With the pattern below you can make french heel also known as round heel for cuff down socks. The pattern works for any stitch count and gauge. Just insert the stitch count for your sock and the calculator will do the math for you!
On knitgrammer.com you can find also patterns for dutch heel (cuff down), afterthought heel (toe up or cuff down), flap and gusset heel for toe up socks and german short row heel (toe up or cuff down).
sts on my needles
The pattern is written for the magic loop method, but can be adjusted for double pointed needles as well. You should now have a total of 56 sts divided evenly on two needles (28 sts / needle).
Following rows 1-2 are worked flat on needle 2 only.
Row 1 (RS): knit all
Row 2 (WS): k1, p until 1 st remain, k1
Repeat rows 1 & 2 until your heel flap has 28 rows.
Turning the heel
Following rows 3-6 are worked on needle 2 only.
Row 3 (RS): k16, ssk, k1, turn
Row 4 (WS): mds, p5, p2tog, p1, turn
Row 5 (RS): mds, k to double st, ssk, k1, turn
Row 6 (WS): mds, p to double st, p2tog, p1, turn
Repeat rows 5 & 6 4 more times. A total of 16 sts remaining on needle 2.
Resume working in the round.
K to end of needle 2. With needle 2 pickup and knit 14 sts along the left side of heel flap (pickup the thread between the garter bumps). The beginning of round / end of needle 2 will be now here. K to end of needle 1. Pickup and knit 14 sts along the right side of heel flap. K to end of needle 2.
You should have now a total of 44 sts on needle 2 and 28 sts on needle 1.
Needle 1: k all
Needle 2: ssk, k until 2 sts remain, k2tog
Needle 1: k all
Needle 2: k all
Repeat rounds 7 & 8 7 more times. A total of 28 sts remaining on needle 2.
The heel is now finished.
k = knit
mds = Make double stitch. Slip 1 stitch purlwise with yarn in front. Bring yarn up, over and back to pull on the slipped stitch until it slides around to show two legs. If you are unfamiliar with the technique see a tutorial with images here.
p = purl
p2tog = purl two stitches together
ssk = Slip 1 st kwise, slip another st kwise, then slide the left-hand needle into the front part of both stitches and knit them together.
st = stitch
RS = right side
WS = wrong side