same. Call this point R. Now, lets do some trigonometry...

The angle ARN is 90 degrees, and the angle NAR is 30 degrees. We know that cosine theta is adjacent over hypontenuse, so cosine 30 is AR over AN. Lets solve for AN, in terms of AR and thus AB.

cos 30 = AR / AN
AN = AR / cos 30
...but AB = 2 AR so...
AN = AB / 2 cos 30

Now, lets look at 2 cos 30. It turns out that 2 cos 30 is the square root of 3, so AN = AB / square root of 3.

Back to the picture. AN is line voltage and AB is phase voltage, so line voltage = phase voltage / square root of 3, or line voltage = phase voltage / 1.732.

Line voltage is phase voltage multiplied by square root of 3
In a "Star" or Wye system think of three windings arranged so one end of each is connected together and grounded (this will give you the shape of a Y). The voltage across each winding is the "Phase voltage" (voltage to ground of say 120V). The other end of each winding would be your "hot" or phase conductors in your panel. "Line voltage" is the voltage between any two phases, you would be measuring across two windings arranged 120 degrees out of phase. 120V x 1.73 equals 208V.