Decipher Your Quilt - the calculations behind 9 patch blocks

For today's Decipher Your Quilt post, Leanne of She Can Quilt and I will both be talking about 9 patch blocks - Leanne is showing you how to identify 9 patch blocks and quilts, and I will be discussing the maths behind them. I've managed to avoid the evil 'M' word up until now, but maths is a really important part of quilts and geometry so I can't really avoid it any longer. Hopefully I will present it all in an easy to understand way, but as always if you have any questions please just leave a comment and I'll answer as best I can.

If you're interested in making some of the blocks we are showing you during this series, Leanne and I are planning on using our blocks to make a sampler-style quilt at the end of the series. We will be making our blocks of various sizes but with a common factor; if you would like to join us, you could make your blocks so their sizes have a common factor too - for example multiples of 3 (3", 6", 9", 12") or multiples of 4 (4", 8", 12", 16"). We will show you some techniques for joining these blocks into a quilt at the end of the series. This was also the thinking behind the How Far Will You Go? QAL I co-hosted with Jess of Scrappy n Happy in 2012 - we used 5", 10" and 20" finished blocks to create a modern sampler quilt.

For today's post, Leanne will be going into a lot more depth about what a 9 patch block is, but to put it very simply a 9 patch block is any block that can be divided into a 3x3 grid of equal sized squares. If you've been quilting for any length of time, you've probably made lots of these blocks as 9 patches are very common blocks. As always, these are just my thoughts on how to approach 9 patch calculations :o). I've added a few examples of 9 patch blocks randomly in this post, just to add a bit of colour.

So, what size should my 9 patch be?

Quilters are pretty smart - we like to make things easier for ourselves by choosing a block size that means cutting fabric in whole or half-inch increments, rather than horrible fractions (like 3/8" for example). Not only is it easier to get your head around whole numbers and the maths involved, it seems to be more comfortable to accurately cut fabric - possibly because the whole and half-inch markings on rulers are generally easier to see.

Since a 9-patch block is three squares across by three squares down, it would make sense to choose a finished block size that is divisible by three (ie 3", 6", 9", 12", 15" etc). This will mean dealing with whole numbers, rather than fractions.

For example, if you chose to make a 9" finished 9 patch block, you could calculate the finished size of each of the squares by calculating 9/3 = 3, a nice round number. This is far easier than choosing a finished block size of, say, 8", where you would be dealing with difficult fractions when cutting fabric, which is far more likely to end up with wonky points and blocks that aren't quite the right size. Jess and I learnt this the hard way when we ran our QAL - one of the blocks we chose to include was the Weathervane block, which is a 9-patch. The problem was, it needed to be a 10" finished block, so we ended up needing to paper piece it in order for it to end up the correct size - rather than being a simple rotary cut block if it had been 12" or 9".

What about seam allowance?

Learning how to add seam allowance to your measurements is one of the big tricks in quilty maths - and it is critical to learn how to do it so you end up with blocks that are the right size. If you don't account for the extra fabric that will end up within the seam allowance, you will be cutting fabric the wrong size and end up with blocks that are not the size you want.

Quilters use a 1/4" seam allowance, so a 1/4" on each side of every piece of fabric will be 'lost' in the seam when you join them to another piece of fabric.

For example, if the desired finished size of a square is 3",

 you need to account for the 1/4" on all four sides that will be taken up in the seam allowance.

 So when cutting fabric for a 3" finished square, you will need to add the seam allowance to all sides ie (1/4" + 3" + 1/4") = 3.5".

So the rule of thumb is to add 0.5" to each finished measurement in the block.

Maple Leaf Block Example

I thought it might be useful to give an example of resizing a 9 patch block, so I will show you how I'm re-sizing the Maple Leaf block from 12" finished, to 15" finished for a quilt I'm making at the moment. A free tutorial for the 12" finished block is available here. 

The first step in re-sizing a block is identifying what the finished size of each of the patches will be within the block. The Maple Leaf block is three squares across, by three squares down, so if we want a 15" finished block, we can divide the length of one of the sides by the number of squares to find the size of each of the patches - ie 15/3 = 5" square.

There are three different components in the Maple Leaf block; squares, half square triangles, and the stem square.

SQUARES:
We have already figured out what the finished size of each of the squares will be, so we can simply add 0.5" to account for seam allowance to each of the sides. Here, the calculation will be 5 + 0.5 = 5.5", so we must cut 5.5" squares for those units.

HALF-SQUARE TRIANGLES:
We know from calculating the size of the squares above that the half-square triangle units will need to be 5.5". Using the HSTs two at a time method, we can work out that by starting with 6" squares of background and print fabric, we will be able to make 5.5" HST units.

STEM UNIT:
The stem unit is a little trickier to calculate, especially since in the original tutorial it is made much larger than required, and then trimmed down to size. The background fabric for this step in a 12" block is 4.5" square, cut on the diagonal. So for a 15" block, the background fabric would need to be 5.5" square cut on the diagonal. These values are both based on the size of the squares we figured out above.

To figure out the width of the stem piece, I used the ratio between unit or patch size and stem width. This is a really simple calculation to do. We know from the tutorial that for a 4" finished patch, the stem width is 2", and our desired finished patch is 5".

So as ratios, we have Stem width:5 = 2:4
We can convert these to fractions, so stem width/5 = 2/4 = 0.5.
By mulitplying both sides of the equation by 5, we can figure out stem width = 0.5 x 5 = 2.5'.

Leanne and I both have pretty crazy schedules next week, so we will be taking a week off from our Decipher Your Quilt posts. We will be back to talk about 16 patch blocks on the 7th of April. As always, if you make something using any of our tutorials in the series you can use the hashtag #decipheryourquilt on Instagram, or add it to the Flickr group.

xx Jess