Psst: if you just want the calculator and don’t want to even SEE any math never mind all the exposition, you can skip straight to it.

## Why a calculator?

There are loads of denting charts online (often called reed or sett substitution charts) but in my opinion a chart just doesn’t cut it. For one thing, there are often entries missing. For another, they don’t explain the math behind the calculations, so that you’re dependent on the chart to provide magical answers.

Calculating how to sley a particular number of ends per inch (EPI) in a reed with a given number of dents per inch (DPI) is actually very simple:

- Divide the EPI by the DPI – long hand, to get a quotient and a remainder. Leave the remainder, if any, as a fraction.
- Reduce the remainder as far as possible.

That’s it. That’s all you need to do. The quotient is the number of ends to put in EVERY dent, and the remainder tells you how many dents get an extra thread.

*NB: The math is exactly the same for imperial and metric – just use ends per <unit> and dents per <that same unit> and Bob’s your uncle.*

For instance, take 20 EPI in a 12 dent reed. 20 divided by 12 equals 1 with a remainder of 8…

…which equals 1 and 8/12. So by the rule above, you’d put 1 (the quotient) into every dent, and eight more dents (the remainder) out of each 12 (the DPI) would get another one.

If you reduce the remainder from 8/12 to 2/3, it makes things easier: two dents out of every three gets an extra thread. (That’s the same as eight dents out of 12.)

Here’s a labeled diagram. I had it first before, but was afraid math averse people would see all the extra words and give up.

## Okay, but what does this look like in the reed?

The quotient – in this case, 1 – is the number of ends that goes in every dent:

Then you take those same dents in groups the size of the remainder’s denominator – in this case, 3:

And each of those groups gets additional ends equal to the numerator of the remainder – in this case, 2:

It doesn’t matter which of the three dents get the extra ends (for a total of two ends in that dent) and which doesn’t (just one end in the dent) but it’s a good idea to follow the same pattern all the way across. Note that there are eight extras per 12 dents, just like our original, UNreduced remainder.

The equivalent to this on most reed substitution charts would be 2-2-1. Or, more likely, 1-2-2, since reed substitution charts usually start with the fewer number of ends per dent. Either way, it means the same thing: two of the three dents get two ends and the third gets just one.

What if you want fewer EPI than DPI? It still works. All that happens is that the quotient is zero, so you don’t put ANY threads in every dent:

And there you have it: eight ends spread across 12 dents, which equals one inch, or 8 EPI in a 12 dent reed.

## The calculator, as promised

The math is simple but still requires mathing, so of course I’ve made a calculator that does it for you:

For example, if your desired EPI is 20 and your reed is 12 DPI, the results say “1 per dent, plus an additional 2 in every 3 dents.” This is what that looks like:

The “1 per dents” are shown in red and the “2 in every 3 dents” are blue (the groups of “every 3 dents” are bracketed in green). There are 12 dents in the diagram and, if you count up all the red and blue ends, you’ll see there are 20 total. Hey presto: 20 EPI in a 12 dent reed.

## Denting plan

I added the “denting plan” to the calculator for folks who prefer that format. It isn’t perfect: it’ll put all the extra ends at the end of the plan rather than distributing them evenly across, but it’s unusual to have a denting plan with so many dents that it makes a difference.

Still makes no sense to me. I need a chart. Math was the traumas of my entire education. I changed my major in college to avoid the required one term of statistics.

This is great! Love the colors and pictures as well as the words. I never liked relying on the charts without understanding the source of the numbers. Thanks for the great explanation!

Love it! Makes perfect sense the way you explain it.

Love it – useful and clear. Charts are great and all, but it is fantastic to see what is driving it so that where needed I can do it for myself.

One of the things about making things I love is breaking them down and understanding how they work so that I am not limited by what others prepare for me – so I love the teaching rather than just a chart or just a calculator (that said, I’ll definitely use the calculator lol).

Your calculator is awesome. I can never find my substitution chart when I need it. If I had to I could even do the math as you have explained it. Thanks!

Thank you!

Continues to feel like too much work….all hail the gods who gave us the reed substitution chart, although with my example (see next sentence) it wasn’t on the chart (jokes on me!). I did 32 epi in a 15 dent reed = 2 per dent plus 2 left over threads which I can throw in willy-nilly?? Or do I have to determine which end goes where to avoid more confusion….oh, nap time! I do admire your work ethic though!!!

32 EPI in a 15 DPI reed gives you the result “2 per dent, plus an additional 2 in every 15 dents.” So… yeah, you could just throw those extra two ends in wherever you want. I like to spread them out as evenly as possible, so I’d put one in the first seven dents and the other in the last 8.

The reason the result gives you so much leeway is that 32 and 15 have no common factors, so there’s no way to subdivide the 15 that makes sense. You can think of the “2 in every 15 dents” as being “1 in every 7.5 dents” and then round up the first time and round down the second.

If you could find a sett chart with 32 EPI from a 15 dent reed, it’d say 2-2-2-2-2-2-3-2-2-2-2-2-2-2-3, or something very similar. Which is, if you think about it, the same as “two per dent, plus one extra in 2 out of 15 dents.” It’d make the columns or row labels way too wide, though, so I doubt you’ll ever find it on a chart. 😉

I added a line to the calculator that prints out the results in the usual 1-2-2 format. You’re still not going to love the results for 32 EPI in a 15 dent reed, though. 😉

What do you think of the Ashenhurst Rule for determining sett? I found it in one of Peggy Osterkamp’s books. For me, it’s work pretty well figuring the sett of odd knitting yarns. I know this is not in the scope of your blog post today, but am curious about you think of the Ashenhurst Rule. I put the formula below. 🙂

WPI = 0.9 x √ of YPP

WPI = wraps (diameters) per inch

√ = square root of

YPP = yards per pound

I like Ashenhurst! It’s super mathy, so I super love it. 😉 My ability to apply it depends, as always, on the measurement of diameters per inch, which – as I’ve written about elsewhere – is not my strong suit. I haven’t yet tried applying Ashenhurst to WPI as measured right on a spool. I should do!

I made an Ashenhurst calculator since we had this conversation, too! It's on the Academy's membership site, though, along with my tie-up converters and the Twill Generator. If you'd like to try any of those out, we have a seven day free trial. 🙂 You can find all the deets on our main page: https://my.handweavingacademy.com/

This is great. One of the things I love about weaving is the logic behind the math of it all. You explained and demonstrated it perfectly.

I just finished watching your course on craftsy … awesome!!! And now, I was going to attempt to make something … have my yarn selected … no idea how to figure out how to put them in the reed … then poof! Your email this morning. Thank you so much!

Ps … do you have classes or a group or something for me to join? I love your detailed teaching method. So grateful.

Blessings to you and all you do ~ Karen

I’m teaching my first online class other than the Craftsy class right now and I have plans for many, many more! For more info on those classes when they’re available, you can join my mailing list (the form to join is on the home page of this website) and/or follow my Weaving with Janet Dawson page on Facebook. 😀

Love your calculator, now I can get the best use of the reeds I have! Thank you so much!

This is AWESOME! Thank you Janet!

Janet! You have saved me!

The charts all say I can’t get to 18 epi with a 10 dpi reed but your calculator says I can.

Thank you! Karen Shannon

Thank you!

Thank you, Janet – the calculator is great and so is the explanation !!!

Janet, you are making it easier for me (and others) to put up with this Covid, at least in the USA. It is a mess, especially right now,with all the politics going on. Thanks for that!

Is there room in Sydney for me? Ha, I am ready to move out of this mess! Between now and then I am loving following you and others to inspire weaving. I love Overshot and I keep one loom just for those projects. Frankly, I thought I new it all…. HA! You have taught me so much and thank you for that. I look forward to taking your next class too! You are a Weaving Rock Star!!!

I am working on your excellent Craftsy class "Floor Loom Weaving" I have just sleyed a 12-dent reed (I didn't;t have the 10-dent reed you suggested) 0 and 5undefined6 or 1-1-1-1-1-0, skipping every sixth dent. When I finished, the center of the warp was off-center in my loom by 1 1undefined2 inches. Of course, this makes sense because I skipped 36 dents over the width of the warp in the reed. But how can one calculate a better starting point so that the warp ends up more or less centered?

If you figure out half of the warp width and start sleying that distance to one side of center, the warp will be centered regardless of how many dents are filled or empty.

The good news is that, unless your reed is the full width of the loom and can’t be moved in the beater, you can just skootch the reed over in the beater by however much is required to recenter the warp.

Janet, I can't wait for another class from you. I love this denting calculator.

Really great description, Janet!! I love the mathy bits, and your diagrams are helpful too. And let us not forget the calculator. Very convenient ! Thanks!!

OH MY GOODNESS!! I finally get it! Thank you for explaining it so well. FYI – math was my favorite subject so that helps.

Fantastic resource! Used the calculator but understood the maths too. Amazing! Thank you so much.

New weaver here!

I love your math and I can completely understand it! Lol

I am stuck on how to thread my heddles with this substitution?

Do I thread the heddles the same way or use more heddles and thread on per?

You thread the heddles the same way regardless of how the threads are sleyed. On a rigid heddle, threading and sett are closely related because the same part of the loom controls both, but on a floor loom those two things are entirely independent.

Hi, Janet!

Thank you very much for this wonderful reminder! I don't know what happened today, but neither of my brain cells were having any of it.

Hope all's going well there and that you did get your power back. Brace yourself, tho. We're headed back into all over again.

Cheers,

Jon

Thank you so much!. I did not know this existed.

Wow! This is so helpful!!

… I understand the sleying, but I don't understand how you'd actually *weave* with a whole mess of ends in one slot/hole …

This doesn’t apply to a rigid heddle loom. On a shaft loom, the reed only serves two functions: to keep the threads at the right density and to bang the weft into place. It doesn’t control the structure of the cloth at all.

I sat still for at least an hour yesterday and figured this out for myself. The whole time I was thinking, "Janet ought to have a denting calculator. I wonder if she has time to help me make one."

Today I turned on my computer, googled "denting calculator," and here it is! Thank you for anticipating all the weaver needs.

Talk about timing! I JUST made another calculator related to sleying and sett. You can find it on the Academy’s site right here: https://handweavingacademy.com/figuring-out-epi-from-an-irregular-sleying-pattern/