How to Make Half Square Triangles: Three Methods and a Size Chart

There is no formula for a half square triangle.

That is the thing nobody tells you, and it is why the numbers never seem to agree. There are three common ways to make the unit, they cut different numbers of triangles out of the same two squares, and each one has its own sum. Look up "what size do I cut for a half square triangle" and you will find three different answers, all of them correct, none of them labeled. The math is different for each method, and almost nobody says which method they are doing.

So this page has all three. Yvonne made them on three consecutive Technique Tuesdays, two at a time, then four at a time, then eight, and her videos are in the sections below. Underneath each one is the math, written down so you can come back to it at the cutting table. There is a half square triangle chart you can print, a cheat sheet for all three methods, and it costs nothing.

The two numbers, and why they trip people up

A half square triangle is a square made of two triangles, cut on the diagonal. Quilters shorten it to HST, and the HST unit is the one most of us make more of than any other. Whole quilts are built from nothing else, and it turns up inside most of the quilt blocks you already know.

You will also meet it under older names. Pieced triangle squares, two-triangle squares, split squares, bias squares. Same unit every time.

Every HST has two sizes, and half the confusion in this subject comes from not saying which one you mean.

Finished is what the unit measures once it is sewn into the quilt, with its seam allowances hidden inside. Unfinished is what it measures on the cutting mat before it joins anything, and it is always the finished size plus 1/2 inch, a quarter for each side.

So a 4 inch finished HST is trimmed to 4 1/2 inches. A pattern that says "trim to 4 1/2" and a pattern that says "4 inch finished" are asking for exactly the same unit.

That half inch is not special to this unit. Every patchwork piece carries a 1/4 inch seam allowance on each of its four sides, so unfinished is always finished plus 1/2 inch, whether the piece is a triangle or a plain square.

What is special to the HST is the 7/8 inch in the two at a time formula. Half of it is the ordinary seam allowance. The rest covers the diagonal seam running through the middle of the unit, which a plain square does not have, and leaves a whisker to trim.

If you want the exact number, it is 0.854 of an inch. Half of that is the ordinary quarter inch on each side. The rest is a quarter inch measured across the diagonal rather than straight, which is a quarter inch multiplied by 1.414 and comes to about 0.354. Seven eighths is 0.875, so the formula rounds the awkward number up by two hundredths of an inch, and those two hundredths are the whisker you trim away.

That is also why patterns sometimes tell you to cut at the finished size plus a whole inch and trim down. They are buying more margin than the sum needs. It costs a little fabric and it forgives a lot, and if your cutting is not yet exact it is a fair trade.

The half square triangle size chart

This is the half square triangle chart. Every number in the three method columns is the square size to cut for your two starting squares. Trim the units to the size in the second column, whichever method you used.

All measurements in inches. Two at a time gives two units from two squares, four at a time gives four, the Magic Eight gives eight.

All three are the same idea: sew the larger pieces first, then cut them into units, rather than cutting small pieces and sewing them one at a time.

For any size that is not in the chart, the three formulas are these. Two at a time, cut both squares at the finished size plus 7/8 inch. The unit next door is the quarter square triangle, which is the same square split twice instead of once and is cut at the finished size plus 1 1/4 inches. It has a size chart of its own. Four at a time, divide the unfinished size by .64 and add 1/4 inch of wiggle room, then round to the nearest 1/4 inch. Magic Eight, double the finished size and add 1 3/4 inches.

Download the size chart as a free PDF. It is the whole cheat sheet on one page: the table, the three formulas, the precut sizes and the bias note. Tape it inside the lid of your thread box and you will never look this up again in the middle of a quilt.

Choosing the two fabrics

A half square triangle is a contrast unit. It has one job, which is to read as a triangle from across the room, and it only does that job if the two halves are far enough apart.

Far apart in value, not in color. Value is the lightness or darkness of a fabric rather than its hue, and it is the thing that decides whether a pieced design holds together or turns into a blur. A quilt built from fabrics that are all the same value can look dull and flat no matter how pretty the individual prints are, and a pair of triangles is where that shows up first.

Two tricks catch it before you cut. Squint at the pair until the detail goes and only the light and dark are left. Or photograph them side by side on your phone and look at the picture in black and white. If the line between them disappears, swap one of them.

Contrast does not have to be light against dark, either. Warm against cool, print against plain, one large motif against a small busy one, all of them give the eye something to hold. A pair of mid-value prints that differ in scale can work where two mid-value prints of the same scale will not.

One thing worth knowing before you cut a directional print. A half square triangle is cut on the diagonal, so a stripe that runs up the length of the fabric ends up at 45 degrees inside the unit, and it runs one way in half the units and the other way in the rest. Sometimes that is the effect you wanted. More often it is a surprise, and it is easier to see coming on the cutting mat than in the finished top.

For the fabric that repeats in every block, usually the light one, buy it all at once and buy a little more than the sum says. It is the background the triangles are read against, and a dye lot change halfway through a quilt is visible in a way that a change in one of the prints never is.

Marking, and when you can skip it

Each method asks for a different amount of drawing. Two at a time wants one line. The Magic Eight wants four. Four at a time wants none at all, which is part of its appeal.

Mark on the wrong side of the lighter of the two squares, where the line shows and where nothing will see it afterward. Use a long ruler. The diagonal of a 9 3/4 inch square is close to 14 inches, and a short ruler means joining two strokes, which is exactly where a drawn line starts to wander.

Whatever you mark with, test it first on a scrap of the same fabric, and test that it comes out again. That second half is the part people skip. A line that survives a hot iron has a habit of surviving everything else too, so mark, then press, then check, before you do it to forty squares.

If your quarter inch is not yet automatic, draw the sewing lines as well as the cutting line. On the two at a time method that is three pencil lines instead of one, and it turns a guess into following a line. You can stop doing it as soon as you stop needing it.

There is also a whole shelf of tools for avoiding the marking. Specialist rotary rulers for cutting triangles, commercial templates, and pre-printed foundation papers you sew straight through all exist and all work. None of them is necessary. If you make half square triangles constantly, one of them will pay for itself; if you make them occasionally, a pencil and a ruler will not let you down.

Two at a time

This is the method everyone learns first, written 2 at a time in most patterns and called sandwich piecing in the older books, and the one to reach for when you need one or two HSTs of a pairing, or when you are working scrappy and every unit is a different pair of fabrics.

Put two squares right sides together and draw a diagonal line on the wrong side of the lighter one. That drawn line is the cutting line, not the sewing line. Sew 1/4 inch either side of it, cut on the line, and press open toward the dark. Two HSTs.

Yvonne has one detail here that is worth more than the method itself. When you sew, aim one thread to the inside of your quarter inch rather than dead on it. Pressing the unit open folds the fabric over the seam line and eats a hair of width, and that one thread is what gives it back. It is the difference between units that trim easily and units that trim short.

If your quarter inch is not yet automatic, draw the two sewing lines as well as the cutting line. Three pencil lines and no thinking beats two lines and a guess.

Chain piece it. Sew down one side of every pair without cutting the thread, clip them apart, then go back up the other side. Eight units take about as long as two.

One thing about chain piecing triangles rather than squares. The point of the next pair does not always feed in cleanly on the tail of the last one, so lift the presser foot a fraction and position it yourself rather than letting the feed dogs find it.

Four at a time

Two identical squares, right sides together, and a 1/4 inch seam all the way around the outside. No drawn lines at all. Then cut both diagonals, corner to corner, and four units fall apart in your hands.

The cut goes from stitching corner to stitching corner, not fabric corner to fabric corner. Those are not the same point, and the difference is what decides whether the four units come out even.

The sum is the awkward one of the three. This is Yvonne's: take the unfinished size you want, divide it by .64, and add a quarter inch of wiggle room. For 4 1/2 inch unfinished units that is 7.03 plus 0.25, so cut at 7 1/4 and trim down. Below about 1 1/2 inches finished the wiggle room runs out and the method stops being worth it.

There is a catch with this one, and it is the reason the section below exists. Read that before you decide where these HST units go in a quilt block.

The Magic Eight

Eight matching units in one pass, in under ten minutes. When a block or a quilt wants six or more of the same pairing, nothing else comes close.

Two squares right sides together. On the wrong side of the lighter one draw both diagonal lines, so the square carries a large X, then a horizontal and a vertical line through the same center point. Sew 1/4 inch either side of both diagonals, which is four seams. Then cut on the horizontal and the vertical, and cut on the diagonals.

The straight lines are cutting lines only. Sewing on them is the mistake people make the first time, and it costs the whole square.

The sum is the friendliest of the three: double the finished size and add 1 3/4 inches. For 4 inch finished units that is 9 3/4 inches, which is why a 10 inch layer cake square is such a comfortable starting point. It gives you the wiggle room to trim.

One note about the sewing machine. Use a quarter inch foot without the guide for this method. You are sewing across the middle of the fabric rather than along its edge, so the guide has nothing to run against and only pushes the fabric around.

We have longer walkthroughs of the last two on their own, if you want to sit with one at a time: four at a time and the Magic Eight.

Where the bias ends up, and why it picks the method

This is the part that turns three techniques into one decision, and it is the reason to know all three rather than just your favorite.

Fabric does not stretch along the weave. It stretches on the diagonal, and a cut edge on that diagonal is a bias edge. Every half square triangle has bias in it somewhere. The methods differ in where they put it.

Worth being precise about, because the whole decision rests on it. Cloth is woven from lengthwise threads and crosswise threads. The lengthwise ones are the strongest and have the least give. The crosswise ones are firm but give a little more. At 45 degrees to both of them is the bias, which has the least strength and the most stretch of any direction in the fabric. That is not a small difference. Pull a strip along the grain and almost nothing happens. Pull the same strip on the bias and it grows in your hands.

Two at a time and the Magic Eight put the bias inside the seam. The outer edges of the unit come from the original edges of your squares, on the straight of grain, and they do not move.

Four at a time puts the bias on all four outer edges. Pull one and you can feel it give.

That single fact tells you where each unit belongs. A stretchy outer edge is no trouble in the middle of a block, where the units around it hold it steady on every side. It is trouble on the outside edge of a block, where it gets pinned, pressed and handled with nothing to stabilize it, and where it ends up next to the seam that joins one block to the next in the quilt top.

So: four at a time for units that will sit inside, two at a time or the Magic Eight for units that touch the edge. Size matters too. A little bias on a 3 or 4 inch unit is manageable. The same proportion of stretch on a 6 inch unit is a bowed block.

The old rule of thumb behind all of this is simple enough to carry around: when in doubt, have the straight grain on the edges. Every method here is just a different answer to that one question.

If you are stuck with bias on the outside, spray starch buys you some of the difference back. It firms the fabric up and makes both cutting and sewing easier, which is exactly what a stretchy edge needs. Go easy with it. Over-spray and the fabric distorts as you press it, which is the problem you were trying to solve.

Trimming, and the eighth of an inch that adds up

Every unit gets trimmed, whichever method made it. This is the step that decides whether the rows line up later, and it is the one people skip because the units look close enough.

Lay the 45 degree line of a square ruler along the seam. Set the two edges of the ruler on the size you want. Cut two sides, turn the unit 180 degrees, line the diagonal up again, and cut the other two. You can tell which side you have not done yet, because it still has its dog ears.

The instruction in the books is worth quoting almost word for word, because it is the whole of it: trim the units to the exact size, aligning the diagonal line of the ruler with the seam line of the square. Not the edge of the fabric. The seam.

How you hold the ruler decides more than people expect. Splay your fingers across it, well away from the cutting edge, and keep one finger or thumb off the ruler and down on the mat. That contact is what stops the ruler twisting as you cut.

The number to carry around is the eighth of an inch. It looks like nothing on the mat. Eight units later it is a whole inch, and a row that will not meet the row above it.

Two things help here more than trying harder. A square ruler with a 45 degree line through the middle, in the size you trim to most often, and a sharp rotary cutter. Our square rulers carry that 45 degree line, and a fresh rotary blade before you start a stack beats one changed halfway through. A blunt blade stops slicing and starts dragging, and the unit shifts under the ruler without you feeling it.

Pressing without stretching the seam

Press toward the dark, and set the seam first, which is just running the iron over the closed unit to settle the stitches.

That first pass is not a formality. Pressing the work as it comes off the machine settles the stitches into the fabric and takes out the small puckers that the needle left behind, and a seam that has been set opens cleanly instead of fighting you.

Then open it, give the fold a small finger press to start it, and hook the point of the iron into the corner and press straight across the unit rather than along the diagonal. The seam of an HST runs on the bias. Push the iron along that line and a perfectly cut unit turns into a slightly leaning one.

Press, do not iron. In patchwork the word means what it says: a restrained lifting and placing motion, not the sweeping back and forth you would use on a shirt. Sweeping is how a square unit becomes a slightly diamond shaped one.

Not everything needs the iron at all. Small units can be finger pressed, which is enough to open the seam and settle it and costs you nothing in stretch. On a stack of small half square triangles, finger press each one as it is cut and save the iron for the end.

Joining the units to each other

Trimming gets each unit right on its own. This is the step where they have to agree with each other, and it is where most of the visible failures in a finished block actually happen.

The first thing is the direction you pressed. When two units are going to be sewn together, press their seams in opposite directions. The two seam allowances then butt up against each other from opposite sides and lock, which quilters call nesting, and a nested join holds itself in place before a single pin goes in. It also spreads the bulk instead of stacking it, so the finished work lies flatter and is easier to quilt later.

Pressing the seams open is the other school, and it is not wrong. An open seam is the flattest option and can give greater accuracy, and on very small units where four seam allowances meet it is often the only way to get the intersection to behave. What you cannot do is mix the two without thinking, because an open seam has nothing for a nested seam to lock against.

Then the pin. Put the units right sides together with the seams running opposite ways so they nest. Push a pin down through the seam line of the top unit exactly where the two existing seams cross, and out through the same point on the bottom unit. That pin is not holding the fabric. It is marking the one point the new seam has to pass through. Pin either side of it, take the marking pin out as you reach it, and sew so the stitching goes through that point.

Get that right and the points stay sharp. Get it wrong by a thread or two and the tips of the triangles vanish under the next seam, which is the single most recognizable sign of a block that was hurried.

Press the finished join to one side, and if you are joining rows of units, alternate the direction from row to row so the next set of intersections nests too.

Straight from a precut

Half the appeal of this unit is that precut squares are already the right shape, and two of the common sizes land on friendly numbers.

• 5 inch charm square, two at a time. 4 inch finished units, trimmed to 4 1/2.
• 5 inch charm square, four at a time. 2 1/2 inch finished units, trimmed to 3.
• 10 inch layer cake square, two at a time. 9 inch finished units, trimmed to 9 1/2.
• 10 inch layer cake square, Magic Eight. 4 inch finished units, trimmed to 4 1/2.

None of those four need the square cut down first, which is the point. You open the pack, pair the squares, and start sewing. The only decision left is which method, and that is the decision the chart and the bias section above are there to settle.

A charm pack and a layer cake between them cover most of what a scrappy HST quilt needs. For the background, which repeats in every block and is what the triangles are read against, fabric by the yard keeps the whole quilt on one bolt, and solids keep the points crisp.

How many squares for a whole quilt

This is where the choice of method stops being a preference and starts being an afternoon of your life.

Work backward from the block, not forward from the fabric. Decide the block, count the half square triangles in one of them, multiply by the number of blocks, and only then divide by what your method gives you per pass. Two at a time divides by two, four at a time by four, the Magic Eight by eight.

A worked example, because the arithmetic is more convincing than the principle. Say a quilt of pinwheel blocks finishing at 6 inches, set ten across and twelve down, which gives a top of 60 by 72 inches before borders. That is 120 blocks. A pinwheel takes four half square triangles, so the quilt wants 480 of them, each finishing at 3 inches.

Four hundred and eighty units two at a time is 240 pairs of squares and 240 trips to the machine. The same 480 units the Magic Eight way is 60 pairs of squares and 60 trips. That is the whole argument for learning the third method, in one line.

Now the fabric. The chart says a 3 inch finished unit the Magic Eight way is cut at 7 3/4 inches. Sixty squares of each fabric, and a 7 3/4 inch square gives you five across a 42 inch width of fabric, so that is twelve strips. Twelve strips at 7 3/4 inches is 93 inches, which is two and five eighths yards. Buy two and three quarters of each and you have the offcuts for the binding.

Two habits are worth building into that sum. Round the yardage up rather than down, because a quilt that runs out of background fabric three blocks from the end is a quilt that waits for a reorder. And make two or three units before you cut the rest, press them, trim them and measure them. Five minutes there tells you whether the other 477 are going to behave.

What to make with them

A pile of half square triangles trimmed to one size is never wasted, because the layout is what changes and the math never does. Most half square triangle quilt patterns are the same unit in a different order.

Four of them in a two by two grid, each turned a quarter turn from the last, make a pinwheel. The same four turned differently make broken dishes. Four on the sides of a nine-patch, with plain squares in the corners, make a friendship star. Three quilt blocks, one HST unit, no new math.

Rearranging is the whole game. Take the four units of a pinwheel, turn them differently, and the same four become broken dishes. Turn them again across a whole quilt and you get barn raising, or streak o' lightning, or a plain field of diagonals. The units never change. Only the direction they face does, which is why a pile of them trimmed to one size is the most useful thing in a sewing room.

Set enough of them together and you have a half square triangle quilt with no other unit in it, which is why so many modern quilt patterns are built this way. Two of our block guides go further into it. Hovering Hawks is a 12 inch block that deliberately uses two of these methods in one block, so you can see the bias rule decide something real. And the Ohio Star is what happens when you take two half square triangles and cut them a second time, which is the next unit along.

A pieced border of them

A row of half square triangles all facing the same way makes one of the classic pieced borders, and it is the place where everything on this page has to be right at once.

Start by measuring the quilt top you are going to put it on, across the width and down the length, and take half an inch off each measurement for the seams that will attach the border later. Those two numbers, not the size you hoped the quilt would be, are what the border has to fit.

Then pick a finished unit size that divides into them. That is the whole trick, and it is worth choosing the unit to suit the quilt rather than the other way around. A 36 inch side divides by 3 into twelve units and by 4 into nine, and both are comfortable. The same side divides by 3 1/2 into a number with a decimal in it, and that decimal turns into a border that is short at one corner.

When the numbers refuse to come out, there are two honest fixes. Put a plain inner border between the quilt and the pieced one and trim that plain strip to make up the difference, or work a spacer into the pieced border itself. Both are older than any of us and neither one shows in the finished quilt.

One thing is not negotiable here. A pieced border runs along the outside edge of the quilt top, with nothing beyond it to hold it steady, and it gets handled every time the quilt is turned. Make those units two at a time or with the Magic Eight, so the straight grain is on the outside and the bias is locked inside the seam. This is the one place where four at a time units will cost you.

The blocks that are mostly triangles

If you want to practice these until they are automatic, the traditional sampler blocks are full of nothing else, and they give you a reason to make a hundred of them that is more interesting than making a hundred of them.

Port and Starboard is pieced from half square triangles and nothing else, sixteen of them. Barbara Frietchie Star and Catch Me If You Can are built from the same thirty-two triangles in a different arrangement. Star of the West, Strength in Union and the New England Block each want eight units and a handful of plain squares. Hovering Hawks wants ten. Tennessee wants exactly six, which is the moment the Magic Eight starts earning its keep. Fox and Geese mixes two sizes of unit in one block, and Union Square and the Pinwheel block itself want four.

The numbers line up with the chart above, which is the reassuring part. In an 8 inch finished sampler block, the common unit finishes at 2 inches, and the traditional cutting instruction for it is a 2 7/8 inch square cut once on the diagonal. That 2 7/8 is exactly the two at a time number in the chart, because it is the same sum arrived at from the other end.

One warning from the same set of blocks. Yankee Puzzle looks like a half square triangle block and is not one. Its squares are cut twice on the diagonal rather than once, which makes quarter square triangles, and the sum for those is the finished size plus 1 1/4 inches. The quarter square triangle page covers that unit properly.

Half square triangle questions we are asked most

What size squares do I cut for half square triangles?

It depends on the method, which is the part that catches people out. Two at a time, the finished size plus 7/8 inch. Four at a time, the unfinished size divided by .64 plus a quarter inch. Magic Eight, the finished size doubled plus 1 3/4 inches. The chart above has all three worked out.

What is the formula for a half square triangle?

There is not one. Each method cuts a different number of units out of the same two squares, so each has its own sum. That is the single most common reason quilters end up with units that are the wrong size.

What is the Magic Eight method?

Two squares right sides together. Draw both diagonals on the back of the lighter one, then a horizontal and a vertical through the center. Sew 1/4 inch either side of both diagonals, cut on the horizontal and vertical, then cut on the diagonals. Eight matching units in one pass.

Which half square triangle method is best?

The one that matches how many you need and where they are going. One or two, or scrappy, use two at a time. Exactly four, going inside a block, use four at a time. Six or more the same, use the Magic Eight.

Do I have to trim them?

Yes, and it is the step worth defending when you are in a hurry. Units that were never square do not become square when the block is squared up. They lose their points instead.

What is a scant quarter inch?

A quarter inch seam sewn a thread or two narrow, to allow for the thickness of the thread itself and the tiny amount of fabric taken up when the seam is pressed to one side. Most patchwork teachers ask for a scant quarter rather than a true one, and on a unit with a diagonal seam running through it the difference shows up faster than anywhere else.

Should I press the seam open or to one side?

To one side, toward the dark, if the units are going to be joined to each other, because seams pressed in opposite directions nest together and lock at the intersection. Open, if the units are small and four seam allowances are about to meet in one spot, because an open seam is flatter and can be more accurate. What does not work is mixing the two in the same block without deciding, since an open seam gives a nested seam nothing to lock against.

How do I stop the points getting cut off?

Two places lose points, and neither of them is the sewing. The first is the trim: put the 45 degree line of the ruler on the seam rather than on the edge of the fabric, and the point takes care of itself. The second is the join: pin through the exact spot where the existing seams cross, and make the new seam pass through that spot.

Can I make them without marking a line?

Yes, with the four at a time method, which sews all the way around the outside of two squares and needs no drawn lines at all. There are also specialist triangle rulers, templates and pre-printed foundation papers that do the marking for you. None of it is necessary, and a pencil and a long ruler have never let anyone down.

Why do my half square triangles come out too small?

Usually the fold at the press rather than the seam itself. Pressing the unit open takes up a hair of fabric across the seam, which is why sewing one thread inside your quarter inch line, rather than on it, makes the difference between trimming and re-cutting.

Where to start

Before any of it, test your quarter inch. Cut a 2 1/2 inch strip, cut three 1 1/2 inch segments off it, sew two of them together down the long side and press, then sew the third across the top. It should fit exactly. Too long and your seam is too wide, too short and it is too narrow.

Then print the chart, cut two 5 inch squares out of whatever is nearest, sew them two at a time, press and trim to 4 1/2 inches.

If it trims to 4 1/2 with a whisker to spare, your quarter inch is honest and every number on this page will behave. If it trims short, move your needle one thread and do it again. That is a five minute test that saves a quilt.

Marbelia Fernandes
The Fabric Hut Co-Founder

P.S. When you make a Magic Eight and only need six, do not put the two spares in the scrap bin. Put them in a jar with the others. A jar of odd half square triangles all trimmed to the same size becomes a quilt of its own about two years later, and it is usually the one people ask about.