Seems to me you just pick a day in a winter month. Measure the length with a ruler and note that length. Then the same day the following month, measure again. That would tell you what you've gained in a month. Then you can consider that your general growth rate (per month). If you want to be really technical, you can keep track of the lengths you achieve over several months and then add those changes in length together and divide by the number of months you kept track and you'd have an average of your growth rate/mth.
For instance, in Dec you gain 0.5 inch, and 0.7 inch in Jan and 0.6 inch in Feb. That is a total growth of 0.5 + 0.7 + 0.6 = 1.8 inches.
That was over a period of 3 months so we divide 1.8 by 3 = 0.6 inch
So your average growth rate over the three months is 0.6 inch per month.
ETA: Just noticed that Sonce had already responded. Sorry for being redundant.