When I taught maths I would be asked the question: “how is this useful?” Or the student might say “I’m never going to need this in real life!”
First of all, you need it for your exams in 3 months time…
Anyway, one of my hobbies is sewing.
Interested Blog Reader: “Sewing and maths, you say? They don’t seem like they go together!”
NumberJacqui: “Oh, but they do! The mathematical and logical aspect of sewing is one of my favourite parts!”
Slightly Worried Blog Reader: “Err, ok then…”
NumberJacqui: “Here, let me show you!”
Let’s talk circle skirts. Cute on small girls and big girls alike, right? There are lots of circle skirt tutorials out there so if you want more detail on how to actually make one then look elsewhere (I recommend Made Everyday with Dana), I’m just all about the maths here! We’re going to work out the measurements for your skirt and how much fabric you need. I haven’t added in hem or seam allowances, however, so you may wish to add in an inch or so of length and seam allowances if you need to make a two-piece circle skirt.
So you need your/her waist measurement. I’m going to use a fictitious 30″ (30 inches = 30 x 2.54 cm = 76.2 cm if you prefer to work in cm), and let’s not examine the reason behind that!
We know from our school days that the length around the edge or circumference of a circle, C, is: C = 2πr, where π (pi) is 3.14159265… and r is the radius of a circle, the distance from the centre to the edge or circumference.
I’m going to rearrange this formula for you (kind, huh?):
C = 2πr
C/2π = r
So to find the radius of the waist measurement, which will be the hole in our skirt, which we will call h, (assuming a circle – please don’t be offended!) we calculate:
h = 30/2π = 30/6.2831853…
But actually I’m just going to use 30/6.28, because basically my cutting and measuring skills (not to mention the circle assumption) aren’t accurate enough for the rest to matter… If I use the correct value for π I will get h = 4.774648292… and if I use 3.14 then h = 4.777070… So that’s pretty close, out of interest it is a percentage difference of 0.05%! And when I see I need to use 4.77″, I’m really going to cut 4 3/4 anyway. Always remember to go on the small side for this because you can always cut a bit bigger again, but you can’t put it back if you make the hole too big.
So now I know the radius for my waist hole is 4 3/4 inches. How long do I want my fictitious skirt to be? I’m going to say 25″ (63.5 cm). Let me clarify that I do not have a tape measure right now so I can’t say if this is actually a skirt length I would wear.
Length l = 25, so the radius of the whole skirt (let’s call this r) can be found by adding the two quantities together, f = l + r = 25 + 4 3/4 = 29 3/4 inches. Now you have enough information to start cutting out your skirt… Or do you?!
It depends on your personal fabric stash. How big a piece of fabric are you going to need? You need to know the diameter of your skirt. This is 2 x f = 59 1/2 ” in my example. So you will need fabric which is 60″ wide (150 cm) and you will want 60″ of it, which is 1 2/3 yards (1.5 m), so you might need to buy 2 yards to make this skirt.
If your chosen fabric doesn’t come in 60″ width, and instead comes in 44″ width, you will need to buy a lot more and cut two semicircles out to sew together. The maximum you will need is 2 times your diameter, or 120″ = 3 1/3 yards = 3 m. You should be able to squeeze it together a bit and not have to buy quite this much (3 yards for example) but please don’t just take my word for it! And pay attention to pattern direction etc.
I have worked out some maths for you if you really want to know how small a piece of fabric you should be able to fit your two-part circle skirt into.
Here is a picture of what your fabric cutting guide would look like. We need to find out the length of fabric we need. This will be (from the picture) r + x + r. The w is the width of the fabric.
To find out the length of x we need to use Pythagoras’ theorem on the triangle in the middle of the picture.
This shows us that the length of fabric needed for this skirt is 100.79″, which is 2.56 m, under 3 yards.
I’m going to give you the formulae you need to work all this stuff out for yourself!
Letters: h = radius of hole; C = waist circumference; l = length of skirt; r = full radius of skirt; w = width of fabric; q = quantity (length) of fabric to buy; x = extra quantity of fabric needed when making a skirt in two parts, as described above. For r, you can use a value with seam and hem allowance added in too. Then you can use this value to find the quantity of fabric you require as I have calculated below.
Radius of hole, h:
h = C/6.28
Full radius of skirt, r:
r = h + l
Now the fabric options:
If 2r < w (if the diameter, or two times full radius, of your skirt is less than the width of fabric), q = 2r and you can make your skirt in one piece.
Or if 2r > w, you need to make a skirt in two pieces, so you need to find x:
x2 = (2r)2 – w2
x = √( (2r)2 – w2)
q = 2r + x
So this can definitely save you money at the fabric shop!
Hence, erstwhile teenage student of mine, why you must pay attention in maths! 😉
Please don’t solely trust my calculations on this one, I would hate to be the cause of a sewing disaster. What I would do is give a little bit more wiggle room for cutting and for seam allowance, and draw a scale diagram. My fabric cutting guide picture was actually a scale diagram to check my maths. I used 2 mm = 1″ if that’s not too confusing! In other words instead of drawing semicircles with radius 30″ I used semicircles with radius 6 cm (60 mm); for fabric width 44″ I drew the rectangle 8.8cm (88 mm) wide, and it turned out close enough that I was happy I had done my calculations correctly.
I hope you have fun twirling in your circle skirts! Bunny and I do!