# Math Can’t Lie- The Truth Behind Cake Servings

Posted by on Mar 20, 2013 in A Piece of Cake- Blog | 3 comments

The most common question a baker will ask is: how many cake tiers do I need for X amount of guests? Cake tiers range from 4″ in diameter to 18+” (it must be pretty awesome to have an oven large enough to accommodate 20″ diameter pans!) and are usually 4-5″ in height.

When I was an amateur baker I took a lot of care in measuring my cake pans to calculate the correct servings. Thanks to my engineering background I even used math for my calculations! My equation was simple for a 2″ tall cake:

C=πD    (C= circumference, π=3.14, D=diameter)

It boggled my mind when I started talking to other cake decorators and they were quoting 25 servings out of a cake that I could (and personally have) cut 50 servings from! I didn’t understand how that was possible, math can NOT lie! To add to this confusion, the cake decorators told me about  iPhone apps they used to calculate the servings for them and the program was also quoting low numbers. For example, I can serve 18-20 slices from a 6″ tier that’s 4″ in height, but other bakers quote 10-12 servings!

I consulted with a math genius friend of mine, and this was his answer (loved it!):

“For a 6inch cake: So the circumference is roughly 18inches. Doing some trigonometry, with each slice having 3 inch long sides, and a base angle of 20degrees (360/18), each slice will have width (at the widest point) of a little over an inch (1.026 inches to be exact). And the curvature length is 18.84/18=1.0466 like you said.
So in my mind, each slice is roughly a triangle with dimensions 3x3x1.026 inches and a depth of 4inches , and this is understated because it doesn’t include the part that is between the curvature and the 1.026 inch side of the triangle. I think that’s a decent size for a slice.” Apart from being a math genius, he was also raised around a catering business, so I’m pretty confident he knows what he’s talking about.

I have personally called every customer the day after their events to touch base with them and ask how everything worked out. I KNOW my cake calculations are correct because I always ask my customers how the servings worked out for their events. They always say it worked out perfect and half the time they even have some left over!

Take a look at my serving chart, and use this to guide you when ordering a cake. I can’t control how your venue serves your slices, they may cut them way larger than necessary, but these are actual servings you can get from these tier combinations.

1. How did you come to those crazy servings combinations? o.O…..I hate to say this, but this is way off. Cakes are not sliced in wedges, can you imagine an 18″ diameter cake sliced in really long skinny wedges? Lol

It is a simple matter of volume, not trig. Cakes and wedding cakes are cut in rectangles, the wedding industry standard being 1″x 2″ x 4″ (4″ being the height) or in this case, 8 square inches. You need no trig to figure it out. Volume of a cylinder = π r^2 h

So an 8″ cake that is 4″ tall would be: 3.14 x 16 x 4 = 200.96 square inches; divided by 8 square inches (our slices) = apron 25.12 (or the industry standard for an 8′ cake of about 24 servings. Easy peasy.

And this works great if someone wants a double barrel or a 6″ tall cake; you just plug in the different height. You don’t have to deal with angles or anything silly, since you don’t cut a cake that way anyway. I would never charge my clients for 4″/6″ and saying 25-30 servings unless I’m basing it off of 1×1″ slices LOL. It serves 18, or 10 2×2 party size servings.

Please don’t overcomplicate things for your self or your genius friend. And stop over charging clients for servings they are not getting, unless you tell them they’re sliver-sized. I’d rather under estimate and they get more cake out of it for what they’re paying already.

• Hello!

Thanks for your comment! It was a good reminder that the chart I originally had up there had incorrect values. I agree with everything you said and have uploaded the correct chart showing my servings. These have been tried and true with my customers. I normally only bake real cakes up to 12″ in diameter and supply the rest of the servings in sheet cakes to make cutting easier (not to mention keep the cakes refrigerated).

Again, thanks for your input. Though you need to rest assured I don’t over charge my clients. I understand why you’d think so with that previous chart,but now it should make more sense. Yes, I do let them know they’re not monster sized cakes and I also use the same online calculator you do for serving sizes 😉 I just get a little bit more than the program states.

2. alice, unfortunately, when dealing with round cakes, you can’t get exact slices from a round cake. how do you account for the curvature of a cylinder? math actually does provide a better way – using an 8inch cake as an example – circumference is roughly 25inches. if u want a 1inch width slice, thats 25 slices. the second measurement of a slice is 2 inches, so if u cut 2inches deep into the cake all the way around, it wld leave you with a 4inch center cylinder. calculating a new circumference wld get you 12.56inches so lets say 12 slices for ease. conveniently, a 4 inch cylinder will automatically yield a 2 inch depth. so you actually can get 25 plus 12 for a total of 37 slices out of an 8inch diameter, 4inch height cake. for larger diameter cakes, you’d be left with possibly 3 or even more concentric circles. i offer my clients printed cutting guides and sometimes some clients prefer a 1.5x2x4 slice…. there will never be perfection but this way seems more consistent than trying to get square slices from a round cake.