I don't know if this qualifies as a hack, but just do the math:
You need to have two ends to tie together of a somewhat appropriate length, estimated at 4 times the distance between the eyelet columns, or find a given constant you are satisified with
The laces needs cross over at the bottom and top of the eyelets, that is twice for each pair of eyelets
In other words, given 6 pairs of eyelets, and an approx distance between the left and right column of eyelets to be 5 cm (or 2 inches), you'll get a formula like the following:
- lace for tieing plus number of eyelets, multiplied with the distance between eyelet columns
- For 12 eyelet pairs with a distance of 5 cm (or 2 inches) this would give "2*4 + 12" multiplied with 5 cm (or 2 inches) giving 100 cm (or 40 inches)
Another way of putting this is: Start of with 40 cm (or 16 inches) and add 10 cm (or 4 inches) for each pair of eyelets
But, your safest bet is simply to pull out either the one lace which are still intact, or the two pieces of broken lace and simply measure the length.