How can I store the return value/output of a command in a variable?

Well, that depends on whether you want to store the command's output (either stdout, or stdout + stderr) or its exit status (0 to 255, with 0 typically meaning "success").

If you want to capture the output, you use command substitution:

    output=$(command)      # stdout only; stderr remains uncaptured
    output=$(command 2>&1) # both stdout and stderr will be captured

If you want the exit status, you use the special parameter $? after running the command:

    command
    status=$?

If you want both:

    output=$(command)
    status=$?

The assignment to output has no effect on command's exit status, which is still in $?.

If you don't actually want to store the exit status, but simply want to take an action upon success or failure, just use if:

    if command; then
        echo "it succeeded"
    else
        echo "it failed"
    fi

Or if you want to capture stdout as well as taking action on success/failure, without explicitly storing or checking $?:

    if output=$(command); then
        echo "it succeeded"
    ...

What if you want the exit status of one command from a pipeline? If you want the last command's status, no problem -- it's in $? just like before. If you want some other command's status, use the PIPESTATUS array (BASH only). Say you want the exit status of grep in the following:

    grep foo somelogfile | head -5
    status=${PIPESTATUS[0]}

Bash 3.0 added a pipefail option as well, which can be used if you simply want to take action upon failure of the grep:

    set -o pipefail
    if ! grep foo somelogfile | head -5; then
        echo "uh oh"
    fi

Now, some trickier stuff. Let's say you want only the stderr, but not stdout. Well, then first you have to decide where you do want stdout to go:

    output=$(command 2>&1 >/dev/null)  # Save stderr, discard stdout.
    output=$(command 2>&1 >/dev/tty)   # Save stderr, send stdout to the terminal.
    output=$(command 3>&2 2>&1 1>&3-)  # Save stderr, send stdout to script's stderr.

It's possible, although considerably harder, to let stdout "fall through" to wherever it would've gone if there hadn't been any redirection. This involves "saving" the current value of stdout, so that it can be used inside the command substitution:

    exec 3>&1                    # Save the place that stdout (1) points to.
    output=$(command 2>&1 1>&3)  # Run command.  stderr is captured.
    exec 3>&-                    # Close FD #3.

    # Or this alternative, which captures stderr, letting stdout through:
    { output=$(command 2>&1 1>&3-) ;} 3>&1

In the last example above, note that 1>&3- duplicates FD 3 and stores a copy in FD 1, and then closes FD 3. It could also be written 1>&3 3>&-.

What you cannot do is capture stdout in one variable, and stderr in another, using only FD redirections. You must use a temporary file (or a named pipe) to achieve that one.

Well, you can use a horrible hack like:

   result=$( { stdout=$(cmd) ; } 2>&1; echo "this line is the separator"; echo "$stdout")
   var_out=${result#*this line is the separator$'\n'}
   var_err=${result%$'\n'this line is the separator*}

Obviously, this is not robust, because either the standard output or the standard error of the command could contain whatever separator string you employ.

And if you want the exit code of your cmd (here a modification in the case of if the cmd stdout nothing)

   cmd() { curl -s -v http://www.google.fr; }

   result=$( { stdout=$(cmd); returncode=$?; } 2>&1; echo -n "this is the separator"; echo "$stdout"; exit $returncode)
   returncode=$?

   var_out=${result#*this is the separator}
   var_err=${result%this is the separator*}

Note: the original question read, "How can I store the return value of a command in a variable?" This was, verbatim, an actual question asked in #bash, ambiguity and all.

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