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I would like to know how to calculate how much thread I need for a pattern when I know how many points I have for each colour.

I know that it is highly dependent on how the points are spread on the pattern and how many time I have to stop the tread. But I am looking at a base value when all the points are contiguous, to use it as base for estimation of more complex design.

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From my knitting experience, the empirical way to find out would be a swatch - make N stitches, then rip it out. Measure how much thread you used and divide by N to get a rough estimate of thread per stitch.

If you want to calculate it from first principles, you also need to take into account the fabric count. For example, 14-count Aida has 14 holes per inch. That means each "X" is made inside a block which is 1/14" on each side. So the diagonal of the square is then sqrt(2)/14 inches, so an X is 2 * sqrt(2)/14.

Of course, you aren't just stitching the front of the "X". This is where the way you arrange stitches makes a difference. You may want to adjust this based on your method, but for contiguous areas I usually end up with a couple horizontal lines on the back. This corresponds to another 2/14" of thread (edges of the square your "X" is stitched into).

Putting it all together, for a fabric count C and number points N:

N * (2*sqrt(2)/C + 2/C)

As you note in your question, I would of course add more length depending on how complicated the areas are, and to allow for weaving in ends.

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    Cross stitching swatches take much more time than knitting or crocheting them. You're better off just starting on the project than wasting the time on a swatch. The math version seems much more viable to me. I'll bet there's actually a site that does this as the sites that convert images into cross stitch patterns can often tell you how many skeins of floss to buy.
    – Catija
    Jan 23, 2017 at 15:07
  • @Catija I did find this site on a cursory search which talks a bit about how they estimate, but unfortunately it's only for the patterns they sell. This site has some example calculations, but it's mostly rule of thumb and based on a swatch. I agree that gets very tedious, even with knitting! :)
    – user812786
    Jan 23, 2017 at 21:35
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An alternative to making swatches but still getting measurements from embroidery you have done, work with pre-cut lengths and count what you have done with a given number of lengths.

This will work best if you work a fair block or a lot of smaller blocks, so you can use several lengths and have something to count.

This will obviously work when you can order (more) after you have started (but it might be a way to calculate whether you had ordered enough or whether the pattern came with enough tread to allow you to finish it, (while it is still possible to order extra.)
If you do not want to order before you have done your test, you can do a smaller canvas, as long as you use the same fabric, tread and stitch the result will be valid for the bigger project.

This is the way knot tyers measure lengths for some projects, not undoing but by calculating how much was done with a known length.

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