A half-square triangle is the most-used unit in patchwork: two right triangles joined along their long edge to make a square. Pinwheels, flying geese variations, sawtooth stars, broken dishes and a large share of every sampler quilt are built from them. The arithmetic is small but unforgiving, because the diagonal seam consumes fabric in a direction that does not line up with the ruler, and a unit cut a sixteenth short will not square up.
This half square triangle calculator gives the cut size for any finished size and seam allowance, for all three common construction methods, and then works out how many squares and how much fabric the whole batch needs. Arb Digital publishes it as part of a free tools library of practical arithmetic. It sits next to the quilt fabric calculator, which sizes a whole quilt top and its backing, and the fabric yardage calculator, which converts an area of fabric into yardage — this page is specifically about the HST unit and its cutting geometry.
What This Half Square Triangle Calculator Does
You give it the finished size — the size the unit measures once it is sewn into the quilt with its seams taken — plus your seam allowance and how many units you need. It returns the size to cut your starting squares, the unfinished size of the units that come off the machine, the number of squares required from each of the two fabrics, and the length of fabric that many squares occupies across your usable width.
All three methods produce the same unit. Two-at-a-time pairs two squares, sews on both sides of the drawn diagonal and cuts between the seams. Four-at-a-time sews all four outer edges of a pair and cuts both diagonals. Eight-at-a-time uses much larger squares with two drawn diagonals. Method choice is about batch efficiency and how much you enjoy trimming, not about the result.
How to Use It
- Enter the finished size. If your pattern says "3 inch HST", that is almost always the finished size. If it gives a cut size, you do not need this tool for that step.
- Confirm the seam allowance. A quarter inch is standard, and a scant quarter inch — a thread or two narrower — is what most quilters actually sew to allow for the fold of the pressed seam.
- Pick a method. Two-at-a-time for small numbers and scraps, eight-at-a-time when you need dozens of identical units from two fabrics.
- Decide whether to oversize. Adding an eighth or a quarter inch and trimming every unit down afterwards is slower but far more accurate.
- Read the fabric length. That is the length needed from each of the two fabrics at your usable width, before any allowance for shrinkage or error.
The Formula / How It's Calculated
The unfinished unit is the finished size plus two seam allowances, because a seam is taken on each side. The starting square must be larger again, by the amount the diagonal seam consumes. That extra is the seam allowance multiplied by the square root of two, because the seam runs at 45 degrees to the grain of the ruler.
So the exact two-at-a-time cut size is finished + 2a + a√2, where a is the seam allowance. At a quarter inch that is finished + 0.5 + 0.354 = finished + 0.854 inch, which rounds up to the familiar 7/8 inch. The four-at-a-time square is that exact figure multiplied by √2, and the eight-at-a-time square is it multiplied by two. Every result is then rounded up to the nearest eighth of an inch, because that is what a quilting ruler can actually be read to.
Worked example, which is what the page loads with. A 3 inch finished HST at a quarter-inch seam: exact cut size 3.854, rounded up to 3 7/8 inch squares. The unfinished unit is 3.5 inch. Forty units by the two-at-a-time method needs 20 squares of each fabric. Across 42 inches of usable width, ten 3 7/8 inch squares fit per row, so 20 squares occupy two rows, or 7 3/4 inch of fabric length from each colour. Switching to the eight-at-a-time method changes the cut size to 7 3/4 inch squares and needs only five of each.
Why the Diagonal Seam Costs √2, Not 1/2
This is the part that trips people up, and it is worth understanding rather than memorising. On the straight edges of the block, a quarter-inch seam removes a quarter inch from each side — half an inch total, measured along the ruler. The diagonal seam is different: it runs at 45 degrees, so a quarter inch measured perpendicular to that seam is not a quarter inch measured along the square's edge. Projecting the seam allowance back onto the horizontal and vertical directions multiplies it by the square root of two, roughly 1.414.
That gives 0.25 × 1.414 = 0.354 inch of additional square needed, which added to the half inch for the two straight seams gives 0.854. The 7/8 rule rounds that up by a bare twentieth of an inch. Change the seam allowance and the relationship holds: at an eighth-inch seam the extra becomes 0.25 + 0.177 = 0.427, so the rule of thumb changes entirely. This is why the calculator takes seam allowance as an input rather than hardcoding 7/8.
Bias Edges Are Why HSTs Come Out Wonky
Cutting a square across its diagonal produces edges on the bias, and bias-cut cotton stretches. In the two-at-a-time method the seam is sewn before the cut, so the bias edge is stabilised by the stitching — one of the reasons that method is recommended for beginners. The four and eight-at-a-time methods cut the diagonal after sewing the outer edges, so the units come apart with bias on two sides and can distort under the iron.
The practical mitigations are all about handling rather than arithmetic: press rather than iron, so the fabric is lifted and set down rather than dragged; press the seam before opening the unit to set the stitches; and starch or size the fabric before cutting if distortion is a recurring problem. Cutting oversize and trimming to the unfinished size afterwards fixes almost everything else, at the cost of some fabric and a lot of time at the cutting mat.
Trim Down or Cut to Size?
Cutting exactly to size is fast and wastes nothing, and it works well when the finished units are large, your quarter-inch seam is genuinely consistent, and the pattern is forgiving. Cutting oversize and trimming produces units that are accurate to the thread, which matters enormously when HSTs are joined into pinwheels or sawtooth borders where every seam intersection has to line up.
The rule of thumb worth applying is that error compounds with the number of joins. A single HST in a nine-patch can be a sixteenth out and nobody will see it. Sixteen HSTs forming a border will accumulate a whole quarter inch of drift from the same error and the border will not fit the quilt top. If your project has long runs of units, use the oversize option here and trim. The quilt fabric calculator handles the top-level yardage once you know your block sizes.
Seam Allowance, Scant Quarters and Why Blocks Finish Small
A quarter-inch seam is the near-universal standard in patchwork; the piecing instructions in university extension quilting guides such as Utah State's panel quilt with prairie points and Iowa State Extension's Introduction to Quilting both specify it throughout. But the fabric folded over at a pressed seam takes up a small amount of width, which is why blocks sewn at an exact quarter inch tend to finish a fraction small.
The standard fix is the scant quarter inch: sew one or two thread widths inside the quarter-inch mark so that the pressed seam finishes at a true quarter inch. It is not something to enter in the seam allowance field — the field wants your nominal allowance, and the scant adjustment happens at the machine. If your blocks consistently finish an eighth of an inch small across several units, the seam is the place to look, not the cutting.
Arb Digital maintains a large free tools library covering measurement, materials and everyday arithmetic, and our team is happy to point you at the right one.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Confusing finished and unfinished sizes — the unfinished unit is half an inch bigger at a quarter-inch seam, and using the wrong one throws every calculation out.
- Applying the 7/8 rule at a different seam allowance — the extra depends on the seam allowance times the square root of two, so 7/8 is only correct at a quarter inch.
- Rounding the cut size down — always round up to the next eighth. A square cut short cannot be recovered.
- Ignoring bias stretch — pressing rather than ironing, and setting the seam before opening the unit, prevents most distortion.
- Cutting exactly to size for long borders — small errors compound across many joins, and a run of sixteen units can drift by a quarter inch.
Related Free Tools From Arb Digital
Use the quilt fabric calculator for whole-quilt yardage, the fabric yardage calculator to convert an area into yards, the curtain fabric calculator and circle skirt calculator for other cutting layouts, the cross stitch calculator for counted work, and the cm to inches converter when a pattern is metric. Everything else is in the tools hub.
Frequently Asked Questions
Because two straight seam allowances take half an inch and the diagonal seam takes the seam allowance multiplied by the square root of two, which is 0.354 inch at a quarter-inch seam. The exact figure is 0.854, and 7/8 is that rounded up to the nearest eighth so it can be read on a ruler.
Finished size is what the unit measures once it is sewn into the quilt and its own seams are taken. Unfinished size is what it measures as it comes off the machine, which is the finished size plus two seam allowances — half an inch larger at a quarter-inch seam.
No. All three produce identical half-square triangles. They differ only in how many units come from each pair of starting squares and in how much bias edge is exposed during construction, which affects how easily the units distort.
It depends on the project. Trimming produces units accurate to the thread, which matters when many HSTs join into pinwheels or borders because small errors compound across seams. For a few units in a forgiving block, cutting to size is faster and wastes less fabric.
Usually because the fabric folded over at the pressed seam takes up a small amount of width. Sewing a scant quarter inch — a thread or two inside the mark — compensates. If units are consistently an eighth small across a batch, look at the seam rather than the cutting.
The arithmetic works in any unit, but the fields and the eighth-inch rounding are set up for inches, which is how HST patterns are almost always written. Convert a metric finished size to inches first, calculate here, and convert the cut size back if you need to.
The fabric length shown is the minimum the squares occupy at your usable width, with no allowance for shrinkage, cutting error or directional prints. Add a margin, and prewash before cutting if the quilt will be washed, since cotton shrinks and shrinkage varies between fabrics.
This tool performs cutting arithmetic only, based on the finished size, seam allowance and fabric width you enter. It cannot account for fabric shrinkage, directional prints, cutting error or the accuracy of your own seam, and it is not a substitute for making a test unit and measuring it before cutting a whole batch.
