Why does multiplying 120 by 1.73 give me 208 volts in a 3 phase system?

[Evil Bunny]

Ok... This is a simple question that I'm having a hard time with. I'm forgetting something that I learned and I want to clear it up...

I know that a 120/208 3 phase system has 3 hot leads that are 120 degrees out of phase with each other with respect to the neutral.

If you multiply 120 X 1.73 (square root of three), you get 208 volts. I'm not sure why...

If I add 120 + 120@120 degrees, my calculator tells me the answer is 120@60 degrees.

I expected it to say 208.

Why? What am I getting confused here?

 

[uart]

Hi Evil Bunny. The voltage between two points is equal to the difference in their voltages, not their sum.

Try calculating 120 - 120@120 degrees.

 

[Evil Bunny]

Thank you!