POSIX numeric time zone

I can get the numeric time zone like this:

$ date +%z
-0600

However I recently discovered that POSIX date only supports printing the timezone name:

$ date +%Z
CST

Can I get the numeric version with shell or some other tool while sticking with POSIX?

Solution

Steven Penny's answer only works if the day hasn't changed between your time zone and UTC. It also omits minutes, which won't work if you're in India for example.

To account for that, you need more date information: The day of the year and minutes past the hour.

#!/bin/sh

T='+%j*1440+%H*60+%M' # minutes in year: DAY/Y * 1440 min/d + H * 60 h/min + MIN
Z=$(( ( $(date "$T") - ( $(date -u "$T") ) ) * 100 / 60 )) # TZ offset as hr*100

H=${Z%??} # hours ($Z is hundredths of hours, so we remove the last two digits)
if   [ $H -lt -13 ]; then H=$((H+8712))    # UTC is a year ahead
elif [ $H -gt  13 ]; then H=$((H%8736-24)) # UTC is a year behind
fi
if   [ $H -lt -13 ]; then H=$((H+24))      # UTC is a day ahead of a leap year
elif [ $H -gt  13 ]; then H=$((H-24))      # UTC is a day behind a leap year
fi

M=${Z#$H} # hundredths of hours (to become minutes on the next line)
if [ $M != 00 ]; then M=$(( $M * 60 / 100 )); fi # Minutes relative to 60/hr

printf '%+03d%02d' $H $M # TZ offset in HHMM

This lets you change the time zone by altering $TZ, so TZ=Asia/Calcutta myscript.sh should yield a TZ offset of +0530. (This part may not work on older POSIX systems.)