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How long does it take to attain fluency in a language?

How long does it take to attain fluency in a language, say German?

Step #1

To estimate the time here, let’s define what a language is. Simply and very crudely, language is a collection of words. And these words are derived from scripts.

What script is German? Quick search tells us German is derived from the Latin subscript.

Step #2 It is reasonable to assume that if one knows the Latin system (which I assume you know because you’re reading this) – learning languages derived from this system such as German, French, Italian should be much easier compared to say, the Abjad (Hebrew, Arabic) script.

Step #3 Knowing just scripts of course, is arbitrary. But, we can guess that the time we spend on English will be similar to its sister languages – German, Italian, French (as again, they are all derived from the same script)

Step #4 So, how long does it take to learn English? Let’s just say I know English if I know what most of English words mean. How many words do I need to know for this? Oxford English dictionary has about 200,000 words. Which means the German language has about the same words (of course, this is a crude guess – we aren’t taking into account compound / technical words)

Step #5 If we learn about 100 words everyday (studying for say - 2 hours), we can expect to attain native level fluency in about 5 years. This of course, is not how a language is learnt – words do not give insight into grammar or sentence structure. But, it gives us a back of the envelope estimate about the time we’ll need to spend to master a language.