What size vent for a 4″ drain 80 feet away?

Notes

• Two rules, and people only remember the first. A vent is never smaller than half the drain it serves and never below 1¼″ — that gives 2″ here. The second rule is developed length: friction grows with the run, so a long vent has to be larger. At 80 ft that pushes this one to 4″.
• Developed length is measured along the pipe. Every elbow, every offset and the whole vertical rise count. It is not the distance from the fixture to the roof measured on a drawing — running 60 ft of 1½″ because the roof looks close is exactly how a trap at the far end gets siphoned dry.
• What the vent actually does is protect the trap seal. Water falling down a stack drags air with it. Without a path for replacement air, that suction pulls the water out of the nearest trap, and then sewer gas has an open door into the room. A vent that is undersized does not fail loudly — it fails as a smell nobody can place.
• A dry trap smells the same as a broken one. Floor drains and guest bathrooms that go months without use lose their seal to evaporation, not to venting. Before re-plumbing anything, pour a bucket of water down and wait a day.
• Figures here follow the IPC. UPC jurisdictions differ on several points — wet venting and island fixtures especially — and the local inspector decides. Use this to size a plan and to read a quote, not to argue at inspection.