The word metre (the American spelling is meter), the name of the unit of length, only has five letters. Because we use and hear this word so often, we are well aware of the correct pronunciation: [ˈmiːtə] (BE) or [ˈmiːtər] (AE); you can listen to it here.
Things become more complicated when we consider words that contain the phrase meter: parameter, kilometre, thermometer, barometer (you can already see that many of these words are related to physics and measurements). First, the distinct British and American spellings exist only for words that describe multiples or fractions of a metre, such as millimetre, centimetre, etc. Hence we have, for example, kilometre and kilometer, but not
parametre and parameter.
The other problem I want to talk about is pronunciation. Since the English language is in general not phonetic, the phrase meter is not necessarily pronounced in the same way when it is part of a longer word, such as parameter. The Oxford English pronunciation is [pəˈræmɪtə(r)], listen here, so the meter in parameter is pronounced as [mɪtə(r)]. The same is true for thermometer and barometer. Compare this to the frequently heard but incorrect pronunciations given here. Interestingly, the word Parameter is very often mispronounced (even by scientists) in German by stressing the first syllable, listen here, whereas the correct pronunciation (according to the Duden and to my experience) is to stress the second syllable, listen here. On the other hand, words such as Barometer and Thermometer are not typically mispronounced in this way.
Only kilometre and its siblings millimetre, centimetre, etc. can be pronounced in both ways: [kɪˈlɒmɪtə(r)] and [ˈkɪləmiːtə(r)]. In the second variant, metre is pronounced in the same way as the word metre itself (listen to it here). The difference is the pronunciation of the first letter e in -meter, which can either be pronounced long [iː] or short [ɪ].
An important detail of the phonetic spellings given above is the location of the apostrophe, which indicates which syllable is to be stressed. [kɪˈlɒmɪtə(r)] means that the stress is on lo, whereas [ˈkɪləmiːtə(r)] means that the stress is on ki (listen to both versions again to really notice the difference). Having understood this aspect of phonetic spelling, we can convince ourselves from the phonetic spelling [ˈkɪləmiːtə(r)] that parameter is always stressed on the second syllable, ra, never on the first (see here).