How your needle size really affects your gauge

Have you ever wondered why just a small difference in needle size can make a big difference in your gauge?  One of my knitting buddies has and it inspired us to do the math.  When you look at your needle size in Millimeter (mm) it tells you the diameter of your needle.  Now your yarn goes around the circle formed by that diameter; the circumference.  For example a 4  mm needle has a 12.56 mm circumference (Pi (3.14) times diameter) whereas a 4.5 mm needle will give you a 14.13 mm circumference.  So the difference is not 1/2 mm but 1.57 mm and this will be a bit more or less depending on how tight you knit. Thinking about it this way helps when you decide to go up or down a needle size. Happy knitting!