It's the wrong question.
That doesn't stop well meaning but misguided people
telling you that the thing should come up to your chin or giving you a random number so you can go off and waste
your money on the wrong board. There are even websites which will generate a number for you; wrapping a
fallacy in a little JavaScript presumably makes more people believe it. It's still wrong and a bit stupid.
No. The board can't tell how tall you are. It doesn't know and it doesn't care. Take a look at any snowboard manufacturer's website and you'll see a recommended weight range for each board (they're all different), but not a recommended height. Or age, or hair colour or star sign.
Snowboards come in all sorts of different shapes and sizes. You need a large number of parameters to describe a single snowboard (length, width, sidecut, camber, flex, stiffness...). These characteristics are all of similar importance: length is no more or less important that any other, although it is easier to quantify.
A stiff snowboard of a given length will ride differently from a soft one of the same length. Depending on the boards' design, boards of widely differing lengths may be suitable for a particular rider. I own and use powder boards from 1.74m to 1.56m in length: they are all "the right size" for me.
Trying to buy a board armed with a single number "length" doesn't work.
Manufacturers usually build several "sizes" of board in each model range, so that the boards can be used by riders of different weight and experience. Typically there will be three to six boards to choose from of a specific model. It would be entirely possible to make all the boards to be the same length, tuning the boards for everything from lightweight novices to heavyweight racers using the various parameters described above. However it's much easier to simply use board length, so that riders can easily tell the boards apart and go up or down a size.
Hence "length" is intended to be used as an indicator when choosing a board within a single model range from a specific manufacturer. But it's only tenuously useful in comparing boards across different models or manufacturers.
So it's easy to see how this can lead to confusion.
It depends on precisely which model (and year) of snowboard you're looking at. Assuming you've chosen a model based on what you want to do with it, then look at the manufacturers' recommended weight range and take your first test ride on the board intended for your weight. Then depending on how it feels to ride, either go one size down or one size up. If none of the boards seem perfect, then try alternative models or manufacturers. Once you have the right board, you'll know it.
At this point you will be able to read the length of the board which will be written on it somewhere. That's the right length board in this model range for you.
There are retailers who're quite happy to sell boards to people who haven't ridden them. The retailers almost certainly haven't ridden them either and quite possibly don't much care so long as you buy something from them. If you're really rich enough to take this sort of risk, then the best you can do is to look at the manufacturer's weight range for the board you have in mind and pick a board where you're in the middle of that range. You will note that they don't have a recommended "rider height",
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