I have a large large large table with many many many rows, and it's a certain size in pg_relation_size -- there's a timestamp with tz column on this table that's mostly kind of useless, and I want to figure out how much space it would free if we just dropped it. Can I easily do this?
The DROP COLUMN form does not physically remove the column, but simply makes it invisible to SQL operations. Subsequent insert and update operations in the table will store a null value for the column. Thus, dropping a column is quick but it will not immediately reduce the on-disk size of your table, as the space occupied by the dropped column is not reclaimed. The space will be reclaimed over time as existing rows are updated.
To force immediate reclamation of space occupied by a dropped column, you can execute one of the forms of ALTER TABLE that performs a rewrite of the whole table. This results in reconstructing each row with the dropped column replaced by a null value.
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But you could still try to get a rough estimate, you could use pg_column_size() and pg_stat_user_tables to get an approx set of tuples and multiply with the size. (Not including indexes though)