I need to sum all the values in a column across multiple files - awk

Question

I have a directory with multiple csv text files, each with a single line in the format:
field1,field2,field3,560
I need to output the sum of the fourth field across all files in a directory (can be hundreds or thousands of files). So for an example of:
file1.txt
field1,field2,field3,560
file2.txt
field1,field2,field3,415
file3.txt
field1,field2,field3,672
The output would simply be:
1647
I've been trying a few different things, with the most promising being an awk command that I found here in response to another user's question. It doesn't quite do what I need it to do, and I am an awk newb so I'm unsure how to modify it to work for my purpose:
awk -F"," 'NR==FNR{a[NR]=$4;next}{print $4+a[FNR]:' file1.txt file2.txt
This correctly outputs 975.
However if I try pass it a 3rd file, rather than add field 4 from all 3 files, it adds file1 to file2, then file1 to file3:
awk -F"," 'NR==FNR{a[NR]=$4;next}{print $4+a[FNR]:' file1.txt file2.txt file3.txt
975
1232
Can anyone show me how I can modify this awk statement to accept more than two files or, ideally because there are thousands of files to sum up, an * to output the sum of the fourth field of all files in the directory?
Thank you for your time and assistance.

Answer 1

A couple issues with the current code:
NR==FNR is used to indicate special processing for the 1st file; in this case there is no processing that is 'special' for just the 1st file (ie, all files are to be processed the same)
an array (eg, a[NR]) is used to maintain a set of values; in this case you only have one global value to maintain so there is no need for an array
Since you're only looking for one global sum, a bit more simpler code should suffice:
$ awk -F',' '{sum+=$4} END {print sum+0}' file{1..3}.txt
1647
NOTES:
in the (unlikely?) case all files are empty, sum will be undefined so print sum will display a blank link; sum+0 insures we print 0 if sum remains undefined (ie, all files are empty)
for a variable number of files file{1..3}.txt can be replaced with whatever pattern will match on the desired set of files, eg, file*.txt, *.txt, etc

Answer 2

Here we go (no need to test NR==FNR in a concatenation):
$ cat file{1,2,3}.txt | awk -F, '{count+=$4}END{print count}'
1647
Or same-same 🇹🇭 (without wasting some pipe(s)):
$ awk -F, '{count+=$4}END{print count}' file{1,2,3}.txt
1647

Answer 3

$ perl -MList::Util=sum0 -F, -lane'push #a,$F[3];END{print sum0 #a}' file{1..3}.txt
1647
$ perl -F, -lane'push #a,$F[3];END{foreach(#a){ $sum +=$_ };print "$sum"}' file{1..3}.txt
1647

Answer 4

$ cut -d, -f4 file{1..3}.txt | paste -sd+ - | bc
1647