Which style of Latin plurals should I use?
If my memory of Latin lessons serves me correctly, it should really be
However, I think most people would probably write
Which is right?
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The correct usage would be stadiums.
Though most dictionaries disagree, Stadia in its strict sense is supposed to used only to measure lengths in excess of 1 stadium (which is equal to 200 metres approximately)
This is what Wikipedia says - "Stadium" comes from the Greek word "stadion" (στάδιον), a measure of length equalling approximately 200 metres. The oldest known stadium is the one in Olympia, in the western Peloponnese, Greece, where the Olympic Games of antiquity were held since 776 BC. Initially 'the Games' consisted of a single event, a sprint along the length of the stadium. Therefore the length of Olympia's stadium became somewhat of a standard measure of distance. A Roman stadium was slightly smaller, a distance of 125 passus (double-paces), equal to about 185 meters or 607 feet.
The English use of stadium comes from the tiered infrastructure surrounding a Roman track of such length. Although most dictionaries provide for both "stadiums" and "stadia" as valid plurals, etymological sticklers sometimes apply "stadia" only to measures of length in excess of 1 stadium.
Merriam-Webster gives both stadiums and stadia, so it comes to which one of them you prefer. Note, my Google Chrome doesn't know stadia and asks me to correct it :)
Both stadiums and stadia are reported as plural of stadium, on the NOAD.
Looking at the Corpus of Contemporary American English, stadia is found 19 times, and stadiums 1119 times. To make a comparison, stadiums is found 210 times in the _Corpus of Historical American English (stadia is found 76 times) and 58 times in the British National Corpus (stadia is found 63 times).
You should use the one that people understand. There isn't much point in using words that are not understood. You could perhaps make a note that you are uncertain about the "correct" plural form.
The plural form could either be borrowed from Latin, or formed in English. It's quite common that only the singlar form of a word is borrowed from another language, and that the plural form is formed as is common in English.
The noun window for example has the plural form windows, and not from the Old Norse plural form where it would be something like windogo.