I've already told you about two other types of skirts that are pretty easy to make, without a pattern, i.e. gathered skirts, and circular skirts. This is a fully circular skirt.
Flared and part circular skirts
Skirts which are not full circles, can be three quarters, half, or even quarter of a circle, or in fact any other fraction in between. To make these, you'd need to do a slightly different calculation of radius. I've given you some links at the bottom of this post if you'd like to get more on the maths. I've also summarised the maths down at the bottom if you'd like to use it to help you draft a pattern. On the other hand, if you do an internet search, you will pretty quickly find an automatic radius calculator in which you enter the waist measurement and it will give you your radius measurement. BUT - don't switch off, I'm going to show you an easier way than calculating with lots of maths.
The advantage of part circular skirts is that they will generally require less fabric than a fully circular skirt. You will always have at least one join (which would be centre back, and which would still need a lot of fabric width) or more likely, two or more. When you have two or more seams, it's easy to make sure your pattern is the right way up both on the front and back of the skirt. And with two sides seams, you can add pockets.
Let's just talk about cutting out. You'll remember that for a fully circular skirt, you will fold the fabric twice, if possible, and cut out one quarter of the circle. For a semi circular skirt, you can fold the fabric once, and again cut one quarter. That will give you a centre back seam. Or you can cut out two separate quarters, adding in seam alllowance, and have two seams at the sides. 
This is a semi-circular skirt. You can see that it is not quite as wide as the orange fully circular one at the top, but it is still quite full and twirly.
With a quarter circle, you will cut one quarter on unfolded fabric. I don't make a lot of these - in fact, I don't think I ever have, In my view they'd be more suitable for an adult, as they give a very A-line profile.
Which leave us with the perhaps less usual 3/4 circle skirt. There are two main ways: one, you can cut like a circle skirt on a double fold, and then just remove one quarter. This seems like a waste of fabric - you might just as well make the full circle. The more sensible way is to split the three-quarter pattern in two, adding seam allowance, so you actually have 2 3/8 circles. Then you can be more economical with the fabric. This will give you two side seams, again enabling you to insert side pockets if you want.
And here's one of my favourite 3/4 circle skirts.
In fact, for this one, I was seriously short of fabric, but I'll show you how I made it work. In fact, I first split the pattern into 4 pieces, not two. And even then I had to sheer off a little more. You can see I've folded the pattern edges leaving the top untouched - I didn't want to make the waist smaller. So I veered it from nothing at the top to an inch or so at the bottom.
Next, I was fortunate in that my fabric was non-directional, in the sense that the little bears were scattered over it in all directions. So I was able to reverse the direction of the pattern to use the fabric as economically as possible. These are the cut-out pattern pieces, but I've laid them out as they were cut, and the pink dotted lines show you where the edges of the fabric were - it was a long thin strip of fabirc that I had.
And when all the pieces were put together (and a little waistband added) it looked like this. Not perfect, but you didn't notice that in the earlier picture, did you?
Now, I promised you an easier way than doing lots of maths. (This series of posts is all about easy ways to make skirts, right?) I learnt another way to create a template for a flared skirt which is now my go to for girls' skirts, and so I'll share it with you now. I'd like to be able to give credit to the designer I learned this trick from, but I'm not going to attempt to give you the link, because the last time I tried to look at it, I got a message that the web site was corrupted and dangerous, sadly. It originally came from This Mama Makes Stuff, so all credit to her. You may still find links via Pinterest - I strongly suggest you don't click on them. She called it the Twrrly Whirly Skirt.
It's not strictly a 'fraction of a circle' skirt, but somewhere between that and a gathered skirt.
Here's the trick. Start once more with your waist measurement x 0.75 (approximately - that isn't set in stone), and skirt length. And draw a rectangle on some paper using those measurements, adding a bit of seam allowance at the top and and enough for your hem at the bottom. The reasoning for the 0.75 multiplier is this. If you multiply by 1.5, you'll be back in the gathered skirt territory. But you are going to cut on the fold, so you can halve it, hence 1.5 / 2 = 3/4, or 0.75. But you could use a slightly smaller multiplier, which will make it less gathered.
Next, mark some lines from the bottom hem to just below the top (waistline). I usually mark them at about every two to three inches, depending on the size, so you might have somewhere between 5 and 8 sections. And cut along these lines, being careful NOT to cut right through to the top. (If you do, just stick it back together with a bit of cellotape.)
Then, put this on another sheet of paper, and start gently spreading the sections about 2-3" apart at the bottom, sitcking them in place as you go. You can then join the top (waistline) and bottom (hem) in a nice curve, and there's your pattern. One side goes on the fold of your fabric.
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