The x, y dimensions of snowflakes get all the attention for obvious reasons, but the z dimension must be interesting too, in its own humble way. In fact, I have lived more than half a century and never seen anyone refer to snowflakes' third dimension at all!

So I'd like to know what a snowflake's cross-section looks like, and what forces/phenomena make it that way.

There are numerous possibilities:

  • that snowflakes are a single molecule thick
  • single crystal thick then grown over with hoarfrost
  • thousands or millions of nearly identical snowflakes glued together like slices in a loaf of bread
  • something else

No doubt, the ratio between x and y dimensions is extremely similar across all snowflakes, but an interesting part of the phenomena involved would be that which defines the ratio between x and z dimensions.

  • $\begingroup$ My observations of individual lumps of snow suggest the shapes may a lot in all dimensions. Most lumps consist of more than one crystal, though. Even so, the crystals vary a lot in size. $\endgroup$
    – matt_black
    Apr 13, 2018 at 16:52

1 Answer 1


There are many different types of crystals and their fromation is far too difficult for me to understand. This answer simply deals with the thickness part and that too merely gives a rough approximation due to the lack of data. From CalTech

enter image description here

We have two formulae for calculating the width:

  1. For Dendrite $$\mathrm{h =a_2 D^f} $$
    D: crystal diameter (cm) (major dimension)
    h: crystal thickness (cm) (minor dimension)
  2. For Needles $$\mathrm{d = a_2 L^f} $$
    D: crystal length (cm) (major dimension)
    d: crystal thickness (cm) (minor dimension)

This is a table for $\mathrm{a_2, f}$

enter image description here

For d and l (right most column )
enter image description here

I calculated the thickness of a $\pu{3 mm}$ Dendrite which is coming around $\pu{24 \mu m}$.



  • $\begingroup$ As a Canadian I have seen some of those possible forms, but by no means all. Unfortunately, I've never seen a snowflake anywhere close to 2.4 mm thick. For a 0.5 cm dendrite, using their formula h = aDf, I get 0.009 × 0.5^0.377=0.0069cm or 0.07mm -- so something less than a tenth of millimetre to make it easy to remember. I do appreciate your digging that out though. Thanks very much! $\endgroup$ Apr 14, 2018 at 11:32
  • $\begingroup$ Just a word of caution regarding your source: Google drive links frequently become invalid; you did the right thing to include the relevant portions here. (It would have been nice if the author of the slides would have included actual references, but I guess those are on a different handout...) $\endgroup$ Apr 16, 2018 at 8:19
  • $\begingroup$ @ Martin - マーチン I changed the link but wasn't able to find the original document. $\endgroup$ Apr 16, 2018 at 8:33

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