Posted by: mspremiseconclusion | March 14, 2010

The Ideal Crochet Sphere

Making a sphere is something that comes up a lot in the realm of crocheting stuff. But how do you make a really good sphere?

This is something that I pondered one day. After a very brief and half-hearted go of it with google, I decided to answer the question myself… by throwing some math at it. How do you create a sphere when you are working in a row-by-row system (like crochet) where all you can alter is the number of stitches per row?

Well I assumed that each row is equal to a fixed polar angle , Δθ, within the sphere. At each θ, the circumference of the circle that is traced out within the sphere is proportional to sin(θ) (this was just a quickie derivation). Below, is a plot of what the circumference (y-axis) looks like for each θ (x-axis). So, to completely recreate this, I would want the number of stitches in each row to scale to fit this plot:

So far, so good. In the past, I have only ever used one method to make spheres. It’s fairly common because it’s really easy and, once you stuff it, it makes for a decent sphere. But… it’s not ideal. This method has you increase by the same number of stitches every row until you hit the middle bit, where you work rows even for a little while before you start decreasing by the same amount for each row.

Problem: this is what this method looks like when plotted against the ideal case (the blue dots represent the old method):

It’s just not the greatest. So what I did was to figure out what the ideal number of stitches per row would be, given the sin(theta) dependence. Result: I can make an ideal sphere for however number of rows I want. It’s not as clear as the tried and true method and it’s not intuitive, but it makes a nice looking sphere.

Here is a pdf file where I’ve written up the pattern for ideal spheres of different sizes. I haven’t tried all the different sizes out myself (since I would up to my eyeballs in spheres) so they *should* all work out nicely. Let me know if they don’t.


p.s. Math rules!

UPDATE: Here is a link to a newer post where I include the pattern for some even bigger spheres! Embiggen!

***03.25.10 Update: An error has been spotted on the 10 Row Sphere, rows 5 and 7. (Oops – sorry all!) So this mistake has been fixed and the link has been updated.

***03.27.10 Update: Oops#2 located on 16 Row Sphere and is now fixified.



  1. Oh. My. I would love to scale this for knitting, too! — as the row gauge for a knit piece will not be the same as the row gauge for a crocheted piece of equivalent stitch gauge. This much I know. The plotting of “X” and “y” axises, however, are just hopelessly vague recollections from long-ago High School Calculus and so I despair of building on your genius…
    (but I can’t wait to incorporate the crochet version into this year’s felted xmas decor!)

  2. I agree, lisab! It would be great to figure out an ideal sphere in knitting too! Learning to knit is on my to-do list… so maybe someday I will try to figure that one out!

  3. I just found you through Ravelry and was so impressed with your sphere! I can’t wait to try one out! Thank you for sharing!

  4. This is wonderful! Here I was thinking that I was the only one who thought the other way of making spheres comes out skewed and not circular at all. I am thinking of making this the base for some spherical patterns. Thank you.

    • Thanks!! I’m glad you like the pattern and I hope it works out with your spherical patterns!

  5. There are a couple of knitted perfect spheres. The best-looking one is by Brent Annable, at rav link .

  6. hi! um.. i couldnt get the pdf pattern….can u plz post it on ur blog ??

  7. oh, my! I totally agree… math rules!

    I’ll try this pattern today for a baby present I’ll give this afternoon… hope to post something tomorrow…


  8. This PDF is amazing! I’m using them to make a molecular structure and they’re coming out beautifully.
    Forgive me if this has already been asked/addressed but I didn’t see it brought up – do you have any sort of copyright or ownership restrictions with these patterns? As in, if I want to use some of these with a design, would I be allowed to sell that pattern or items made with the pattern?

  9. Thank you thank you thank you for this!

    I’ve been using the “tried and true” method, but havealways had trouble getting it to turn out curved without much convincing (and tugging and stretching).

    The first time I tried the 20 row pattern, it came out perfectly curved- no finagling required!

    [claps hands with glee] ^_^

  10. Oh this so rocks! I love you for posting that pdf! I’m trying to make an oddish and the sphere pattern I’ve got for it just turns out nasty. Your spheres are beautiful. I’ve made a Bob-omb, a Voltorb and soon an oddish out of your spheres. When I take a swing at my Despicable Me minion, I might just take one of your spheres and make it a capsule.

    With the Voltorb, since he’s two colors I cheated a bit. At the center round I finished off and did the second half using the increases again and simply whip stitched the top and bottom together. It came out lovely. 🙂

  11. Wow…you are a genius! I’ve always wondered why my spheres came out looking so wonky! Thanks so much!!!
    Any way to work out the math for a GIANT sphere? I’ve never seen someone crochet a huge one and I’m wondering how it would go.

    • I would also love to know how to make a gigantic spere! Maybe 10-15 inches diameter?? I’m making an Umbreon for a friend, and want to package it nicely within a big hollow pokeball… any suggestions?

  12. Thank you for this pattern!

  13. Thanks for the sphere! Math rocks and so do you! 😀

  14. […] sick at home… It’s a 30 row sphere based on the pattern by Emily which can be found here. Using a 2.5mm hook it ended up slightly bigger than a tennis ball. Tags Categories ball, cat […]

  15. hey try saying it as an odf not a pdf because i couldn’t download it because of that.

  16. i mean saving.
    not saying

  17. this is AMAZE-BALLS!! what a beautiful sphere! i do a lot of amigurumi and got tired of being able to see the increases and decreases! i can’t wait to try this pattern 😀 THANK YOU in advance!

  18. This is so cool – the worlds of mathematics and crochet collide. I think this together with your crocheted holy hand grenade make you my new crocheting hero 🙂

  19. […] After I threw a little bit of math at it, I came up with a pattern for the number of stitches required in each row to make an ideal sphere! I posted the pattern on my craft blog along with a description of how I solved the problem. […]

  20. […] wanted to share a link to MsPremise’s blog:         Here she has a pattern that I’ve been using a LOT, and I find it extremely […]

  21. […] lot of the legwork for this kind of sphere was done by Ms Premise-Conclusion on her blog post: Ideal Crochet Sphere. There she explains her model and compares the standard method to the ideal case. A good read for […]

  22. You are my new hero 🙂

  23. […] with the theme of “round,” coming in at 72 on my crochet bucket list is this ideal crochet sphere courtesy of the blogger known as Ms. Premise-Conclusion: Ms. Premise-Conclusions ideal crochet […]

  24. […] the blog,  Ms Premise-Conclusion ,the author shares the following instructions for crocheting an ideal […]

  25. […] then decrease the same way you increased. But one clever crocheter/mathematician has come up with the PERFECT! sphere! She’s got directions for several sizes – above you can see a ball I crocheted using […]

  26. i’m wordless… awesome! Respect your dedication and patience 🙂

  27. […] profite de cette balle à grelot pour vous donner deux liens. Le premier vers le tuto de la sphère parfaite, par Ms Premise-Conclusion ( la mienne manque de bourrage, mais elle est belle et bien […]

  28. Thanks so much for the pattern! I made some Dragon Ball Z balls with it…

    Love love LOVE your work 🙂

  29. thanks !!!

  30. Thank you for your pattern. New to this. What does Row 10) 4 scdec.mean?

    • Hi! 4 ScDec means Single-Crochet-Decrease the next two stitches together. Repeat this four times.

  31. I feel terribly dense admitting this but I’m having the worst trouble trying to understand the pattern for the 12 row sphere. Once I hit row 3 I became befuddled. Could someone clarify what it means? Just the structure of the instructions. For instance, when it says “1, inc, 2, Inc, 1, inc, 2, inc, 1”, does that mean increase once, sc twice, inc? Sorry, I am quite new to crocheting.

    • Hi! Check out the top of the pattern for a break down of the lingo. “Inc” means “2 Sc in next stitch”. “1, inc, 2, inc, 1, inc, 2, inc, 1” means “Sc in next stitch, Inc, Sc in next 2 stitches, Inc, Sc in next stitch, Inc, Sc in next 2 stitches, Inc, Sc in next stitch”.
      Hope this helps!

      • Oh thank you so much! 🙂 on with my pokéball 😀

  32. Hi
    I have a problem, I don’t understand if I have in row 9, 12 stitches and I do 4scdec as you explained, I don’t understand what to do with the final stitches , could you please explain what this: “Weave loose end through each stitch in the opening” means exactly. Thanks.

    • I think you’re looking at the final row of one of the spheres? When I say ‘4 ScDec’ it just means to ScDec 4 times. This will not use up all of the stitches from the previous row, but that’s ok. With the loose end of the yarn, weave it through each of the last 4 ScDec stitches and pull the yarn to close the opening.
      Hope this helps!

      • Great, now I understand, Thanks a lot, I going to translate into Spanish if you aloow me to do it. maybe i is translated yet…I don´t Know and many people ask me. Fantastic work

      • I’m glad I read these comments! I’m currently on round 26 of the 26 row sphere, where it says 4 scdec around, leaving me with four unworked stitches. I was wondering what to do. Thanks!

      • Sorry but I’m still a bit confused. The row before the 4ScDec has 12 stitches. After the 4ScDec 8 of the 12 will become 4 stitches leaving 4 stitches. Do you mean weave these last 4 stitches together that are left? (You said last 4ScDec which is confusing as they haven’t been decreased.
        Also, I’m wondering why you don’t ScDec all 12 to make 6 stitches and then weave these together so it mirrors the start.
        Thank you. Awesome pattern 🙂

  33. […] serie de patrones (en inglés) con los aumentos precisos por corrida para crear lo que ella llama la esfera de crochet ideal. Toda un geek del […]

  34. […] for the face and embroidered the details and attached two safety eyes.  The ball pattern is from this blogger who mathematically figured out how to crochet perfect spheres.  She’s amazing!  I want to […]

  35. […] the incredible Darci found this link and shared it with me. It’s about crocheting an ideal sphere. It totally reinforces and […]

  36. Today, I went to the beach with my kids. I found a sea shell and gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell to her ear
    and screamed. There was a hermit crab inside and it pinched her ear.
    She never wants to go back! LoL I know this is completely off topic but I
    had to tell someone!

    • Hahahahaha I always have things I have to share to. I have 4 boys, 14y, 13y, 6y, & 19m, and they are all nuts!! Haha you made me laugh! 😊

  37. Would it be possible to get a bit more info on how to read this pattern? I’m struggling with what the actual numbers mean. For example, does 2, inc, 3, inc mean stitch 1 sc in next 2 chains, then in the next chain, stitch 2 sc into the next stitch, etc…?

  38. I do hope you’re receiving comments on this so many years later- I was hoping for more information on using your math to scale the sphere to much bigger proportions, I was hoping for roughly a basketball-sized sphere. Sadly, it’s been many years since I forgot how to do this kind of math. Thanks!

  39. OMG, I loved how you used math and crochet! Those are like my 2 favorite things in the world! Lol. Thank you so much for this pattern. 😀

  40. Hi! I am currently working up your 30 row sphere with super chunky yarn and an N hook… but I was wondering, is there any way I could get you to write up a pattern for a 80 row sphere? I am attempting to make a giant pouf pillow. The 30 row pattern with chunky yard is turning out to be about 12 inches in diameter, but I’d like to make one that is much bigger.

    Thanks so much for sharing. My 12 inch sphere is going to make a fun pillow.

  41. […] be much smaller.  OR you can completely adapt the pattern to any size ball you want.  I used the Ideal Sphere pattern for mine, and she has a whole slew of sizes you can choose from, I used the 12 […]

  42. […] For the pattern for the bunny, I kinda mixed and matched I made a 16 row sphere using this […]

  43. In the pattern, when you say
    example: 5, inc, 5 (11) = “Sc in each of next 5 stitches. Inc in next stitch. Sc in each of next 5 stitches. (11 stitches in this row).”
    I think that should be 12 stitches after increasing
    Love your pattern, thanks,

  44. I’m working on the 22 row sphere and can’t seem to get passed row 8. 6,inc, II, inc, II, inc, 5 (39) Please help.

    • Hi, Here is the row in regular (non jibbery) language. “Single crochet in the next 6 stitches. 2 single crochet in the next stitch. Single crochet in the next 11 stitches. 2 Single crochet in the next stitch. Single crochet in the next 11 stitches. 2 single crochet in the next stitch. Single crochet in the next 5 stitches”. Hope this helps!

  45. Thank you for sharing, my sphere came out great!
    I was just wandering how you calculated the ratio between the amount of rows and the maximum amount of sticthes i.e. 22 stitches near sin(pi/2) for a 10 row sphere. Did you use certain height to width ratio for a sc?

    • I think I used roughly a 1:1 ratio for a single crochet stitch.

  46. Reading this post sounded like this in my head: ‘Blah, blah, blah, math, blah, blah-de-blah, blah, blah, math, blah.’ I have NO idea what all of the math nonsense means, but I can’t wait to try your pattern! Thanks for figuring it out for those of us who don’t do math!

    • Haha that’s exactly what I heard. We were paying attention in class. 😉😁

  47. Probably common crochet sence, but these are worked in a spiral, right? No joining? TIA

  48. Does inc mean increase in the pdf? I am fairly new to crocheting and don’t understand all the lingo yet so if you could give me something like a table of your abbreviations I would be very appreciative. 🙂

    • Yup – you’ve got it. The explanations for the abbreviations will be in the pdf near the top.

  49. Thanks a bunch!!!! I’m gonna give these a go right away!!!

  50. Just started making amigurumi’s and I did not like the systematical decs that give slight ribs…was about to rethink those…but you’ve done it for us!! Many thanks from a mathematical crocheteer ;-))

  51. Can I Marry you? Ok… Maybe not, but you are officially on my idol list! Math AND crochet, Get OUTTA HERE with that stuff!! I have now pinned you and will be scouring your blog for other useful tidbits! Thank you!

    Much Respect! RESPECT!!!

  52. Absolutely fantastic. Thank you so much for figuring this out and sharing with the world.

  53. […] these balls I used this pattern for an ideal crochet sphere. Of course I couldn’t resist the math behind this pattern ;-), […]

  54. Fabulous, thanks for your work. I used your tuto and the result is perfect. I would ask you to authorize me to traduce it in french in my blog, for many of my friends don’t speak english and would adore to use it.

  55. Great mathematics.. I couldn’t read the labels on the axes… print was too tiny on my screen, so it took me a little longer than it should have to follow what you did. Hope you can add larger labels. I’ll be bookmarking this site.

  56. Is it weird to say that I loooooove you?

    • No. I don’t think it is, because I love her too now! Haha

  57. My UC-Berkeley Math major Mom would LOVE this!! I need to make one in her memory.

  58. […] por la red este post en el que la autora ha calculado matemáticamente cómo hacer elegantes esferas de ganchillo. Con […]

  59. Thank you! It’s very interesting and useful!

  60. […] tan orgullosa… La forma del cap tan rodoneta la vaig fer seguint les instruccions d’aquí (un tutorial fantàstic per fer esferes matemàticament perfectes). La resta va ser sense […]

  61. Thanks for the sphere!

  62. 0.o I’m so confused, but Thank You, you’re awesome.

  63. If we create a pattern based on your tutorial, is it ok to sell the pattern if we include acknowledgement?

    • I created an amigurumi pattern using your tutorial and I just want to make sure what is acceptable, before I decide to sell the pattern.

      • Hello, Anything that I offer on my site is just for people to use for fun and not to sell as their own. Please do not use my work in a pattern that you wish to sell. I offer this as something for people to make for fun and for free.

        Thank you,

        • Thank you for the reply. I figured as much but wanted to make sure!

  64. Reblogged this on Everything Anna and commented:
    Testing this baby out!

  65. […] a follow up to my reblog from yesterday, I tried out the sphere pattern by MsPremiseConclusion and … it turned into an […]

  66. What are the finished dimensions of the balls? I’m looking for a 12 inch or so size. Thank you

  67. Thanks very much for sharing this, it’s great and I would never be able to figure this out on my own.

  68. Доброго вечора! Дякую за вашу статтю і за те, що поділились своїми розрахунками.

  69. I found the link to your site while reading Moogly. Thanks so much for sharing this. It was very easy to follow. :

  70. That is awesome! Um…I don’t suppose you could do an ideal flat circle?

  71. This pattern is PERFECT!!! Thank YOU. I am also interested in a ideal flat circle. My Dr. Who Fez top never turns out flat enough for me.

  72. Hi

    My name is Marianne.
    I am starting up a forum for crochet women in Denmark, we are only just finding our feet and are working out how to get started.

    We have a Links Library, everything to do with crochet – only small so far, but it’s a start 🙂

    There is now a link to you:
    We have taken the liberty using a single photo from the DIY/pattern to represent the link, so that it is easy to see what it is.

    You can access our Links Library here:
    It is open for guests.

    We might also, in the furture want to make other links to you, using other pictures, to show with the links.

    If you do not want us to use your pictures with links to you, please let us know, we will then remove them right away.

    You can contact me at this email address:

    Love from Denmark

    – Marianne

  73. Many thanks for sharing this with the people of yarn ^_^

  74. Hi! I am wondering if you can tell me about what size each row equals out to? I am looking forward to making this, however, not sure what “row” size to stop at. A toddler size is needed. Thank you.

    • Maybe needing about 16″-19″ if possible. Thanks. (See previous comment). Thank you.

  75. Hi Alicia, If you’re looking for a sphere that large, you might want to check out the customizable sphere post – you just need to input how large you’d like your sphere to be and it will generate the pattern for you!

  76. Thank you thank you thank you!!!! I’m currently keeping two kids who have a lot of issues and the younger sister loves anything spongey. After her biting holes in a nerf ball I decided I’d crochet a couple of balls for them to play with. This is PERFECT!!!!

  77. […] second mathematical approach was the Ideal Crochet Sphere. This is based on viewing each round as a latitude line and calculating its circumference from its […]

  78. Great info. Lucky me I recently found your website by chance (stumbleupon).
    I have saved as a favorite for later!

  79. whoah this weblog is excellent i like studying your posts.Keep up thee
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    will be waiting for your further post thanks once again.

  81. […] Yesterday I started with some basics. I found, where I learned the magic circle starting method and the invisible decrease, and then I tried out a sphere (following one of the ideal sphere patterns found on […]

  82. I love these! Thanks for sharing!
    For the 10 row sphere it reads:
    Row 10) 4 scdec.
    Could you please explain this? I’m pretty new to crochet, and cannot figure this last row out?

    • Hi Sally, I’m glad you’re enjoying the sphere! The final row is just 4 single crochet decreases in a row. You won’t complete the entire row, but you should fasten off after this point. This is so that the base of the sphere doesn’t look pointy.


  83. I can’t get to the pdf file either. I would love to try this 😕

    • The PDF link is just under the last sphere photo. See where it says PDF, it should be a different color. Click on it but you need to have some type of PDF support software like Adobe. Just search pdf software in Google. You should pay nothing for this. If you do this or already have it then it’s probably a matter of finding where the pattern file was saved. For this you can do a search for the file name. If you need anymore help find me on Facebook or reply to this, I will try my best to help.

  84. […] I definitely let my creativity go wild over the last few weeks. The first project that I’ve spent a lot of time has been for a friend who absolutely loves gnomes and everything magical about them. I really wanted to make something completely from scratch and without any pre-made patterns. I did cheat a little though…I used these lovely calculations for perfect spheres that I found on the blog, Ms Premise-Conclusion. […]

  85. This is awesome. Thanks!

  86. Are you the best… or are you the VERY best!? Thanks so much for this! I love the math. I love the fiber-craft. I love the Simpsons reference. You’ve put a smile on my face! 🙂

  87. […] baseerde me op het patroon voor een Ideal Crochet Sphere, en na enkele trial & errors had ik “mijn” patroon gevonden. Voor de liefhebbers […]

  88. Hello! I do not understand what the formula. Or is it secret?

  89. Glad to be one of the numerous visitors of this excellent site.

  90. Wow! This is super helpful! Thank you for this! (I’m also really impressed at you application of math!)

  91. I’ve been frustrated with my favorite amigurumi pattern book because I could never get their heads to come out right. I’d been looking for a new head pattern and you just solved my problem in an awesome way.

    Awesome work!

  92. Can someone tell me what size ball each pattern makes? I want to make a 1″ ball…think Cake Pops! And I don;t know which pattern to choose.

    • They work up fairly quickly and as you get to about the 3-5 row you will clearly start to see the size. That said it has been a while since I made one but I believe I used a 3.75mm hook and made the 10 or 12 row ball and it came out a perfect 1″, you can see the results here I suggest you just start working up a sample. Hope I helped, I would love to see a pic of your finished project and let us all know what worked for you.

      Have fun.

  93. […] anyway, I found this awesome blog post about making perfect round balls (she uses the word « sphere » but […]

  94. Question: I have a sphere that is 33 rows and has 96 stitches at the most so how would I figure out the increases for rows? I am in awe of math and think it’s great but I have no idea how to use it!
    Thank you for any help you can give me!

  95. Is this done in a spiral?

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  101. […] want to use a more dense stitch like single crochet.  My go-to source for single crochet balls is Ms Premise-Conclusion.  Her balls are very aptly called ‘Ideal Crochet Spheres’.  She also has an amazing […]

  102. […] los que quieran saber cómo hacer las tres bolas que componen el cuerpo, podéis pasaros por este post. Es la solución para hacer esferas de ganchillo que queden bien […]

  103. […] decreases, I use invisible amigurumi decrease, like this one. For back shaping I used this tutorial as a […]

  104. […] pattern is pretty straightforward, I used this 30-row sphere pattern and sewed on a crocheted circle for the […]

  105. […] are totally worth it! If you’re in need of a perfect sphere of any size, check out her original sphere pattern, large sphere patterns, or custom […]

  106. […] Ideal crochet Sphere by Emily […]

  107. […] orange is a version of Ms.Premise-Conclusion‘s Ideal Crochet Sphere pattern. She actually did the math (which I admit to not understanding!) that shows you how to make a […]

  108. Thanks so much! Math rules! 🙂

  109. […] wzorów na Free Amigurumi Patterns, skąd zostałam przekierowana bezpośrednio na blog autorki, Ms Premise-Conclusion. Na blogu znajdziecie wiele wartych uwagi wzorów, polecam 🙂 Wzory na kule są dostępne w […]

  110. […] używałam żadnego konkretnego wzoru BB8, posłużyłam się za to rozpisanym przez Ms Premise-Conculsion wzorem na idealną kulę (na 24 rządki wysokości). Jeżeli zajrzycie również na główną […]

  111. […] robi się szybko i prosto; Stosujemy niezawodny wzór na idealną kulę o wysokości 30 rządków autorstwa Ms Premise-Conclusion i w zasadzie robota zrobiona 😉 […]

  112. I love this pattern. What I’ve been looking for, for a long time.

  113. Hi, I apologize if you already mentioned this…can you share what size hook and weight yarn you use? Can’t wait to try it! Looks beautiful.

    • Hi there, I use a 3.75 mm hook with worsted weight yarn. But really, as long as you can make stitches tight enough so that the stuffing won’t poke through, you can use whatever yarn/hook combination that you like!

  114. Hi There,

    I am not sure if you are still checking this link. But I wonder if you could help. Your somewhere are awesome. So clever.

    I made your 30 row sphere for a project, but it wasn’t big enough for my project. I need something slightly bigger. Could you tell me please if you don’t mind, how to increase it to 35 or 40 rows.

    I would appreciate the help. Thank you so much.

  115. […] metki 😛 Trudno, nie ten, to kolejny 😉 Wzór mój, ale nie udało by się bez pomocy nieocenionej Ms Premise-Conclusion i jej genialnego wzoru na idealną kulę, który powoli znam na pamięć 😉 Głowa Weedla to kula […]

  116. […] Ideal Sphere by Ms Premise-Conclusion […]

  117. […] Ideal Sphere by Ms Premise-Conclusion […]

  118. 18 row sphere, row 17. If you start with 17 sts & (dec,1) around then you will be 1 st short bc there’s no lady st to put the 1 sc into. You will end up with 11 sts, last st being a dec. I went ahead & did alt (dec,1) and (dec,2) around like the 16 row sphere to get 12.

  119. […] the way, I took the start of this pattern from here and the sphere patterns there are quite lovely, so please go and check them out whenever you need […]

  120. […] Red Heart Super Saver hot red, a 3.75 mm hook, and Ms. Premise Conclusion's pattern for the ideal crochet sphere, I gave it a […]

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