Half square triangle chart: every method, every size, in inches and centimetres

The half square triangle chart (inches)

Finished means the size of the HST inside the quilt, after it is sewn to its neighbours. Unfinished (the trim size) is finished + 1/2 in. Every cut below is a square, and every method uses one light and one dark square per pair.

Yield per pair of squares: 2 at a time makes 2 HSTs, 4 at a time makes 4, 8 at a time makes 8, oversize and trim makes 2.

The formulas, so you can extend the chart:

• 2 at a time: finished + 7/8 in.
• 4 at a time: (finished + 7/8 in) x 1.414, rounded up to the next 1/8 in.
• 8 at a time: 2 x (finished + 7/8 in).
• Oversize and trim: finished + 1 in, then trim each unit to finished + 1/2 in. Many quilters go up to finished + 1 1/2 in for extra room.

The half square triangle chart (centimetres)

Metric quilters sew a 0.75 cm seam, so the metric chart is computed from scratch, never converted from inches. The HST allowance becomes 2.6 cm, and the trim size is finished + 1.5 cm. Cuts round up to the next millimetre.

Metric formulas: 2 at a time = finished + 2.6 cm. 4 at a time = (finished + 2.6 cm) x 1.414, rounded up to the next millimetre. 8 at a time = 2 x (finished + 2.6 cm). Oversize = finished + 3 cm, trimmed to finished + 1.5 cm.

Why do you add 7/8 in to a half square triangle?

Squares get finished + 1/2 in, because each of the two edges gains a 1/4 in seam allowance. Triangles need more, because one of their seams runs on the diagonal.

Picture the finished triangle with two legs of length f. The two straight legs each gain a 1/4 in allowance, just like a square. The long diagonal edge also gains a 1/4 in allowance, but that allowance is measured at 90 degrees to the diagonal. Where the extended diagonal meets each leg, it has travelled 1/4 in x 1.414 = 0.354 in further along the leg. Add it up:

leg of the cut triangle = f + 1/4 + 1/4 + 0.354 = f + 0.854 in

That is the formula s x (2 + sqrt 2), with s = 1/4 in. A rotary ruler is marked in 1/8 in, so 0.854 in rounds up to 7/8 in. That tiny extra (about 1/50 in) is a gift: your HSTs come out a hair large, which is exactly what you want before a final press and a tidy trim. This is the whole "HST 7/8 rule".

In metric the seam is 0.75 cm, so the exact allowance is 0.75 x 3.414 = 2.56 cm, used as 2.6 cm. That is why a metric pattern never says "finished + 2.2 cm" (the straight conversion of 7/8 in). The seam is different, so the number is different.

Where does 1.414 come from in the 4 at a time method?

In the 4 at a time method you sew around the outside of the square and cut on both diagonals. The edges of each HST are half diagonals of the big square, so the big square must be the 2 at a time size times the square root of 2 (1.414). Then round up to a line you can cut on your ruler. Some charts compute this from the exact 0.854 in instead of 7/8 in and land 1/8 in smaller on a few sizes (for example 6 7/8 in instead of 7 in for a 4 in HST). We print the larger, rounded up number because 4 at a time units have stretchy bias edges, and a whisker of extra fabric to trim is far kinder than a unit that comes up short.

Why is 8 at a time simply double?

Draw both diagonals on a square that is 2 x (finished + 7/8 in), sew 1/4 in on both sides of each diagonal, then cut it in half vertically and horizontally first. You now hold four squares of exactly finished + 7/8 in, each already sewn like a 2 at a time pair. Cut each on its diagonal and you have eight HSTs. The 8 at a time chart is the 2 at a time chart, four times over, in one square.

How do you make half square triangles 2 at a time?

This is the method every quilting teacher starts with, and for good reason: straight grain on the outer edges, easy to mark, very accurate.

1. Cut. Cut one light and one dark square at finished + 7/8 in (metric: + 2.6 cm). For 3 in finished HSTs, that is 3 7/8 in (for 8 cm finished, 10.6 cm).
2. Mark. Draw a diagonal line corner to corner on the wrong side of the light square with a fine pencil or a fabric pen.
3. Layer. Place the squares right sides together, edges aligned, and pin away from the line.
4. Sew. Stitch exactly 1/4 in (0.75 cm) from the line on both sides. A 1/4 in foot rides the drawn line nicely. Keep your stitch length at 2.0 to 2.2 mm.
5. Cut apart. Rotary cut on the drawn line. You now have two HSTs.
6. Press. Set the seam first, then press it to the dark side or open (see below). Press, do not iron.
7. Trim. Trim the two little tails (dog ears) and check the unit: it should measure finished + 1/2 in, so 3 1/2 in (9.5 cm).

Example: a Churn Dash at 12 in has four 4 in finished HST corners. Four HSTs need two pairs, so cut 2 light and 2 dark squares at 4 7/8 in.

How do you make HSTs 4 at a time?

1. Cut one light and one dark square at the 4 at a time size from the chart (3 in finished: 5 1/2 in; 8 cm finished: 15 cm).
2. Layer them right sides together. No marking needed for the seams.
3. Sew 1/4 in (0.75 cm) around all four edges.
4. Cut on both diagonals. Four HSTs fall out.
5. Press gently and trim to finished + 1/2 in.

The bias warning. The outside edges of every 4 at a time unit are cut on the bias, the stretchiest direction of woven fabric. They grow if you tug them, iron back and forth, or handle them a lot. Starch or use a starch alternative on both squares before cutting, press with an up and down motion, and trim each unit square. Use 4 at a time where the HST edges will be sewn to straight grain pieces, and avoid it on the outer edge of a quilt. When you want a little extra security, cut the squares 1/4 in (0.5 cm) larger and trim.

How do you make HSTs 8 at a time?

1. Cut one light and one dark square at 2 x (finished + 7/8 in). For a 3 in HST that is 7 3/4 in; for 4 in, 9 3/4 in; for 8 cm, 21.2 cm.
2. Draw both diagonals on the wrong side of the light square.
3. Layer right sides together and sew 1/4 in on both sides of both diagonals: four seams.
4. Cut the square in half vertically and horizontally, then cut each smaller square on its drawn diagonal.
5. Press and trim. Eight HSTs, straight grain on the outside edges.

This is the speed method for big HST quilts. A 10 in layer cake square happens to fit it beautifully: 10 in = 2 x (4 1/8 + 7/8), so a pair of layer cake squares gives eight HSTs that trim to 4 in finished (4 1/2 in unfinished).

Oversize and trim: the accuracy method

Cut your squares at finished + 1 in (metric: + 3 cm), sew them 2 at a time, press, then trim every unit to finished + 1/2 in (+ 1.5 cm).

How to trim well:

1. Lay a square ruler on the HST with its 45 degree line exactly on the seam.
2. Position it so the HST extends a little past the trim measurement on the top and right edges. Trim those two sides.
3. Rotate the unit 180 degrees. Line up the freshly cut edges with the trim measurement on the ruler, keep the 45 degree line on the seam, and trim the other two sides.

A dedicated HST trimming ruler speeds this up, but any square ruler with a diagonal line works. Yes, trimming takes time. For points that must meet perfectly in a star or a Bear's Paw, it is time well spent.

Pressing: open or to the side?

Both are correct. Choose by what the block needs.

• To the dark side (the traditional choice): the dark fabric hides the seam allowance, the seams nest against neighbouring units, and the seam is a touch stronger for hand quilting.
• Open: the flattest HST, and the easiest to trim accurately because the diagonal seam sits dead centre. Best for small HSTs (2 in or less, 5 cm or less), blocks where many points meet, and modern quilts. Shorten your stitch to 1.8 to 2.0 mm so the open seam stays closed.

Always set the seam first (press it flat as sewn), then open the unit and press. Lift and lower the iron. Sliding an iron along a diagonal seam stretches it out of square.

HST yield planning: how many pairs for N units?

The formula is one line: pairs = N divided by the yield per pair, rounded up.

One pair is one light square plus one dark square, so double the pairs to get the total squares you cut.

Worked example in inches: 48 HSTs at 3 in finished

Your fabric gives 40 in of usable width after the selvages (42 to 44 in quilting cotton).

• 2 at a time: 24 squares of each colour at 3 7/8 in. Ten fit across a strip (40 / 3 7/8 = 10.3), so you need 3 strips: 3 x 3 7/8 = 11 5/8 in of each fabric.
• 4 at a time: 12 squares of each colour at 5 1/2 in. Seven per strip, so 2 strips: 11 in of each fabric.
• 8 at a time: 6 squares of each colour at 7 3/4 in. Five per strip, so 2 strips: 15 1/2 in of each fabric. The sixth square costs a whole second strip. If 40 HSTs (5 pairs) will do, one strip covers it.

Add 2 to 4 in for straightening, then round up to a buyable cut: 1/2 yd of each fabric covers 2 or 4 at a time, and 5/8 yd covers 8 at a time.

Worked example in centimetres: 48 HSTs at 8 cm finished

Usable width is 102 cm.

• 2 at a time: 24 squares of each colour at 10.6 cm, 9 per strip, 3 strips: 31.8 cm of each fabric.
• 4 at a time: 12 squares at 15 cm, 6 per strip, 2 strips: 30 cm.
• 8 at a time: 6 squares at 21.2 cm, 4 per strip, 2 strips: 42.4 cm.

Add 5 to 10 cm for straightening and round up to the next 10 cm: 50 cm of each fabric covers 2 or 4 at a time, and 60 cm covers 8 at a time.

Which HST method is best? A side by side comparison

Here is the surprise the numbers show: the first three methods use almost exactly the same fabric per HST. Speed is the real difference. 8 at a time halves the sewing per unit and keeps the grain friendly; 4 at a time is fast but trades accuracy for bias edges; oversize and trim spends roughly 6 to 7 percent more fabric to buy you perfect units. Our advice for a first HST quilt: 2 at a time with a 1/8 in oversize, trimmed. You learn the unit, and every unit comes out true.

HST mistakes and how to fix them

• HSTs finish 1/8 in small. Your seam is a little wide. Sew a scant 1/4 in (a thread or two inside the line) and do the quarter inch test: three 1 1/2 x 3 1/2 in strips sewn together must measure 3 1/2 in wide (metric: three 4 x 9 cm strips measure 9 cm).
• Wavy or stretched units. Bias edges were ironed back and forth. Starch before cutting, press straight down, and trim square with the diagonal on the seam.
• Using a chart from another seam system. An inch chart sewn with a 0.75 cm seam (or a metric chart sewn with a 1/4 in foot) drifts on every unit. Plan the whole quilt in one system.
• Rounding 4 at a time down. If your calculator shows 5.48, cut 5 1/2 in, never 5 3/8 in. Round up, then trim.
• Trimming with the ruler off the seam. The 45 degree line must sit on the seam, not near it. A HST trimmed off the diagonal gives blunt points.
• Pressing to the light side. The dark allowance shadows through. Press to the dark side, or press open.
• Dog ears left on. Those tails throw off alignment when you join rows. Snip them before sewing units together.