Hit your local farm supply store or small engine shop if you want to get it local and buy some good quality starter rope, take a piece of your broken rope with and just compare size, i forget what size it is, 5/16" maybe, or its 1/4", dang this rotten memory of mine...
As for length, you need to turn the recoil by hand and have a large clamp to hold it, i usually spin it by hand pulling the remainder of the rope out then put a large strong spring clamp on it to hold it, cut the knot and remove the old rope, slide the new rope in, tie the knot and then hold the new rope and remove the clamp, then just let it slowly retract the new rope until it stops, then cut the rope and install the pull handle, pulling a little bit back out so as to preload the recoil starter a bit so it keeps the pull handle tight to the rope hole.
I have never measured the length of one, i just give the starter what it wants and cut it off. Buy at least a couple feet, i usually buy like 5-10 feet every time i buy stuff like this so i have extra laying around for the next rebuild.
I take it your electric start doesn't work?
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....