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:

1. Divide the EPI by the DPI – long hand, to get a quotient and a remainder. Leave the remainder, if any, as a fraction.
2. 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.