How many characters can UTF-8 encode?
If UTF-8 is 8 bits, does it not mean that there can be only maximum of 256 different characters?
The first 128 code points are the same as in ASCII. But it says UTF-8 can support up to million of characters?
How does this work?
Solution 1:
UTF-8 does not use one byte all the time, it's 1 to 4 bytes.
The first 128 characters (US-ASCII) need one byte.
The next 1,920 characters need two bytes to encode. This covers the remainder of almost all Latin alphabets, and also Greek, Cyrillic, Coptic, Armenian, Hebrew, Arabic, Syriac and Tāna alphabets, as well as Combining Diacritical Marks.
Three bytes are needed for characters in the rest of the Basic Multilingual Plane, which contains virtually all characters in common use[12] including most Chinese, Japanese and Korean [CJK] characters.
Four bytes are needed for characters in the other planes of Unicode, which include less common CJK characters, various historic scripts, mathematical symbols, and emoji (pictographic symbols).
source: Wikipedia
Solution 2:
UTF-8 uses 1-4 bytes per character: one byte for ascii characters (the first 128 unicode values are the same as ascii). But that only requires 7 bits. If the highest ("sign") bit is set, this indicates the start of a multi-byte sequence; the number of consecutive high bits set indicates the number of bytes, then a 0, and the remaining bits contribute to the value. For the other bytes, the highest two bits will be 1 and 0 and the remaining 6 bits are for the value.
So a four byte sequence would begin with 11110... (and ... = three bits for the value) then three bytes with 6 bits each for the value, yielding a 21 bit value. 2^21 exceeds the number of unicode characters, so all of unicode can be expressed in UTF8.
Solution 3:
Unicode vs UTF-8
Unicode resolves code points to characters. UTF-8 is a storage mechanism for Unicode. Unicode has a spec. UTF-8 has a spec. They both have different limits. UTF-8 has a different upwards-bound.
Unicode
Unicode is designated with "planes." Each plane carries 216 code points. There are 17 Planes in Unicode. For a total of 17 * 2^16 code points. The first plane, plane 0 or the BMP, is special in the weight of what it carries.
Rather than explain all the nuances, let me just quote the above article on planes.
The 17 planes can accommodate 1,114,112 code points. Of these, 2,048 are surrogates, 66 are non-characters, and 137,468 are reserved for private use, leaving 974,530 for public assignment.
UTF-8
Now let's go back to the article linked above,
The encoding scheme used by UTF-8 was designed with a much larger limit of 231 code points (32,768 planes), and can encode 221 code points (32 planes) even if limited to 4 bytes.[3] Since Unicode limits the code points to the 17 planes that can be encoded by UTF-16, code points above 0x10FFFF are invalid in UTF-8 and UTF-32.
So you can see that you can put stuff into UTF-8 that isn't valid Unicode. Why? Because UTF-8 accommodates code points that Unicode doesn't even support.
UTF-8, even with a four byte limitation, supports 221 code points, which is far more than 17 * 2^16
Solution 4:
According to this table* UTF-8 should support:
231 = 2,147,483,648 characters
However, RFC 3629 restricted the possible values, so now we're capped at 4 bytes, which gives us
221 = 2,097,152 characters
Note that a good chunk of those characters are "reserved" for custom use, which is actually pretty handy for icon-fonts.
* Wikipedia used show a table with 6 bytes -- they've since updated the article.
2017-07-11: Corrected for double-counting the same code point encoded with multiple bytes