For some yarn crafters the world of designing seems mysterious, so I thought I’d give you a peek behind the scenes when I am designing. In particular some of the math that I use when designing a triangle-shaped top-down shawl.

Triangles are popular for shawls because they can be worked top-down either with decreases on the ends or increases at the ends and center. There are triangle-shaped shawl patterns out there that are created from the bottom point upward. I don’t like to work that way so haven’t ever designed a shawl using that method.

My “Eleonora Shawlette” is an example of a triangle shape worked top down with 3 increase points.

So is my “Mountain Whisper Shawl”.

The great thing about a triangle shape is that it is relatively easy to figure out the amount of yarn needed for the shawl (or shawlette). The same math can be used to figure out how big a shawl you could make from the yardage you have on hand.

First decide on the dimensions for the shawl you want to make. I’m using an isosceles triangle for this shawl and the center point *(pink line)* is half the length of the base *(blue line).* Now it is time to work a swatch.

Usually I make a miniature version of the shawl. This works very well as I can also use that swatch as the beginning of my shawl if I want. I want my swatch to be at least 6 inches long at the center point. I let the swatch rest for a while, at least 2 hours if not over-night. If I plan to aggressively block my finished shawl and I’m using a fiber that will change a lot with the blocking, I will block my swatch over-night instead of letting it rest.

The next morning I measure and weigh my swatch. I take the same measurement lines that I had marked out for my shawl dimensions. The broad base *(blue line) *of the triangle and the length of the center point *(pink line)*. I’ll use these measurements to figure out the square inches of my swatch.

I have a handy digital scale that I use to weigh my swatches and projects. It can measure in ounces or grams. I prefer to use grams as they are a smaller unit of measurement and that helps me with accuracy. It also helps when using yarns from companies that do not list the weight in ounces.

Most ball bands will tell you the weight and yardage contained in the ball/skein/hank. Here’s where the math starts. Take the number of yards and divide it by the number of grams on the ball band. This gives you the number of yards per gram.

For example, this ball of “Mochi Plus” has 95 yards in a 50 gram ball.

95 divided by 50 = 1.9 yards per gram.

If my swatch weighed 10 grams, then I know that it took 19 yards.

Now it is time to figure out the square inches in my swatch and the square inches for my planned dimensions of the shawl. This is actually not that hard. As my geometry teacher taught us in high-school, all triangles are half of a rectangle. This gives me 2 ways to find the square inches of my swatch and shawl.

Either take the measurement from the base and multiple it by the measurement from the center point, then divide that number in half.

Or my favorite way: Divide the base in half, then multiple by the measurement from the center point.

For some of you it might be easier to visualize this as changing your 1 triangle into 2 triangles.

Then moving one of the triangles to make a rectangle (or in this case a square). *A square is always a rectangle but a rectangle isn’t always a square. *In this case my planned shawl will be 1,225 square inches *(35 x 35)*.

I can use the same equations to figure out the square inches of my swatch. Let’s say in this case that my swatch was 12″ at the base and 6″ at the center point. That works out to 36 square inches for my swatch.

Now I divide the square inches for my planned shawl by the square inches of my swatch.

1,225 divided by 36 = 34.0277777778 times that my swatch will fit into my planned shawl.

Obviously I don’t want to be fighting with such a long decimal in my figures, so I will round up to the next whole number. I always round up, because I don’t want to run out of yarn when I am working on my project.

Now we have to figure out what this means for yardage needed. Remember earlier I said that my swatch weighed 10 grams and used 19 yards of yarn? It’s time to plug that number into our equation.

35 x 19 = 665 yards needed to make my shawl.

So how many balls of “Mochi Plus” do I need for this shawl?

665 divided by 95 = 7 balls.

When I purchase my yarn for a project I usually purchase 1 extra ball to be on the safe side. It’s really a bummer when you run out of yarn just short of completing your project.

Now if all this math scares you a little, the good news is that most patterns are going to have the yardage information you need. Because the designer already did all the math for you.

These equations are handy though if you aren’t meeting the gauge or are substituting a different yarn. Sometimes it is fun to see what you can come up with making a few changes.