http://sequenceconversion.bugaco.com/converter/biology/sequences/

I use that site for convert

You could use FinchTV.

You could use FinchTV.

BioEdit can read ABI trace files and "save as" or "export" in FASTA format.

http://www.mbio.ncsu.edu/bioedit/bioedit.html

it is free, and has many good features for alignment and data analysis.  It is a windows only program, for Mac OS-X you need something else.  See for example:

https://www.roswellpark.edu/shared-resources/genomics/services-and-fees/sanger-sequencing/abi-viewers

Use CodonCode: Sequence Assembly and Alignment Software. It will help you definitely.

You can use the simple but free program Chromas (Chromas Lite 2.1; http://www.technelysium.com.au) .When you have downloaded this program, double click on the sequence (ab1-file) and it will be openend automatically in Chromas. In the Chromas screen, on top, you will see a button with 'export'. Click on it and it will create automatically a fasta file from the sequence openend in the same folder/position of the ab1-file. Chromas has also the possibilty to correct/change the sequence, it gives some indication about the quality  and you can easily reverse-complement your sequence. Check it out! Good luck!

A fasta file is just a text file with a header line starting with the > symbol followed by a piece of text (filename without spaces) end ending with a return. After the return your sequence can be entered without spaces.

I would also recommend FinchTV. In my experience it works excellent and it is free.

ABI should have its own software's base calling of the sequencer trace file. From the facility at my former institution this used to come as a separate file for each .ab1 file, with the same filename but ending in .seq. It was some text format but I don't recall if it was FASTA. Regardless, that file would be easy to manipulate into FASTA. The .ab1 file also contains ABI's base calling embedded within, but not in a way that is easy to extract without specialized tools. Software such as Sequencher can read the  ABI files and display the trace as well as ABI's base calling. I am not familiar with FinchTV that others are recommending, that software may provide similar functionality and user friendliness.

I used to use Phred for (re)basecalling of the .ab1 traces using Phred's algorithm for this, and this can be done in batches for large collections of .ab1 files easily. I believe CodonCode software is a graphical user interface for interactive use of the Phred/Phrap/Consed toolchain for base calling, forward-reverse read assembly and/or contig assembly, and consensus editing or finishing (respectively). Phred and Phrap are command line only without the CodonCode UI. Some of that information may be out of date. 

If you only want to extract the ABI base calling from the .ab1 file into a FASTA file, I would first look into the Chromas Lite tool or the FinchTV tool recommended above. If your institution has license agreements with Sequencher or CodonCode, then check out those. If you are comfortable with UNIX command line and desire scriptable methods for batch processing of large collections, look into Phred and Phrap. 

http://sequenceconversion.bugaco.com/converter/biology/sequences/

I use that site for convert

Mohsen's suggestion was the easiest (http://sequenceconversion.bugaco.com/converter/biology/sequences/).

You don't even need to dl any program.

Easiest way to do batch processing use Biopython: http://biopython.org/wiki/SeqIO

I recommend MEGA 7 free software after downloading you can open the ABI file in MEGA and export the alignment in FASTA format

Also it is helpful for the downstream analysis of your sequences