Having previously looked at sizes for squares and rectangles it is now the turn of triangles, in particular the Half-Square and Quarter-Square triangle units.

There is a ‘formula’ for virtually every shape we need to cut for patchwork. Hopefully the following will help you to work out how to rotary cut your triangles.

Finished size – this is the size of the unit/piece once it is stitched into the block/quilt.

Rounding up to the nearest ⅛ inch. If you have had to use a calculator then you need decimals not fractions**:- **⅛ = 0.125 ¼ = 0.25 ⅜ = 0.375 ½ = 0.5 ⅝ = 0.625 ¾ = 0.75 ⅞ = 0.875

**Half –Square triangles**

Half-Square triangles (HST) are the units made by cutting a square in half. You can find several Hints & Tips on how to piece these units including a couple **here** and **here**.

But what size should your starting squares be?

Add ⅞” to the finished unit size. Cut squares to this measurement and cut in half diagonally.

Remember that two squares (one of each colour) will make two HST units.

You’ve seen a lovely quilt you would like to make; you have managed to break the design down and seen it is made from a number of blocks which have squares and half-square triangle units. But what size?

This block is Ribbon Star and it is a 9-patch block – in other words it is made from nine units, one square and eight HSTs. So the most sensible thing to do is make the block of a size that is divisible by 9 (or 3) – 6 inch, 9 inch, 12 inch, 15 inch etc. For a six inch block your units would be 6 divide by 3 = 2 inches. Your centre square will be cut 2½ inches; your HST units will be cut from 2⅞ inch squares. For a 9 inch block the sums are 9 divide by 3 = 3, so your centre square is cut 3½ inches and your HST units are cut from 3⅞inch squares and so on.

This block is Clay’s Choice and is a 4-patch block in that it is made from 16 units. In this case it would be wise to choose a block size divisible by 4 – i.e.8 inch, 12 inch or 16 inch. For an 8 inch block the units are 8 divided by 4 (the number of units across the block) = 2 inches, so your squares are cut at 2½ inches and your HST units will be cut from 2⅞ inch squares. For a 12 inch block your units are 12 divided by 4 = 3, so your centre square is cut 3½ inches and your HST units are cut from 3⅞inch squares, and so on.

**Quarter-Square triangles**

Quarter-Square triangles (QST) are made from the triangles you get when you cut a square in four across the diagonals.

What size should your starting squares be?

Add 1¼” to the finished unit size. Cut squares to this measurement and cut in 4 diagonally.

These triangles appear in a number of blocks, the most common is probably Ohio Star, but there are plenty of others, such as Aunt Malvernia’s Chain.

There are a variety of ways to make these units apart from just cutting squares in four and joiining them back together again. You can download a worksheet **here** and find some more ideas of blocks using these (and other units) **here**.

Let’s go back to the Ohio Star block – it is a 9-patch block as it has 9 units (3 x 3 grid), therefore we need to use our 3 times table and make blocks that are 6, 9, 12 15 inches square. This time we need to add 1¼ inches to our finished size units to cut the squares for the QSTs. So for a 6 inch block our finished units are 2 inches and the squares for QST units are cut at 3¼ inches; a 9 inch block has 3 inch units so the QST unit square are cut at 4¼ inches etc.

There are surprisingly few 4-patch blocks with QST units but I did find this one, called Triangles. It has both QST units and HST units. But, although it looks like a 4-patch block, when you look at a quarter of the block you can see that each quarter is 3 units across.

The most sensible size to make this block would be one that appears in both your 3 times and 4 times tables – in other words a 12 inch block. Your QST units would therefore be 2 inches finished size and cut at 3¼ inches. The small HST units in the corners are also 2 inches finished so would be cut from 2⅞ inch squares. The large HST units in the centre would be 4 inches finished so are cut from 4⅞ inch squares.

You can download a free table of sizes for both HST and QST units **here**.

Thank you,a very useful post. I tried the download link and it said ‘forbidden to access this’

Thanks Chris, very helpful and I think (!) I understand the maths