See here for my ~~wall of text~~ introduction to making a quilt by using Play Craft’s Equal.

This thing is still preying on my mind, so I decided to crunch some numbers and see if I could calculate yardage estimates for making it! 😀 I adore stuff like this, I really do. (Hey, I’m a scientist – clue’s in the blog name! ;)) This post is likely to get pretty mathsy pretty quick, but I’ll do my best to explain my workings and keep it all clear.

# How many triangles in a strip?

This is a crucial question. We’re not just cutting umpty same-width strips and cutting them into triangle units, as I did here, we need strips of three different widths to match the three triangle heights we know we need, and we need to know how much fabric that will require. So, we need to know how many triangles we can cut from strips of different widths – obviously, wider strips will give fewer triangles and require more fabric overall. After doing some rough calculations on my mobile phone (I was almost embarrassingly excited to discover it had a scientific mode!), I decided that it would be best to calculate the total length required for all triangles of each size and colour, then divide that by the length of a fat quarter (which I’m taking as 21″). Great!

First we need to find the width of a triangle, so we use a bit of trigonometry:

We draw a line right down the middle of the triangle to meet the base at right-angles. We know this height (it’s the width of our strip, aka the Opposite side because it’s opposite the triangle’s corner) and we can use that plus the knowledge that all angles in an equilateral triangle are 60° to calculate the length of the Adjacent (so-called because it is adjacent to the triangle’s 60° corner):

Tan(60°) = Opposite / Adjacent

This can be re-written as:

Adjacent = Opposite / Tan(60°)

The Adjacent is half of the length of the base, so we double it to get the final number we need:

Adjacent x 2 = Triangle width

Ok, that’s the worst of the equations over. With this calculation, I can work out the width of any equilateral triangle I want. However, triangles aren’t squares – finding the length of a strip of triangles is not a case of just multiplying the number of triangles by the width of a triangle. Let’s look at an example strip:

We can see that one side has three triangles and the other has two + two half-triangles. For simplicity, I’m going to count that as a total of six triangles (3 x 2). In my calculations, I will divide the total of number of triangles needed by 2, then multiply that number by the triangle width to give the total length needed; I think this will give a good enough estimate for my purposes.

Once I calculate the total length of strip I’ll need for each triangle I want to cut, I can divide that number by the length of my FQs to find how many strips I should cut of each width. Yay! I’ve used this information to calculate yardage estimates for some example sizes of quilt (based on small triangles with finished sizes of 1″, 1.25″, and 1.5″) to see how big a quilt I can make with the fabric I have (5 FQs and 1 half-meter, which I’m counting as 2 FQs here). I’m in the UK, which means my FQs are metric and should measure 25cm (or 19.5″) wide (assuming the person who cut them knew how to use a rotary cutter; that’s a BIG assumption!). I have 2 FQs of dark fabric, 2 FQs of medium fabric and (effectively) 3 FQs of light fabric.

Note that the calculations for the numbers of strips are *rounded up* – the calculations are based on whole strips and assume that any bits left over from cutting all triangles of a particular size are “wasted” – obviously, this will not actually be the case given I can, for example, cut a left-over large strip into small and medium strips. However, my numbers do **not** include any half-triangles as yet – these will be cut from the start and end of strips, with extras being cut from left-over strips once all the full triangles are cut. They also don’t account for the fact that I’m counting two half-triangles per strip as one whole triangle. Essentially, I’m working on the assumption that what I lose on the swings I gain on the roundabouts. 😉

# Quilt 1 – 30″ x 34″

Triangles finish at 1″, 2″, 4″.

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 1.75" | 2.02" | 141 | 70.5 | 142.46" | 6.78 | 7 | 12.25" |

Medium | 2.75" | 3.18" | 126 | 63 | 200.05" | 9.62 | 10 | 27.5" |

Large | 4.75" | 5.48" | 13 | 6.5 | 35.65" | 1.69 | 2 | 9.5" |

Total width | 49.25" |

Size | Height | Width | # | '/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 1.75" | 2.02" | 71 | 34.5 | 71.73" | 3.41 | 4 | 7" |

Medium | 2.75" | 3.18" | 55 | 27.5 | 87.32" | 4.15 | 5 | 13.75" |

Large | 4.75" | 5.48" | 8 | 4 | 21.93" | 1.04 | 2 | 9.5" |

Total width | 30.25" |

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 1.75" | 2.02" | 60 | 30 | 60.62" | 2.88 | 3 | 5.25" |

Medium | 2.75" | 3.18" | 51 | 25.5 | 80.97" | 3.85 | 4 | 11" |

Large | 4.75" | 5.48" | 11 | 5.5 | 30.16" | 1.43 | 2 | 9.5" |

Total width | 25.75" |

This is easily in range of my fabrics, but it would be nice to make the quilt bigger if I can!

# Quilt 2 – 37.5″ x 44″

Triangles finish at 1.25″, 2.5″, 5″.

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2" | 2.30" | 141 | 70.5 | 162.8" | 7.75 | 8 | 16" |

Medium | 3.25" | 3.75" | 126 | 63 | 236.42" | 11.25 | 12 | 39" |

Large | 5.75" | 6.63" | 13 | 6.5 | 43.15" | 2.05 | 3 | 17.25" |

Total width | 72.25" |

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2" | 2.30" | 71 | 34.5 | 71.73" | 3.90 | 4 | 8" |

Medium | 3.25" | 3.75" | 55 | 27.5 | 103.20" | 4.91 | 5 | 16.25" |

Large | 5.75" | 6.63" | 8 | 4 | 26.55" | 1.26 | 2 | 11.5" |

Total width | 35.75" |

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2" | 2.30" | 60 | 30 | 69.28" | 3.29 | 4 | 8" |

Medium | 3.25" | 3.75" | 51 | 25.5 | 95.69" | 4.55 | 5 | 16.25" |

Large | 5.75" | 6.63" | 11 | 5.5 | 36.51" | 1.73 | 2 | 11.5" |

Total width | 35.75" |

The dark and medium fabric requirements are ok, but the light fabric requirement is much more than I have. **Quilt 1** it must be!

# Quilt 3 – 45″ x 52″

Triangles finish at 1.5″, 3″, 6″.

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2.25" | 2.59" | 141 | 70.5 | 183.16" | 8.72 | 9 | 20.25" |

Medium | 3.75" | 4.33" | 126 | 63 | 272.79" | 12.99 | 13 | 48.75" |

Large | 6.75" | 7.79" | 13 | 6.5 | 50.66" | 2.41 | 3 | 20.25" |

Total width | 89.25" |

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2.25" | 2.59" | 71 | 34.5 | 92.23" | 4.39 | 5 | 11.25" |

Medium | 3.75" | 4.33" | 55 | 27.5 | 119.07" | 5.67 | 6 | 22.5" |

Large | 6.75" | 7.79" | 8 | 4 | 31.17" | 1.48 | 2 | 13.5" |

Total width | 47.25" |

Size | Height | Width | # | #/2 | Length | Strips | Round up | Strip width |
---|---|---|---|---|---|---|---|---|

Small | 2.25" | 2.59" | 60 | 30 | 77.94" | 3.71 | 4 | 9" |

Medium | 3.75" | 4.33" | 51 | 25.5 | 110.41" | 5.25 | 6 | 22.5" |

Large | 6.75" | 7.79" | 11 | 5.5 | 42.86" | 2.04 | 3 | 20.25" |

Total width | 51.75" |

All of these are now well over my fabric allowance. I would need 1.25m (4.5 FQs) of light fabric and 0.75m (3 FQs) each of dark and medium fabric to make this size of quilt.

# Cutting plan

I will start by cutting the largest triangles first and make sure that I have all the full and half triangles needed for each colour before I start cutting the next size down, and so on. And then I will probably fervently wish I had a design board to stick them all on!

# Piecing plan

After pondering the design, I’m thinking that it may be best to construct large triangles from the smaller triangles and then piece them all together in rows.

So the most awesome thing about you writing all these detailed notes? It makes it a LOT easier to add this to the program since you have the formulas right there!

😀 I hoped so! I’ve tried to be as clear as I can because I realise that not everyone who might read this is going to be thrilled by a big pile of maths and equations. *rubs hands* I’m really looking forward to piecing it. 🙂