Calculating clothing combinations…


So, I was quite sick for the last few days and so didn’t get a Monday post up. Rather, I spent my Memorial day in bed, sleeping and eating soup. I hope other people had a better day off. Since I didn’t want anyone to think I’d dropped off the face of the Earth or was eaten by a wild goat, I have decided to post something I wrote last week and never got around to posting. I hope no one minds.

In the wake of doing my astronaut scientist paper doll Emily, I started thinking about paper dolls and math…

Now, I’m pretty bad at math, but I do have a formula I use for calculating outfit options. (By the way, I also use this when packing for trips where it works pretty darn well too. 🙂 )

Here’s how I calculate the number of “outfits” possible from a set of paper doll mix and match clothing pieces. First, we must define our variables. I know a certain former math teacher who would be quite irate with me if I failed to define my variables.

      X=Number of Tops


      Y=Number of Bottoms


      Z= Number of Jackets


      W=Number of Shoes


      V = Number of Dresses


    N= Number of Outfit Combinations

So… the formula looks like this:

    ((X*Y)+V)*(W+1)*(Z+1)= N

Why the formula works…

An “outfit” consists of one top plus one bottom. Since every top can be worn with every bottom, the tops multiplied by the bottom gives us the number of outfit options. Dresses are generally not worn with tops or bottoms and therefore they are added after the multiplication has taken place. The shoes (W) and the jackets (Z) both have to have one added to them, because it is possible to function without wearing shoes or jackets and the one provides for that option. If the assumption is being made that shoes will always be worn than the 1 can be omitted from the (W+1) calculation.

The formula doesn’t always work. Some sets, such as Mia at the Bathing Place or Blossom are done with the assumption that certain pieces will always be worn together or aren’t really mix and match to begin with. Further, not all paper doll sets are mix and match oriented. I generally do not take necklaces, scarves and other accessory items into consideration, because I think they don’t dramatically change the outfit enough to warrant being counted as separate outfits. For example, had I considered them, Spikes and Pleats would have included 5920 combinations, which seems a bit much, even to me.

However, if you want to include the accessory items… than take N and do the following:

      N= Number of Outfit Combinations


      A= Number of Necklaces


      B= Number of Bracelets


      C= Number of Scarves


    D= Number of Outfit Combinations including Accessories

So… now the formula gets to look like this:


And with that little foray into math, I am now going to go take more cold medication. Enjoy the calculations… And ask if you have questions.


  1. thats a really cool way to fidgure out outfit combinations, and i dont really like math at all infact i am dreading haveing to go do my math homework. I hope you feel better soon being sick is no fun at all. I really enjoy reading you websight and seing your unique and awsome paper dolls.

    1. I know sometimes math is tough, but it’s also surprisingly useful in the real world and, though it’s frustrating sometimes, it gets pretty neat at higher levels.

  2. Wowser! LOL. I understood the picture at the top, but you lost me after that. I suppose its a good thing I draw my outfits all together!

  3. I know math is important and it is definatly cool when it makes sence and makes things easier to solve but some things i am learning in math class i feel dont really apply to my real life sistuations. Things like this are definatly really cool and helpful thought

  4. Creepy fairy! Well, they are supposed to be creepy according to the original fairytales, as I’m sure you know, not fluffy and sparkly and light like Disney fairies.

    So, Rachel. Here’s a challenge for you! I’ve started a pregnant paper doll and I’d LOVE to see what you could come up with. For some strange reason, pregnant dolls of any sort are very rare.

  5. Thank you! Funnily enough I was looking for some paper dolls with outfits for…..guess what…..a maths investigation when I stumbled upon your post. I have a group of Year 6 girls who will love this. Will try it with them tomorrow!

    1. Yes, this is algebra. You may find it boring, but I know plenty of girls who like algebra. I find this formula extremely handy, so I thought my readers might also find it useful. If you don’t, then that is just fine.

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