How much string do I need to make a korowai?

I have been asked this question many times and unfortunately there is not a simple answer except LOTS.  Firstly you need to decide what string you will use.  In NZ we can get three sorts of mop string in large rolls, two  (a thick and a thin, both 4kg and costing around $100 with gst and postage) from ICB Cleaning supplies in Auckland and and thin 4.5kg from Browns Brushware also in Auckland for about $130.  These are the main ones used so I will talk about these.
When you have decided which string I recommend doing a sample piece so that you can work out your personal tension and work out from this.  It is a good idea to keep a record of what you make, how long and how many the whenu and of what material etc.  No matter how much I tell others to do so I am a bit lax myself so these ideas have been hard to work out but here goes.
Next is to decide on a pattern.  Are you going full feather with taaniko at the top and mawhitiwhiti on the back or will you have mawhitiwhiti within the kaupapa of the cloak?   Mawhitiwhiti takes up more string as the diversion uses more each time.  But assuming you are making a straight cloak with taaniko and mawhitiwhiti then decide on a finished length.  To this finished length add about 10cm for the turnover and mawhitwhiti on the back. Now add an extra 1/4 that length for somehow it seems to need that.  And then double the whole amount for casting on two whenu strings.  So for instance if your desired length of 110cm. Add 10cm for turnover making 120cm. Now add an extra 1/4 that length (30cm as the weaving takes it up) making it 150cm. Then you double that for it to be cast on in twos.  Oh and if you want a plait and/or mawhitiwhiti on the sides they will need to be half the length again so that they don't get too short. So lots of maths involved. Make sure when you measure the string you don't stretch it but loosely wind around whatever you are measuring on. I have my weaving board with nails which I also use to wind off my whenu.  Now don't sue me if this is too short.  Its better to cut longer than necessary and use any left overs to make small pieces for framing as gifts than to get up to the top and discover its going to be too short.

Now we come to how many.   I have found that as I go up the korowai it gets skinnier. I don't know why. Maybe my tension gets tighter as I put feathers in. However that needs to be allowed for and don't be surprised if it happens. I can sometimes be 10cm shorter in width at the top than at the bottom. But that's ok because the width doesn't show so much unless lying flat and it is better to be that way round as the cloak may come around the hips more. I don't bother with shaping and few I know do. So this is where your tension piece is really helpful as your tension and mine might be different.  Of course the different strings require differing amounts too.  If I use the thinner strings I generally use them double.  This means each 'whenu' is actually two strings held together and woven as one.  If I was using them singly I would use a finer aho cotton than the 4ply knitting and crochet cotton I use at present.  Otherwise there is a tiny gap between the whenu which would make it unstable and the feather down and stems would poke through making the back unsightly and scratchy.
So I can cast on less than 300 ICB thin used double and more than 350 Browns thin double to make an adult cloak.  It also depends on whether you want it to come together in the front or for the strings to tie with a gap in the front so what you wear under can be seen at the top.  Also whether the korowai is for one person or a family of differing sizes.
All I can tell you is what I would cast on for me to achieve 115cm at the top, say, I would probably cast on 290 double  in ICB thin (or 360 double of Browns string.)  ( 250 thin ICB double ended up 100cm wide on the Wakari school cloak I have just finished) You can see from this that the advantage of the ICB string is that it requires fewer stitches per row  than Browns and so takes that much less time.

I would like to hear if others have a formula to tell people.

I hope this helps with approximating what you need but It is not an exact science at least not in my experience.