Special Sunday greetings you naked molerats! Since you’re so naked, I thought you might want to make yourselves some nice little circle skirts. And perhaps, like me, you find yourself with little mole rat patterns just a touch on the small side. But the grading of a circle skirt isn’t so easy, is it you naked rodents? Oh no, not so easy at all…
OK. Goofing around aside, I’ve been giving myself a headache reviewing geometry this morning and I made myself a little calculator and thought I’d share it! I don’t know about you guys, but the math involved with circle skirts is not immediately apparent to me. I mean, I DO get it, after staring at it for a bit, but my understanding totally vaporizes after a few hours and then I have to study up again.
Recently I’ve been plotting about two separate circle-skirt related issues in my head. First, as much as I love my full circle skirt pattern (Kwik Sew 3637 – here’s my last project using it!) it’s just a bit too, um, full circle. I think I’d like to check out a half or 3/4 circle skirt and see how I like that.
For molerats who are unfamiliar with circle skirts, here’s the difference between the three styles. Full circles are full doughnuts, half-circles are half a doughnut – you get the picture. Whether you have a full doughnut or a half doughnut, the inside of the doughnut is the same length as your waist measurement. The green circle on each drawing marks the waist measurement. So if your waist is, say 30″, then that green line is 30″ long in each drawing, but the full circle skirt has twice the volume of the half circle skirt. Get it??
For a much more interesting comparison, here’s a full circle skirt. In action.
{image Whirling Turban}
Here’s the oh, so lovely three-quarter circle skirt.
{image Whirling Turban}
And a slightly pixelated half circle skirt…
{image Get Go Retro}
The other circle-skirt related problem I’ve been mulling over has to do with grading up circle skirts. Since I usually start with a size 18 pattern (in the big 4 sizing) and do an FBA to get the bust to fit, I also have to grade up the skirt as well. To properly grade a circle skirt, one needs to move the waistband DOWN, not add width to the pattern piece! Here’s what I mean…
OK, I admit I usually grade up my circle skirts the ‘wrong’ way. It works, but it makes the bias hang super-extra weird! My problem was I didn’t know how much to move the waistline down to add the inches I needed, as there’s all kinds of geometry involved!
My problem is (hopefully) solved! I spent a while this morning studying helpful posts from other bloggers and practicing the equations in Excel so that I’d have a handy calculator and won’t have to remember what the difference between the radius and diameter is anymore and how pi fits in to all of this. It seemed like a good thing to share!
The Circle Skirt Worksheet
I made two little handy tools this morning – they both live in the same Excel file – in fact, in the same sheet! The first tool is the Circle Skirt Worksheet. I’ll include a screen shot to go over it, but you can download the Excel file here. I saved as an Excel 97-2003 Workbook (I have Excel 2010). I also saved as a public, non-editable document on Google docs (available here), but I’m not sure how that will work – hopefully, it will be accessible to those without Excel.
Before I go any further – I relied HEAVILY on What the Craft and Kadiddlehopper to figure this stuff out! Please click on the links to see more information about making circle skirts! My main goal for the day was figuring out the math and making my Excel cheat-sheet, not the whole drafting process and they both did great posts chock full of illustrations, pictures and videos!
OK, I didn’t want to really make this a whole drafting-a-circle-skirt post, partially because it’ll be super-duper long and partially because there’s already drafting posts out there. I’m just stoked about my calculator to figure out the numbers needed! But here are the basics. To draft a circle skirt (full, 3/4, or half) you need to find out the radius of your waist. I know, whenever I read the word “radius” my eyes roll back in their head (thus the excel worksheet so I don’t have to figure it out anymore…) The radius is the distance from the middle of a circle to the edge. The pink line below shows the radius.
When you draw a pattern piece for a full and half circle skirt, this is what you’ll end up with. (note! 3/4 skirts are a bit different, I’ll show that in a bit!)
You’ll need four of these quarter-doughnut shapes to make a full circle skirt, two to make a half circle skirt. Obviously, the half circle shapes will have a deeper/longer radius, so it’ll still reach all the way around your waist! I’ll return to my mini-drafting lesson after we take a look at the Circle Skirt Worksheet… here it is (click to see a bit larger if you need to, or download in Excel or Google docs.)
Okee dokee. It’s pretty easy to use – at least for me. The white boxes are places where you will enter information, they grey boxes show the numbers you need to draft your pattern piece and correspond to the radius and skirt length measurements in the image above. First, you have to decide what kind of skirt you’re making – full/three-quarter or half – you only use one column at a time. The example is set to make a knee length skirt with a 38″ waist measurement (I use inches, but I think it’ll work the same in the metric system.) Enter your waist measurement in line 5. If you’re starting from scratch you might want to draft for a measurement slightly smaller than your waist measurement, due to the stretching on the bias at the waist. If you do want to adjust down, enter the number of inches to subtract in line 6. I suggested two inches, but Lex from What the Craft suggests four inches in her tutorial (and she certainly knows more than me about this stuff!) You an also just put a zero in line 6. Once you enter these two numbers you’ll get your waist radius in the grey box in line 8 (5.73 in the full circle example.) At this point, you have enough information to draw the green quarter circle in the image above.
Now it’s time to figure out where to draw the pink line – which is the cutting line for the hem. On line 12 enter the length you’d like your skirt – maybe measure a skirt you have to find out?? Then enter your seam allowance on line 13 – I used a half inch and I only need one seam allowance because I’m just attaching to a waistband. Finally, enter your hem allowance on line 14 – I’m super lazy and do a narrow hem on full circle skirts, but I know lots of people like deeper hems! Line 15 shows the number you need (in the grey box) to draft the pink line which is the hem cutting line. Note – the measurement shown on line 15 is the distance of the hem cutting line from the center of the circle, it’s not just the length of your skirt with the allowances!
To continue the mini drafting lesson – I’ll just include drawings of what the pattern pieces would look like for the full, half and 3/4 circle skirts using the numbers in the example. To draw the curved lines it’ll be more exact if you use a flexible tape measure or some other string-type implement to make a giant compass for yourself. Secure in the center of the circle (lower left corner in the drawings below) with your finger or a pin and secure your pencil at the measurement you’re drawing (i.e. 5.73″ for the waist for the full circle skirt) and draw a nice arc. OK, here goes…
For the full circle skirt you’ll need FOUR of these shapes – if you fabric is narrow enough you can fold into fourths and cut one big circle! Otherwise you’ll have to find some folding combination that’ll get you enough of these – perhaps two cuts on doubled up fabric??
For the half skirt, you only need two of these – it may seem like a lot less, but with the waist radius and hem cutting line so much larger, you’ll still need a lot of fabric!
Since a 3/4 circle skirt is, well, three quarters of a circle, it doesn’t break down nicely into the little quarter circles. I SUPPOSE you could cut a pattern piece the same shape as the ones shown for half and full skirts and then cut three of those, but I’d rather have two seams than three (anyone out there know a better way to do this??) If I was starting from scratch, I’d probably draft the full pattern piece and then fold neatly in half to get half a skirt. Fold in half again and it’d be the right size for cutting on a double layer of fabric…
To draw full size, start out by drawing two lines at 90 degree angles (see grey lines below) that are the length of your hem cutting line measurement from line 15 of the calculator. Then make your giant string compass to draw the hem cutting line (pink) and the waist radius (green) from the corner of your two lines.
Let’s move on to the grading stuff, shall we??
The Circle Skirt Grading calculator
Whew! I did NOT intend to cover all of that today!! Really, what I was interested in was resizing an existing pattern, but, as you’ll see, it was necessary to put together the Circle Skirt Worksheet in order to figure out how to grade! Again, please visit What the Craft and Kadiddlehopper for more detailed pictures regarding pattern drafting, cutting and the rest!
Now, I’m not much for drafting patterns whole-scale! Instead I like to start with a commercial pattern and alter – and as I said above, altering a circle skirt takes some math skills! I knew I had to deepen that waist cutting line to make bigger, but I didn’t know how much. What I came up with is more of a worksheet than a calculator – you’ll need to use the Circle Skirt worksheet to complete the grading worksheet! Here’s a look at it – again, you can also download in Excel or view in Google docs. And also again, click the image to see larger.
OK! This is super easy to use. First, enter the pattern’s waist measurement in the field on line 20. In the example moving from a 36 to a 42 inch waist. Next, use the Circle Skirt Worksheet to calculate the waist radius (line 8 ) for the pattern waist measurement and enter that in line 20. Next, enter your new waist measurement in line 22 and calculate the waist radius and enter in line 23. Voila! Line 24 shows how much to move your waist and hem cutting lines down – obviously you’ll have to add tissue to the hemline! Also obviously, you could just use the Circle Skirt worksheet to figure out those waist radii and subtract in your head. Or, perhaps YOU could, I can’t. I’m terrible with math-in-my-head!!
There we have it! I hope it’s helpful to someone (other than me!!) Clever moles may note that There aren’t seam allowances included if you cut the skirt in multiple pieces, but honestly, with circle skirts you’re working on the bias which allows enough stretch to fudge those!
And as always, any of you geometry and/or pattern drafting eggheads, feel free to chime in with corrections to my equations, methods, etc!!
And with that, I’m off. Expect to see some Lucy-sized circle-tutu’s in the near future!
Thanks for some other informative blog. Where else could I am getting that type of information written in such a perfect way? I’ve a mission that I am just now working on, and I’ve been at the glance out for such information.
[...] got to make another circle skirt, but maybe only a half circle. I’ll be making use of this fantastic circle skirt calculator to do it. Its super easy to use- you just plug in your waist measurement, how long you want your [...]
[...] also added a few new links to the links page. I added the circle skirt calculator page, and links to the “Big 3″ site and to Simplicity. I know there are other great [...]
Without your Excel file there is absolutely no way I would have got my head round the calculations for the circular skirt. But when I downloaded it (and opened it in Mac Numbers) it was so easy!Thank you soooooo much for making the Excel file available – you’re a star!
So excited to have found this! I made a circle skirt when I was a “kid”, but it’s been a couple of decades. I’m daydreaming about new floaty spring fabrics and think a 3/4 circle skirt will be perfect! Thanks for making it easy.
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[...] is in a mood now. It’s a 3/4 circle skirt. I used the amazing circle skirt calculator by Patty of thesnugbug. Worked out perfectly. The ruffles are from the leftovers of the white gauze I used here (from the [...]
Since this area is not visible to the eye, chances are that you can rip off the wooden bottom of the cushion and not worry about how it
looks. I recommend starting high and then working low.
When the furniture regains its original look, you will be happy with the decision to turn something old into something new again.
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Fantastic. I have been needing this for a while. Thanks so much
You are amazing! Thank you! I’ve struggled with the correct way to do this for so long- and having a 38 inch waist the vintage patterns always need to be altered- plus I didn’t have the fortune of coming from a sewing family so I’ve had to learn on the fly. Thank you for clearing this up for me, you rock!!!
This is so great! Thank you so much for making/posting this!! You have saved me, I’m in the process of making a dress without a pattern for the first time and tackling the skirt was a bit daunting and this has helped me so much! Thank you!!
[...] free patterns, I came up with very little. I ended up watching a few Youtube videos and reading a blog tutorial on making a circle skirt. Combining these, I made my top. Also, since it was a fitted top with [...]
[...] the measurements was another challenge – I have never been great at Math. But I stumbled on this blog with an Excel worksheet calculator for making full circle and 3/4 circle [...]
[...] per pattern piece (depending on if it’s full or 3/4 circle skirt, calculations courtesy of Patty the Snug Bug and her wonderful circle skirt calculator). For this reason, I can’t fold my fabric in four and cut my pattern piece once: it’s [...]
Yaaaay! Thank you soooooo much for creating this calculator! I’ve made circle skirts before, but I didn’t quite understand how they worked. The spreadsheet helped me understand why the measurements are the way they are. It also helped me grasp the concept of what a circle skirt actually is and what they 3/4 and half circle skirts are. I’ve been to the site you cited as your main source before, but until I stumbled upon this article I didn’t quite get it. Your use of imagery is fantastic! Anyway, I’ll definitely be referencing this post and your page in my future skirt making projects!
You have saved me! I love you and your witty humor! My daughter just began 6th grade and Orchastra. Her tini tiny figure and the need for floor length skirts during recitals created a huge delima. As a seamstress for 18 years I offered my services (floor length skirts for young girls are hard to find and not cheap). I didn’t expect to get the reception I did. I am now making skirts for 2 different schools and needed a simpiler solution than what I had 1st developed. I found your calculator!!! THANK YOU, THANK YOU, THANK YOU!!!!
[...] some trial and error, and patience, I have the circle skirt [...]
[...] First go to this website for an awesome super easy tutorial on how to do that: Full Circle Skirt tutorial [...]
[...] a great tutorial by Patty (in nearby Dallas, I might add!) here and she even created an awesome spreadsheet for calculating full, ¾ and ½ circle skirt waist [...]
Great info. One thing I would change is the word “radius” on the 1/2 circle skirt because I believe it it actually the diameter (radius is 1/2 the diameter)…just a suggestion. But very helpful…especially the pictures of the different skirts. Thanks!
ha ha – I already forgot what a radius was! silly hard geometry -
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Thank you so much! I made a skirt that fits me properly, finally!
https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-ash4/c0.0.403.403/p403x403/426772_4498427857417_1046438707_n.jpg
I was googling “plus size circle skirt” and found your website, an hour later, I had the skirt made.
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[...] Awesome circle skirt calculator from the thesnugbug.com [...]
This is great! Thanks for posting and sharing!
Just popping in with some remarks– like Patty said, the grain is critical on this kind of skirt. The fabric will always “drop” where it forms a bias and the fabric will drop very little on the true grain [warp]. It’s a great idea to hang the skirt before hemming.
Also, I like to stay stitch the waist opening. The circular opening will stretch out incredibly with handling. As soon as I have cut my pieces, without dropping the weight of the fabric from the waist opening, I slide it into the sewing machine, making a medium to large stitch 1/8″ in.
Thank you for this great tutorial! The directions are clear and easy to understand!
[...] for the skirt. I drafted a full circle skirt using two tutorials: Patty Snug Bug’s Circle Skirt calculator and Casey’s Circle Skirt Sew-along posts. For the waistband I just used the one I drafted for [...]
Thank you
this is ever so helpful and the way you’ve explained it has made everything so crystal clear! I love the illustrations too. You’re a gem!
I was also wondering how/where would you put a zip in a circle skirt? I have an existing commercial dress pattern (separate bodice and skirt joined into one dress) I like the bodice pattern but I want a 1/2 circle skirt instead. The dress is meant to have a zip down the center back.
Thanks so much for this – I am attempting a circle skirt for the first time (my mom made them for me all the time when I was little), and this is really helpful. The photos are particularly useful – I’ve decided to do a 3/4 circle model because of my childbearing hips, and I think I’ll be happier with it in the fabric I’m using (a medium-weight chambray).
I love your calculator. I prefer to make my own clothes and this helps a lot with getting my shaping right.
[...] Patty The Snugbug has a great circle skirt calculator. [...]
Thank you for this. I have 5 granddaughters and this looks like a lot of fum to try. especially for the oldest.
I’m making this now. Will tell you how it turns out. So cute.
Genius. What more can I say?
[...] Circle skirt calculator – for the drafting of full, half and 3/4 skirts. With bonus grading worksh… You’ll need four of these quarter-doughnut shapes to make a full circle skirt, two to make a half circle skirt. [...]
awesome awesome awesome! Thank you for writing this and creating the excel file – it’s saved me a lot of time and effort and now I can’t wait to make my circle skirt(s)!
this is a awesome tutorial! thank you so much for sharing it.
I have a question, since I am very new to sewing: is it possible/sensible to use other fractions of the circle, such as 1/8 or 1/6?
And if yes, how should the fabric be folded for cutting?
Thank you
If you choose to use other fractions of a circle, what you’re making is a six-gore (or eight-gore, or twelve-gore) skirt. All the pieces are identical to one another — skirts like this drape beautifully and (if you can find them on the rack at all) tend to be pretty high-end. The math is slightly different if you are using a multiple of six pieces; it’s not necessarily harder, but it’s potentially more fiddly. You would need to figure in seam allowances for each piece.
As for how to fold the fabric: These pieces tend to be pretty big, so the way to fold it is the way that lets you fit the pieces on it!
Just remember that you want the straight lengthwise grain running up and down the center front and back of the skirt (this will be a seamline on an eight-gore or twelve-gore skirt, but not on a six-gore skirt).
great tutorial!
I am new at sewing, and this is wonderful help.
I do have a question: would that make sense to try other fractions of a circle, such as 1/8 or 1/5?
And if so, how would the fabric had to be folded for the cutting? Thank you so much!
Man! Where was this yesterday when I totally let a poodle skirt beat me because I just couldn’t understand the math. Thanks! I’m gonna have another go at it. Thanks very much!
hello, thank you sooooooooo much for the calculations. i am not understanding two things though because i am new to sewing. i am making a half circle skirt. the drawing for this above , is it cut on a fold ? if sew then i would have two peices in total with two side seams? In addition i am hippy so i am thinking a 3/4 is less bulky, how do i orient my fabric and pattern peice? how many peices would i then have cut out. i cant wait to add this skirt to my dress bodice and finish.You ROCK!!!!!! Just saying
Re: the hanging front problem. There are two factors. Bias stretch and butt bulk. The second factor will show itself on the very first time you try on the skirt, the first will need some time to show. In both cases, the solution is the same.
1. Do follow the sound advice to let the finished and washed skirt hang for a month (pegs on a hanger)to stretch all it needs, before doing the hem.
2. To do the hem, stand straight on a stool or chair, and,while you slowly turn around, have a helpful friend on her knees measure the distance from the desired hemline to the ground at many points all around the fabric, marking with pins, . There is an easier way, with a tool on a stand: you choose the desired hemline and then that puffs chalk powder. If you plan on sewing lots of skirts it is a useful investment.
Thank you so much for the great tutorial! Love the excel spreadsheet!
[...] the effect on this fabric. I even topstitched the darts at the back! For the circle skirt I used Patty’s calculator to do the [...]
I have been wondering how to make a circular skirt as I had seen a magic skirt at a shop and felt that I should be able to make one in colours that I like. THANK YOU SOOOOOOOOOOOO MUCH. Guess what all the girls in the family will be getting for Christmas!
Ugh, they always said we’d need that geometry in real life and they weren’t kidding! You should come see my post about building a greenhouse and my geometry issues there!
If they had just SHOWN us in geometry how to make something and use it, it would have made so much more sense to me back then!
Just wanted to say a HUGE thankyou! The calculator was soo helpful!
hello pretty skirts!!
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Thanks for this great download to do the math for us. I’m like you, I’ve done it before but I always forget how haha!
Since you did most of the math for us I did one more step because I’m most interested in the 3/4 circle… to draft just half of the pattern, extend the horizontal line of the original diagram towards the left, measure UP 45degrees from there and draw that line out to the end of the hem line (to follow the example it would be 29.14″). And there’s half of a 3/4 circle skirt pattern.
However, if you want to cut on a folded fabric, I would still fold that 1/2 pattern piece in half because the angle is an odd one that would be difficult to measure out (67.5deg UP from the right hand horizontal of the original diagram)
[...] This calculator is from the snug bug… check out the full post here: http://pattythesnugbug.com/2011/circle-skirt-calculator-for-the-drafting-of-full-half-and-34-skirts-… [...]
I’m wondering with woven fabric (fabrics that don’t have stretch), my concern is that by using the waist measurement that the skirt won’t slide up over the larger hips. So it’s my understanding that the hip measurement should be used, to be on the safe side like in this diagram: http://1.bp.blogspot.com/_X29Ay8F1pMk/Slv6cd3iXEI/AAAAAAAAAWA/yDX_9YO2xbs/s1600-h/Skirts+Cheat+Sheet.jpg
Funny you should mention that! I JUST made a circle skirt with an elastic band for the waist and was concerned about the same thing – how would it slide over my hips? Up until this project, all of my circle skirts have a zipper closure, so that’s how they slid up (or rather, over my head, that’s how I usually put on circle skirts!)
Even with very stable wovens, cutting on the bias (which is what happens with a circle skirt) provides a LOT of stretch.
Anyway – I wasn’t sure how it would work out, but it pulls on just fine. I’t magic. There, oh, and 11 inch difference between my waist and hips, and apparently the bias can totally handle it.
If you cut the waistline of the skirt to your hip measurement rather than waist, I’d think you’d have to do a bit of gathering, which would give it more of a dirndl look. One of the reasons I like circle skirts is they have good volume without adding bulk at the waist in the form of gathers. On the other hand, if the general waist to hip difference is about 10 inches, well, depending on your measurements, the gathers might not be all that noticeable. If I were to gather 10″ at my waist, I’d be gathering 125% of of the total length needed – compare that to the general ratio/rule of thumb for a nice, full curtain of about 200% (twice as much fabric as width to get good folds, etc.)
I didn’t understand some of the notations on your link! (Sunday morning prior to 8 a.m. AND my second cup of coffee…) hope I’m sounding rational!!
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Re the hanging lower in the front problem: While generally it is better to adjust at the waist/hip area, the geometry of making the back waist higher and the front waist lower gives me fits. You could cut the skirt in four segments and make the necessary alterations at the waist. If you’re very large-hipped, as I am, this tends to screw with the “look” of the circle skirt, because it changes the drape from the waist.
I usually just try the skirt on, note how much longer it hangs in the front, then fold the skirt so that the side seams are together and the fold runs through the center front. Then trim the skirt shorter in the front, tapering back to the full length at the side seams. With a circle or half-circle skirt, you have plenty of fullness and swing, so you can’t really tell that it’s a half-a**ed solution. (Note though that I always wear skirts well below the knee, so I can’t say how this would look on a short circle skirt. Try it on a muslin first if you’re doing a shorter skirt.)
It also helps if you make the waistband rather substantial and fairly snug to your waist (elastic helps), because a full circle skirt is pretty heavy, and the waistband tends to stretch a bit, being on the bias.
Wash the unhemmed skirt and hang it to dry before hemming. It’s quicker than waiting several days/weeks for the bias to settle.
Excellent tool! Thanks so much for sharing.
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[...] download a calculator from Patty the Snugbug’s blog. The tutorial on her site can be found here. So this is my inpsiration for the skirt as well as a swatch of the [...]
Thanks for such a helpful post. I’ve been struggling with the geometry of a circle skirt for ages. I couldn’t work out how to grade up the waist of a paper pattern and your calculator in Excel is fantastic. Would just like to point out that I think some of your line references aren’t quite right: Should read subtract line 20 from 23 and use measurement on line 24 to grade up waist measurement. Brilliant anyway!
Thanks so much for this post! With all the pattern manipulation I’ve been doing I’m starting to think I need to get college credit in applied geometry! The photos of the differences between full, three-quarters, and half circles were especially helpful
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This is a WONDERFUL post, definitely bookmarked for fall skirts. Thanks for doing the hard work for us!
I have had many a circle skirt math disaster in my day, complete with some on-the-fly redemption successes.
This one is particularly notable:
The disaster – http://sincerelyyours-kate.blogspot.com/2008/02/circle-skirt-redemption.html
The redemption – http://sincerelyyours-kate.blogspot.com/2008/02/circle-skirt-redemption.html
Have you solved for the pesky problem where the circle skirt is a bit short over the bum and hangs a bit lower on the waist? I am pretty straight hipped and flat bottomed, but I always see my hems pull up over the trunk anyway. Any solutions?
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Thank you so much for this great tutorial and circle skirt worksheet. I love your blog. I only discovered it recently but have been following you since. Now I am off to make a half circle skirt ….
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This is great; thank you!
This spreadsheet is great. Thanks. And thanks for the dog tutu idea. My malamute Tina can expect a doggie tutu in the near future.
Thanks so much for this! Math involved in a circle skirt has always made me want to go screaming in the other direction but now I can make one and twirl til my hearts content.
Dude this is awesome. It’s fun to look at the info as mathematics, since what I do is pivot out the waist dart on a sloper to make the front and back of the circle and then smooth it out, and then measure down in about a bazillon places what the desired hem length will be plus seam allowance. I usually just draft for .5″ since I’d use a rolled hem for a circle skirt, or a facing (horsehair etc).. It doesn’t give you the nice perfect donut hole in the middle using a sloper. I like the donut hole!
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Such a thoughtful and excellent post. I’ve been wanting to make a circle skirt since before I started to sew. And somehow I still haven’t managed it because I couldn’t find a pattern called “circle skirt”. Maybe I’ll get off my butt and try this!
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THANK GOODNESS I have a 38″ waist like you! Thanks for the calculations. Great tutorial! It must have taken you a long time! Love your blog. Very inspirational.
I have been wanting to make a circle skirt forever but could never figure out how to cut one since my measurements are so much bigger than most of the patterns (waist is 43). Your calculator takes the guess work out of the cutting. Now if I can only find some wonderful fabric on sale
WOW! That’s a lotta great work you put in there Patty – thanks sooo much for sharing your maths and calculators with us (plus the diagrams are very helpful too)
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WOW! This is super fantastic! Thanks so much!
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