It's also a bad idea to use an existing roof vent for bathroom exhaust. You'll partially block the vent with the duct pipe, reducing the flow of cooling air through your attic. Moreover ...

Best Bathroom Exhaust Fans for 4-Inch Ducts As a category, these fans perform better in terms of airflow than fans built to fit a 3-inch duct. These models do a good job of evacuating air through ...