Encrypted text length in AES
Plain AES is a block cipher, which can only encrypt 128-bit blocks (i.e. 16 bytes at once).

To encrypt longer pieces of data, one would normally create a stream cipher from the block cipher, by using one of several modes of operation. The simplest (and most insecure) one is the electronic code book mode (ECB), which (for the same key) always produces the same ciphertext for the same plaintext block. Normally one thus would use one of the other modes (like CBC, CTR, ...), each having different advantages.

If you need only sequential access to the whole file, any of these modes will do, as you can always decrypt the file sequentially.

If you need some kind of random access to specific parts of the file, you would break it down into parts which each could be accessed individually. Each of them would then be encrypted as essentially a separate stream, i.e. starting with the initialization vector, and including (if necessary) the padding to fill the last 128-block.

You would also want an index to the parts, so you know which part to access.

Alternatively, you could use CTR mode, which essentially allows random access to the file, only knowing the nonce and the block index, without the need to read or decrypt the blocks before or after the desired block.