Unless you work a sample, it's difficult to tell if your work will end up the required 20 x 20 size. If you work on the diagonal, you can be certain that it will - no matter the yarn or needle size. Here's how:
Cast on 2 stitches
K1 inc 1 in last st.
K2 inc 1 in last st.
K3 inc 1 in last st
Continue this pattern in every row until the side of the work measures 20cm.
K1 row without increasing
Now do the reverse - k along row and decrease (K2 tog) at end of each row to last two stitches. Put last st over first and pull tight, leaving long tail for sewing to next square. (Actually, I usually leave one at the beginning too as 2 sides of every square have to be joined)
It's easy to work in stripes, always joining colours at the beginning of a row and sewing in ends by running them in along the edge. (This makes them double-secure when the squares are joined together.)