Why the answer is two numbers, not one
Increase 14 stitches evenly across a row of 82. The instinct is to divide, get 5.857, and stall. There is no single gap length that works, because 82 does not divide into 15 equal parts, and any attempt to force one leaves a stranded remainder that has to go somewhere.
The correct structure is that 14 increases split the row into 15 segments of plain stitches, and those segments have to sum to 82. Divide and you get a base of 5 with a remainder of 7, so seven segments run 6 stitches and eight run 5. No gap differs from any other by more than one stitch, which is the definition of evenly, and no two increases ever land in the same place. Written out, that is a row like K6, M1, repeated, shifting to K5, M1 partway across, and finishing with a plain segment that carries no increase after it.
Where the odd segments go is a choice with no arithmetic consequence and a visible aesthetic one. This calculator pushes them to the outer edges, alternating left and right, so the row is symmetrical about its centre and the wider gaps sit near the selvedges where the eye is least likely to pick them out. Pushing all the remainder to one end is equally valid arithmetic and looks lopsided.
Decreases eat two stitches each
The same structure applies going down, with one change that people routinely miss. An increase adds a stitch without consuming one, so all the original stitches remain available as plain segments. A decrease consumes two stitches to make one, so the plain fabric available for spacing is the starting count minus twice the number of decreases.
Take 100 stitches down to 88. That is 12 decreases, which consume 24 stitches, leaving 76 to spread across 13 segments. Divide and you get 5 with a remainder of 11, so eleven segments run 6 plain stitches and two run 5. The row reads as blocks of K6, k2tog with a short pair somewhere in the middle. If you had instead divided 100 by 13 and worked K7, k2tog throughout, you would run out of stitches before you ran out of decreases, which is exactly what happens to people who guess.
The hard limit follows from the same fact. With 100 stitches you cannot work more than 50 decreases in a row, and at 50 there is no plain fabric left between them at all. The calculator refuses rather than producing an instruction that cannot be knitted.
Shaping spread over rows instead of across one
A sleeve tapering from a 48 stitch cuff to an 84 stitch upper arm over 60 rows is the same distribution problem turned ninety degrees. The change is 36 stitches, worked 2 at a time as one increase at each edge, so 18 shaping rows. Restricting shaping to right-side rows halves the places they can go, leaving 30 slots for 18 rows, and 30 divided by 18 gives 1 remainder 12. So twelve intervals of 2 right-side rows and six of 1, which in written rows is increasing every 4 rows twelve times and every 2 rows six times, with the wider intervals split between the two ends so the taper is symmetrical.
Two things about that result are worth noticing. It is not a single interval, and patterns that give you one usually got there by adjusting the row count until it divided. And an even spread uses every row it is given, so the last increase lands on row 60 rather than short of it. If you want the last inch worked plain before the underarm, take those rows out of the figure you enter and work them afterwards.
When the change does not divide by the shaping rate
Increasing 2 stitches per row cannot produce an odd total change. Ask for 35 stitches at 2 per row and one row has to do something different: 17 rows of 2 plus one row of 1. Put that odd row where it disappears. On a sleeve the underarm end is the answer, because the last inch before the join is hidden in a seam and nobody has ever looked at it. On a raglan the odd row is worse and it is usually better to change the target by one stitch than to break the symmetry.
The same logic decides the direction of a rounding error anywhere in shaping. Ask what will be visible in the finished object, and let the arithmetic lose in whatever place nobody will look.
Getting the numbers to put in
Everything on this page takes stitch counts as given. If the counts came from a pattern written at a gauge that is not yours, convert them first on the gauge converter, because a taper spread over the pattern row count at your row gauge produces a sleeve of the wrong length. If you are working out the counts from finished measurements, the size planner turns inches into stitches and rows and gives you the row map to place the shaped section in.
Questions people ask
What does increase evenly across the row actually mean?
It means place the increases so that the plain stitches between them are as equal as possible, with no two gaps differing by more than one stitch and no two increases worked into the same place. It does not mean find a single number that divides, because usually none exists. With s working stitches and n increases you have n plus 1 segments to fill: divide s by n plus 1 to get the base gap, and the remainder tells you how many segments get one extra stitch. Distributing that remainder is the whole job, and it is what this page does.
Why is the last segment different from the others?
Because it has no increase after it. Working n increases across a row produces n plus 1 stretches of plain fabric, and the last one runs from the final increase to the end of the row with nothing following. If you write the instruction as n repeats of knit-then-increase, you will finish the last repeat with an increase sitting right at the selvedge, which distorts the edge and makes seaming awkward. The correct instruction always ends with a plain segment, which is why the written row here finishes with a bare stitch count.
How do I space increases on a sleeve?
Switch the mode to over a number of rows. Enter the cuff stitch count, the upper arm stitch count and the number of rows between the cuff and the underarm, and set 2 stitches per shaping row for the usual one-at-each-end taper. The result is normally two intervals rather than one, such as every 4 rows a dozen times then every 2 rows six times, because the numbers rarely divide. Work the wider interval first if you want the sleeve to flare late, and the narrower first if you want the width established early, but keep the number of each as calculated.
Can I shape on wrong-side rows?
You can, and sometimes you must, but it costs something. Shaping on right-side rows only gives even intervals in whole numbers of rows and puts every increase or decrease on the face where it can be worked with a matched pair that leans the right way, which is what makes a fully fashioned edge look deliberate. Shaping on both sides doubles the available slots, which matters when a steep taper will not otherwise fit, at the price of a less regular edge. Set the option to no only when the calculator tells you the rows will not fit.
Does this work for crochet?
Yes, with the same structure and different vocabulary. Increases in crochet are usually two stitches worked into one stitch rather than a made stitch between two, so an increase consumes a stitch instead of sitting between them, which shifts the segment arithmetic by one. Decreases work identically: a single crochet decrease consumes two stitches exactly like k2tog. In practice, treat the increase case as the decrease case for crochet, since both consume from the row, and check the final count against the number the calculator reports.