Where the seven eighths comes from
Every chart says the same thing: to make two half square triangles finishing at a given size, cut two squares seven eighths of an inch larger. The number looks arbitrary until you draw it.
A finished HST needs a quarter inch of seam allowance on all four of its edges, which is half an inch across. That accounts for the first half. The remaining three eighths is the diagonal seam. The quarter inch is measured perpendicular to the stitching line, and the stitching line runs at forty five degrees, so measured along the edge of the square it occupies a quarter inch times the square root of two, which is 0.3536. Half an inch plus 0.3536 is 0.8536, and 0.8536 rounded up to something a ruler can find is seven eighths.
That means the rule belongs to the quarter inch seam and to nothing else. Sew a three eighths seam and the addition becomes 0.75 plus 0.53, which is 1.28, not 0.875. Sew an eighth inch seam on a miniature and it becomes 0.25 plus 0.177, which is 0.427. The calculator computes it rather than quoting it.
Two, four and eight at a time are the same square, scaled
This is the tidy part of the arithmetic and it is not usually stated. Call the two at a time square C. Then:
| Method | Cut square | Units from two squares | Bias on |
|---|---|---|---|
| Two at a time | C | 2 | The diagonal, under the seam |
| Four at a time | C x 1.4142 | 4 | The two outside edges |
| Eight at a time | C x 2 | 8 | The diagonal, under the seam |
Because area goes up as the square of the side, the four at a time square has twice the area and makes twice as many units, and the eight at a time square has four times the area and makes four times as many. Before the cut sizes are rounded up to a ruler mark, the cloth consumed per finished unit is identical in all three. Nobody saves fabric by switching methods.
What does change is everything else. Eight at a time is four seams and two cuts for eight units, against eight seams and eight cuts for the same eight units done in pairs. It is dramatically faster. And the squares pack differently: for a three inch finished unit on 43 inches of usable width, the 3.875 inch two at a time square fits eleven across with three eighths left over, while the 7.75 inch eight at a time square fits five and leaves four and a quarter inches spare on every strip.
Why four at a time has a reputation
Four at a time is the odd one. You sew two squares together all the way round, then cut both diagonals, which produces four units whose outside edges were the cut diagonals. Those edges are on the true bias, and true bias in a woven cotton stretches. Press one carelessly and the unit is no longer square; feed it under a presser foot and the top layer travels.
Two at a time and eight at a time both put the bias on the diagonal seam, where the stitching stabilises it and the outer edges land on the lengthwise and crosswise grain. That is why those two are the usual recommendation despite four at a time being a perfectly good use of a square.
If you want four at a time anyway, add oversize and trim. A quarter inch of extra on the cut square gives you something to cut back to, which is the standard answer to bias distortion in every method.
Oversize and trim, or cut exact and hope
Cutting exact means the finished unit is only square if the seam was exactly right, the pressing did not stretch anything, and the two squares did not shift under the foot. That is a lot of conditions, and it is why an unfinished HST measured across a batch will vary by a sixteenth or more.
Cutting oversize and trimming replaces all of those conditions with one operation you can control. Add a quarter inch, sew, press, then square each unit to the unfinished size with a ruler. It costs cloth and it costs time, and it is the only reliable way to get a hundred identical units. For a scrappy quilt where nothing has to line up it is unnecessary. For a design where four HSTs meet at a point, it is the difference between a point and a smudge.
The trim target is the unfinished size: finished plus twice the seam allowance. A three inch finished unit trims to three and a half. That is the number to set your square ruler to, not the cut size.
Fitting the squares to the bolt
The last step is packing. Squares get cut from strips across the width of the fabric, so what matters is how many of your cut size fit into the usable width after the selvages come off. A 44 inch bolt with an inch trimmed gives 43 inches: eleven 3.875 inch squares, or seven 5.5 inch, or three 11 inch. The leftover at the end of each strip is scrap unless something else in the quilt happens to want it.
This is the same problem as laying out any rectangular part on fixed stock, and the sheet nesting and yield calculator handles the general version. For the whole quilt top rather than one unit, the quilt block and sashing layout calculator works out the grid these units go into, and the fabric yardage calculator handles a mixed list of piece sizes.
Questions people ask
Is the seven eighths rule exact?
No, it is 0.8536 rounded up to 0.875 so that it lands on a ruler mark. The extra 0.0214 inch per square is deliberate slack and it does no harm. Where the rounding matters is at small seam allowances and small units: a scant eighth inch seam wants 0.427 added, and rounding that to a half inch is more than a sixteenth of extra on a unit that might only finish at an inch. Switch the rounding to exact to see the raw number, then decide what your ruler can actually do.
Does eight at a time save fabric?
No. It uses exactly the same cloth per finished unit as two at a time — the square is twice as wide, so four times the area, and it makes four times as many units. What it saves is handling: two cuts and four seams produce eight units instead of eight cuts and eight seams. Where it can lose is packing: for a three inch finished unit on 43 inches of usable width, the 7.75 inch square fits five across and leaves 4.25 inches of the strip unused, while the 3.875 inch two at a time square fits eleven and leaves 0.375 inches.
Why do my HSTs come out too small?
Almost always the seam. A true quarter inch measured from the needle produces units a thread or two small once the seam is pressed to one side, because the fold takes up fabric. Quilters compensate by sewing a scant quarter, a hair under the mark. The other common cause is pressing: dragging an iron across a diagonal seam stretches the bias and the unit distorts rather than shrinks. Set the iron down and lift it rather than sliding. If neither fixes it, cut oversize and trim, which makes the problem irrelevant.
What size should I trim to?
The unfinished size, which is the finished size plus twice the seam allowance — three and a half inches for a three inch finished unit at a quarter inch seam. That is the figure shown on the results as the unfinished unit. Do not trim to the cut size, which includes the diagonal allowance that the seam has already consumed, and do not trim to the finished size, which leaves you nothing to sew with.
Can I use two different methods in one quilt?
Yes, and the units are interchangeable as long as they finish at the same size, because the finished size is the only thing the quilt sees. The practical reason not to is the bias. Four at a time units have stretchy outer edges and the other two do not, so a block that mixes them can behave inconsistently under the iron. If you do mix, trim everything to the same unfinished size and handle the four at a time units gently.