October 12th, 2010

Cake pan size conversion ~ The formula ~

.
One of the many baking questions I get asked is how to scale a cake recipe to fit another size or shaped pan.
.
There is an universal formula you can use:
.
(volume of the preferred tin) ÷ (volume of the original tin)
.
x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x
.
For this, you need to find out the volume of the two tins.
The formulas to work out the volume of a pan according to shapes are the following:
.
ROUND
(3.14 x half the diameter x half the diameter x height)
.
SQUARE or RECTANGLE
(length x width x height)
.
NOVELTY CAKE TIN
First work out the volume of tin by weighing how much water goes in. Water is 1g = 1 cm³
(The mass of 1 cubic centimetre water at 3.98°c equal to a gram. (it’s the temperature at which it is at maximal density roughly). So we can use that number you’ve weighed as the measure of volume.
.
MULTI-CAVITY TIN (like a muffin pan)
Again, work out the volume by pouring water in one cavity, & multiply that with how many cavities there are. Weigh it in grams, & use that number as the volume.

.
x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x
.
Here are two examples:

.
To convert from an 8″ ROUND cake tin (with 2″ height) to 10″ ROUND cake tin (with 3″ height) you’d do this:
.
(3.14 x half the diameter x half the diameter x height) ÷ (3.14 x half the diameter x half the diameter x height)

.
(3.14 x 5 x 5 x 3) ÷ (3.14 x 4 x 4 x 2) = 2.34375
So here we now know that we need to multiply the recipe by 2.4 times.
.
But if the height of the pans are the same, use this simpler formula:
(dimension of preferred tin ÷ dimension of original tin) x (dimension of preferred tin ÷ dimension of original tin)
For example,
(10÷8) × (10÷8) = 1.25 x 1.25 = 1.5625
So here we now know that we need to multiply the recipe by 1.6 times.
.
_ . _ . _ . _ . _ . _ ._ . _ . _ ._ . _ . _ ._ . _ . _ ._ . _ . _ ._ . _ . _ ._ . _ .
.
To convert an 8″ ROUND cake tin A to 10″ SQUARE cake tin B (when height is the same):
.
(length x width) ÷ (3.14 x half the diameter of A x half the diameter of A)

.
(10 x 10 ) ÷ (3.14 x 4 x 4) = 1.99
So here we now know that we need to multiply the recipe by 1.99 times. (I like to round it to 2)
.
x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x
.
Please note:

- If both tins in question are of same height, you don’t need to measure the height for each.
- The examples are in inches, but of-course the same formula works in centimeters too!
- When I get long answers like 1.5625, I personally like to round it UP to 1.6.
- Although the oven temperature should remain the same for both occasions, the baking-time will change.
.
x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x . x
.
It’s all probably elementary bit of maths for you all, but for me it certainly isn’t! There is a reason why I’m a baker & not a mathematician…

61 Comments »

  1. Wow, thank you!! This is super helpful. I’m going to print this out and keep it with my cookbooks. (It’s definitely not elementary maths to me, that’s why I’m neither a mathematician, nor a professional baker, just an art historian who likes to bake. ;) ) xx

    Comment by Rachel - October 12, 2010 5:30 am

  2. Bookmarked!!!! Thank you!!!!

    Comment by Louise - October 12, 2010 11:14 am

  3. Oh cool Rachel! I’m so happy that you think it’s helpful!! ^^ And thank you for always commenting. – I hope things are going well for you in the states? All the best, t xx
    .
    Louise, wooow!! Thank you for bookmarking!! xx

    Comment by tamami - October 12, 2010 11:15 am

  4. ow! my head hurts ;)

    Comment by petoskystone - October 12, 2010 12:34 pm

  5. I know I know – the formula look complicated with all those As & Bs, pi’s & squares, right? If it weren’t for the cakes, I wouldn’t touch upon maths I can definately say!

    Comment by tamami - October 12, 2010 12:58 pm

  6. That is most interesting! Like Rachel, I think it is something to copy and keep w/my recipes. I love things like this, conversion charts, etc. You don’t need them often, but when you need them, you REALLY need them! Thanks for posting…

    Comment by heidy - October 14, 2010 2:33 pm

  7. Hi Heidy!!
    Thank you! It feels special that something I wrote gets printed out & then filed together with your collection of recipe books & that it lives outside of a screen – Because y’know what, I stash things in my (recipe) books too, for me it’s not just print-outs but also cards from friends & loved ones, kids’ drawings, leaves from a memorable walk inbetween the pages! It is a very special space…

    Comment by tamami - October 14, 2010 3:54 pm

  8. Amazing! I have a cookbook that lists interchangeable pan sizes, but this is so much more complete and invaluable!!
    Can I link to this on my website?

    Comment by Diane - October 14, 2010 10:39 pm

  9. Hello Diane!!!!!! Oh how fantastic! Please do link! I’m glad you think it’s good! All the best, t xx

    Comment by tamami - October 14, 2010 10:54 pm

  10. I’m really bad at math, my cakes always fails if i need to change the measures :P well, most of the bakings fails anyway! Yesterday I wanted to make muffins, with our super tiny oven and these did start to melt all over, not looking like muffins but tastes still good. Is it the oven or me, i don’t know, I used to be a good baker when we still had normal size oven and it did work. I even did set fire our tiny oven one day :O and now i’m scared to use it haha. any tips? buy a normal oven i guess ;)

    Comment by sini - October 15, 2010 5:38 am

  11. Hi Sini! Y’know what? My top tip is actually to first get an oven thermometer & test the current oven out. I remember that the oven in my previous house was never precise… so y’never know, perhaps that’s the problem? Also, you might already be doing this, but always preheat til it reaches the correct temperature. – For example, my mum never bothers with preheating…! Anyways, it seems as though you still enjoy baking, & that’s the main thing right? ;) xx

    Comment by tamami - October 16, 2010 1:04 am

  12. oh dear me…i’m terrible at math! but i’m sure this will come in very handy when i have conversion to do…i should remember to come back then! cheers :)

    Comment by Jessie - October 18, 2010 10:42 am

  13. Hi Jessie! No problemo! xx

    Comment by tamami - October 19, 2010 2:28 am

  14. Hi, I just wanted to say the information through the blog has been very inspiring, i have been interested in becoming a chocolatier and getting into trading (not in your patch don’t worry ;)

    so thanks for making such clear and precice posts for baking and working with chocolate etc.

    Comment by Luan - October 20, 2010 10:49 pm

  15. Luan! My pleasure!!!! Thank you to you for posting such kind comment! Comments such as yours really get me going with posting more stuff!

    Comment by tamami - October 21, 2010 7:18 am

  16. Thanks for the conversion, it will be very useful! The thought of ever doing something like that makes me shiver!

    Comment by Alison - October 22, 2010 9:12 pm

  17. Oh! hi Alison!!!! Wowwww, it’s really so lovely to hear from you! Thanks for checking my site out! Sounds like your trip to paris was wonderful!! – Hope to see you soon!! t xx

    Comment by tamami - October 22, 2010 9:15 pm

  18. Thanks so much for setting it out for us! SO helpful!

    Comment by Robyn - November 5, 2010 5:59 am

  19. Hello robyn! That’s fabulous! Thanks for leaving a comment here! xx

    Comment by Tamami - November 6, 2010 3:19 am

  20. hi.. really like your blog.. wondered if you might be itnerested in this video of stall holder in newcastle dancing.. maybe you guys could do the same some time.
    http://www.youtube.com/watch?v=Zq_4ujAOFUI

    Comment by anton - November 8, 2010 9:16 pm

  21. Hi Anton, thank you for the link.

    Comment by tamami - November 9, 2010 9:16 pm

  22. Great information! I’ve been looking for something like this for a while now. Thanks!

    Comment by tech - November 21, 2010 6:45 am

  23. Tech! Thanx!!!!!!

    Comment by tamami - November 22, 2010 2:49 pm

  24. Thank you so much!!!!!!

    Comment by Loryta - May 7, 2011 9:14 pm

  25. Loryta, thank you.

    Comment by tamami - May 8, 2011 7:03 am

  26. Thanks for the wonderful tip! However if I would like to use a smaller (preferred) tin from a bigger (original) tin, do I divide the ingredients according to the calculation results instead of multiplying? Thank you in advance!

    Comment by pearlypearl - August 22, 2011 2:06 pm

  27. Hello Pearlypearl,
    here’s an example:
    .
    if you want to use an 8″ round tin but the recipe says to use a 10″, do this:
    .
    (8÷10) × (8÷10) = 0.8 x 0.8 = 0.64
    .
    So, here we know to use 0.64 of the original recipe (although, best to round it to 0.7)
    .
    Hope this helps!
    .
    Happy baking! T x

    Comment by Tamami - August 22, 2011 9:43 pm

  28. I am not understanding the two formulas. Why in the first example do you divide preferred tin by original tin only and in the second example you divide and then multiply to come up with the answer? Thanks

    Comment by Joelle - April 16, 2012 10:00 pm

  29. Hello Joelle,
    first of all, let me excuse myself! I’m no mathematician! But I’ll try to explain… :)
    .
    So the universal formula is to find out the volume of the two tins in question & then “dividing” those numbers to get the answer… To get those ‘volume’ numbers, we need to do a bit of “multiplication”…
    - Joelle, I very much hope this answers your question? Thanks for visiting the blog. x

    Comment by Tamami - April 16, 2012 10:16 pm

  30. Thanks for the quick reply. Your math equations are a big help to me. I understand that to figure volume multiplying is used. What I am confused about is the universal formula for changing from one pan to another. The formula you gave said to divide preferred tin by original tin to get how much to increase by. In the second example where the heights of the two tins were the same you used the formula (divide a by b) and then multiplied that by the formula again (a divided by b). Why did you use the formula twice? The answer is probably right in front of my nose but I’m not seeing it. Thanks.

    Comment by Joelle - April 16, 2012 10:47 pm

  31. Hi Joelle, no problem! :)
    Is the second example you mention this one below?
    .
    .
    To convert an 8″ ROUND cake tin A to 10″ SQUARE cake tin B (when height is the same):
    .
    (length x width) ÷ (3.14 x half the diameter of A x half the diameter of A)
    .
    (10 x 10 ) ÷ (3.14 x 4 x 4) = 1.99
    So here we now know that we need to multiply the recipe by 1.99 times. (I like to round it to 2)
    .
    .
    …,
    where does it use the formula twice?

    Comment by Tamami - April 16, 2012 11:04 pm

  32. Ah, is it that I wrote the formula in words, then replaced those with proper numbers the second time round??

    Comment by Tamami - April 16, 2012 11:06 pm

  33. The example is: “If the heights are the same Use this simple formula–(10 / 8 ) x (10 / 8 )”. I’m thinking you are rearranging the formula that involves both getting volume and adjusting to a different pan size. I think I’m just thinking too hard and just need to do the formula :) Thanks so much.

    Comment by Joelle - April 16, 2012 11:16 pm

  34. Joelle, I see!! I was looking at the wrong bit! – doh. I’m so sorry that I have confused you… …

    Comment by tamami - April 16, 2012 11:28 pm

  35. Good formula thanks for that!! Alternatively try this – take original tin an fill it up with water – pour the water into new tin and repeat the process until you have filled the new tin completely with water counting how many tins of water you have used – genious and simple (my husband come up with that!!)lol
    ps think that could work with big to small tin conversion also just divide the recipe instead of multiplying!

    Comment by Dannig - June 23, 2012 9:16 am

  36. Dannig, a-ha!!! :) :) that is one awesome idea! Your hus is a genius! Very simple. I’ll give it a go next time I need to convert. Cheers!

    Comment by Tamami - June 24, 2012 6:43 am

  37. Hey, Thanks so much for this is so helpful and to make it even easier I have built an excel spreadsheet up which I can put the sizes of tin into and it does the math for me. Also have added pages for my favorite recipes and it automatically changes the volumes of each item needed so I dont get confused mid bake.

    Comment by Clare - July 14, 2012 11:46 am

  38. Thank you for leaving a comment here Clare!! :) :)
    Oh my! I think you can make a business out of what you have created!! Seriously!! I can imagine soooo many people wanting a system like that, all over the world!! xx

    Comment by Tamami - July 15, 2012 4:35 pm

  39. Best website for explaining this! What would the formula be for going from an 8″ round to a 6″ round?

    Comment by chenae - July 16, 2012 10:47 pm

  40. Chenae! Thank you! The formula would be:
    .
    (dimension of preferred tin ÷ dimension of original tin)
    x (dimension of preferred tin ÷ dimension of original tin)
    =
    (6 ÷ 8) x (6 ÷ 8)
    = 0.6
    … so you make 0.6 times of the original recipe.

    Comment by Tamami - July 17, 2012 10:43 am

  41. Great conversion formulas. I like the idea of measuring the water of one and placing in the other as well but one can’t do that if you don’t have the original tin. I looked you up on google when I did not have a 9 in round cake pan and wanted to halve the recipe so I wouldn’t eat so much anyway. I’m going to try and use two quite small oval pans I have. I’m off to convert now. ha ha

    Comment by Kathryn - August 8, 2012 12:49 pm

  42. Kathryn, thank you for liking the formulas! I hope it went well! All the best, t x :)

    Comment by tamami - August 14, 2012 8:12 pm

  43. Thank you for this!!! I am a Pastry Major in a local culinary school and one of my projects as of late has been to convert 2 basic cakes to 10-inch pans from their original size pans, and then to cost these cakes as if we were going to sell them as a retail item. Your formula worked like a charm (though I am surprised our instructors didn’t give us info like this) and made the project so much easier than what it started out as. Three thumbs up!!!

    Comment by Gordon - August 27, 2012 11:36 pm

  44. Gordon, I’m very glad that I was of help to your culinary school project!! Makes me feel proud! ;) Good luck with the course!!!!

    Comment by Tamami - August 28, 2012 9:01 pm

  45. If my deep dish pizza recipe calls for three 9″ pans, how do I convert this to two bigger ones or one huge pan? Thanks!

    Comment by Lena - January 24, 2013 10:34 am

  46. Hi Lena, you’d need the exact measurement of the ‘bigger’ ones to use the formula…!

    Comment by Tamami - January 24, 2013 10:43 am

  47. You stated, “There is a reason why I’m a baker & not a mathematician…” To be a baker you must be a mathematician, a chemist, and an artist all in one! Happy baking!

    Comment by Suzanne - January 29, 2013 4:19 am

  48. Awww, Suzanne…!! Thank you very much for your kind words!!! ^^ It’s made my day!! Many happy days to you! xx

    Comment by Tamami - January 29, 2013 10:29 am

  49. [...] also thinking of doing some pan conversions. Tags: lesson, surface area, [...]

    Pingback by let them eat cake - February 3, 2013 10:04 pm

  50. Dear Let them eat cake, thank you for linking back!!!!!! All the best, Tamami x

    Comment by Tamami - February 4, 2013 1:38 am

  51. I’m finding this completely impossible to work out!
    Help!
    I’m making a flan – the recipe is for 11 inches in diameter flan tin. (it’s 1 and a half inches deep)
    I wish to make a smaller one -
    a 9 and a half inch diameter flan tin.
    Same depth.
    Can’t work out what percentage of ingredients to use.
    Can anyone else figure it out?

    Comment by Geraldine - May 25, 2013 5:47 pm

  52. Hi Geraldine!

    I think you should use this formula:
    .
    (volume of the preferred tin) ÷ (volume of the original tin)
    .
    But in order to find out the volume of your two tins, you have to use this formula first:
    .
    (3.14 x half the diameter x half the diameter)
    .
    which in your case it is:
    .
    (3.14 x 4.75 x 4.75) ÷ (3.14 x 5.5 x 5.5)
    .
    70.84625 ÷ 94.985 = 0.74586
    .
    Meaning 74%.
    .
    But to allow for a little extra just incase, you should realistically, do about 75% to 80%.
    .
    Hope this helps!

    Comment by Tamami - May 25, 2013 6:36 pm

  53. Hi, thanks a lot for your formula’s . they have helped a lot with me making me wedding cake. What would be the formula to make a smaller cake than the recipe calls for? I.e the recipe is for an 8 inch cake but I wanted to make a 6 inch cake. Sorry if this sounds stupid I’m just awful at math.

    Comment by joe - May 27, 2013 3:44 am

  54. *my wedding cake

    Comment by joe - May 27, 2013 3:46 am

  55. Is it round or square?

    Comment by Tamami - May 27, 2013 10:19 am

  56. Hi guys, I found an app for iPhone on the Apple store that do this, it is called CakeShape and it is a converter from one cake tin to another.

    Here is the link: https://itunes.apple.com/us/app/cakeshape/id662754655

    I already tried it with 4-5 cakes and it works pretty good. Give it a try…

    Comment by Marta - August 10, 2013 7:12 am

  57. Marta! Thank you very much for the link!!! It sounds good!!! I might give it a try!! Cheers!! x

    Comment by tamami - September 4, 2013 4:21 pm

  58. I have my Granny’s fruitcake recipe that I have been making for years in a regular (old-style) sized bundt pan and I would LOVE to change it over to a loaf pan, which I don’t have yet. I understand that I would make more loaf pans out of the batter mix. In a bundt pan, it requires me to bake at 275 degrees for 4 hours (sure makes the house smell Christmas-y & I feel my Granny with me). How long would I bake it in a loaf pan, if the conversion is possible? PLEEEEEASE HELP!!

    Comment by Donna - November 7, 2013 3:32 pm

  59. Hi Donna, I’m afraid I won’t be able to help…, I don’t have a formula for how to logically work out the baking time. I guess you’d just have to find the answer through trials…, doing a skewer-test every 10 minutes. Sorry to be of not much help…! But good luck!!! T x

    Comment by Tamami - November 7, 2013 6:42 pm

  60. […] isn’t on there website anymore :( I think you can buy their app though. Essentially it did this […]

    Pingback by Homemade Naked Wedding Cake | The Goody Blog - April 13, 2014 5:18 pm

  61. Hello The Goody Blog! Thank you for linking back! All the best, Tamami.

    Comment by tamami - April 13, 2014 9:48 pm

 

Leave a comment