Hands up anyone who hasn't used smarties to decorate a cake (OK, sit down if you're not from the UK). Unfortunately I can't get the Smarties of my childhood in a cardboard tube, with a plastic lid with a letter of the alphabet on the bottom, since even in the UK they've switched to hexagonal boxes now. I'm in Malaysia at the moment though, so I have to settle for these boring standard square 'tubes'.

When doing DIY, my father always taught me to measure twice, cut once, and I think it's good to approach cake decorating in the same manner. So when I considered covering a cake with smarties (I was thinking of fish scales) I realised that what the world needed was a way to calculate how many smarties they actually needed. If I wanted to cover a 30cm diameter, 10cm high cake in red smarties, how many boxes should I buy?

I now present to you my Smartie investigation :)

I bought two tubes, so I could get an average (and because my boyfriend banned me from buying any more just to count them)

Tipping them out and arranging I discover that they're not exactly the vibrant colours from my childhood memories, and some of them seem a little... shop soiled.. but then candy covered chocolate snacks don't really survive well in 30 degree humidity so I'll forgive them.

This is one of each colour, placed on 1cm graph paper. You can see from this that each smartie has a diameter of 15mm, and my measurements show a height of 5mm.

In the two tubes I bought the colour distribution was:

13 green, 11 pink, 9 orange, 9 blue, 9 yellow, 8 purple, 8 red, 1 brown, total 68 smarties, so 34 smarties per tube. Each tube (ok, ok. Box) is 32 grams, so a single smartie weighs *just* under a gram (0.95). That's going to be something very handy to remember.

So out of luck if what you were planning requires too many browns... Probably better to stick to Minstrels if those are your requirements

Size wise, they're 15mm radius, and about 5mm depth (although there's a fair bit of variance there) which matches up with what Wikipedia lead me to expect (their pics show nicer colours than mine).

So onto the nitty gritty. How many smarties do I need? Obviously this depends on the tiling pattern you choose..

Maximum density?

Square?

Circular (well, pentagonal)?

The first thing you need to know is the area you're trying to cover - for a rectangular (or square cake) that's easy. The area of the top is the length multiplied by the width. The sides are the height multiplied by the length and the height multiplied by the width.

So for a cake made in a typical 20cm square cake tin, 8 cm in depth (assuming your cake will come all the way up to the top of the cake tin) that I wish to completely cover with smarties I have an area to cover of 20*20 (top) +  20*8*2 (front and back) + 20*8*2 (left and righthand sides). This gives a total area to be covered of 1040cm²

Next we have to figure out what area a smartie covers. Now, it's not just the area of the smartie (1.767cm²) as, being circular, they don't tile up exactly. After some mad scribbling, the maximum density styling above has a coverage of 1.95cm² per smartie. So to cover our cake (total area 1040cm²⁾, we'd need to have  1040/1.95 = 533.33 smarties.  Above we discovered that each smartie weighs 0.95g so, to cover your entire cake in smarties you'll need 533.3 * 0.95 grams of smarties - or just over half a kilo (or about 1lb for those who rather imperial units) .

For the square tiling, each smartie will take up 2.25cm² so that would be 462 smarties or 439grams

If you want to cover in a particular colour, you'll have to multiply that by the typical number of that colour in a box (or tube) - with a fair fiddle factor, since  I assume there'll be a fair amount of variability in that.

Remember, no-body ever complained about spare smarties, so it's not going to hurt to over-purchase!

Can't get smarties? Need other colours? How about these alternatives...

M&Ms, Skittles (not sure about chewy sweets on cake), Minstrels, Revels, Maltezers. To figure out how many you'll need , you'll need to know the radius of the sweet (assuming the sweet is circular). You can calculate the area that a sweet will cover when densly packed as above using (where r = the radius of the sweet):

(r + r / sin30) * (r / tan30) / 1.5 = area covered by one sweet in this tiling pattern

For the square tiling (again where r = the radius of the sweet):

r * r = area covered by one sweet in this tiling pattern.