I think a week or two. It bloomed two years ago, about two thirds this size, but snapped off in the wind last year. From base to purple point it's about 5 feet 6 inches and it needs to be in a sheltered spot.
The stench has abated this morning to a mildly unpleasant waft. The full on dead body stage seems to only last a day. It's pollinated by flies rather than bees, hence the pong.