Looking for the description of the algorithm to convert UTF8 to UTF16

I have 3 bytes representing an unicode char encoded in utf8. For example I have E2 82 AC (UTF8) that represent the unicode char € (U+20AC). Is their any algorithm to make this conversion? I know their is the windows api MultiByteToWideChar but I would like to know if their is a simple mathematical relation between E2 82 AC and U+20AC. So is the mapping between utf8 -> utf16 a simple mathematic function or if it's a hardcoded map.