Adding a bathroom in the downstairs of my barn, hoping not to have to go through the floor and the roof since the upstairs is finished like a house,, is it possible just to vent it out the side of the wall, still 8 feet up or higher but out the side, will it have the same effect?? Thanks

The reason plumbing vents are run inside walls, is because they are damn ugly.they eventually make it outside
Through the roof. Check local codes on sewer vent size and height requirements."don't want any stinky sewer
gas flowing in your windows"also check the type of pipe used on exposed vent systems in your area.

How will you get it past any overhang of the roof?
You need a certain height above the roof according to pitch, and away from chimneys.

I trust you are building the bathroom with zoning permission and a permit; you don't want trouble next time assessments are done or if you are detected.

Check local codes as advised above as some inspectors feel it is a duty to keep ugly vents from running up the sides of buildings, I swear.

Most plumbing codes will allow you to run the minimum 2" size vent outside and up the wall past the roof line (between 6-24" depending on local codes) as long as there is NO WAY to get a vent through the house (check closets here, OK?). There must also be no windows, skylights, vents, etc. within 10 feet of the vent outlet.

Otherwise, should be fine... ;)

Good luck!

Mark