The formula is based on guage and it's okay if that's foreign to you. Basically and assuming that you'll be felting/fulling this bag, size 13s usually guage out at 3 sts. per inch and 4 rows per inch, before felting. That depends on how you knit, number of strands and what type of yarn. I'll use the bag I'm working on as an example.
My plan is for a large totebag so the size will be 11" X 14" X 6" when completed and felted. I am using 100% wool (Patons Classic Merino).
11" - distance from top to roll or edge of bottom.
14" - distance from side to side, not including the gusset, front or back. There will be 2 sides.
6" - width of gussets.
Okay, you're wondering where the bottom comes into play...
The bottom is actually part of the gusset so you must know the size desired for the gusset to make the bottom.
My formula for this bag is: 27/63 x 2 = 180. This is the number of sts. you will have when your bottom is completed.
You will need 4 markers, 3 of one color, 1 of a distinguishable color to mark where your rounds begin.
The 29" needles will work just fine because the bottom of the bag is open until you knit up enough rows to seam it closed and still be able to work your rounds comfortably.
Make this chart on a notepad. You will begin the bottom by casting on 84 sts.(3+39+3+39) placing markers after st # 39, 42, 81 and 84. The marker after st #84 should be the odd color. Join and knit 1 round.
Round 2: (inc) KFB into the first st, knit to st before next marker, KFB, move marker, KFB, knit to st before next marker, KFB, move marker, knit to st before next marker, KFB.
You should then have 41 sts, marker, 5 sts, marker, 41 sts, marker, 5 sts, marker. Look at your notepad- you are at 5/41. Each additional, even numbered round should be an increase row and you will move up the chart to the next.
Round 3 and all following odd numbered rows: Knit
By the time you get to the top of the chart, there will be a total of 180 sts on your needles. Knit 88 rows from this point.
The way this increases lets the bag felt fairly evenly. So now you're at the top of the chart and want to count rows for the bag body... On the first round after your chart and bottom are completed, purl this row so it will be fairly easy for you to count rows from that point. You can also use this purled row to define your bag bottom.
Defining bag bottom: Pick up sts around using the purled defining row. Knit one round. Then BO all sts, loosely. This will make a ridge around the bottom. Remember to do this loosely or the ridge will be too tight when felted.
Logic: 27sts divided by 3= 9" (9"-3(shrinkage of 33%)=6"
63sts divided by 3= 21"(21"-7(shrkge of 33%)=14"
88rws divided by 4= 22"(22"-11(shrkge of 50%)=11"
Shrinkage is never exact and varies according to temperature, guage, aggitation, etc... so everything will always be approximate.
If this is not clear, holler! Will be glad to explain further... Mary