Just copied off a google search, but is reasonably accurate: "Ducks need a little more wiggle room than chickens. Allow about 4-6 square feet per bird in their duck house and 10-25 square feet per bird for the run."
The above is absolute minimums. More space is better. They tend to make their area muddy so the smaller their run, the faster that will probably happen.
Here is our area. Hopefully the hoop roof will be complete today, then painted dark green to blend in. We have 5 ducks in this area and per my original calculations, I think we could have 8 ducks, erring on the side of more space. I think we could even have 10 but they would make the area muddy fast, and it would require more upkeep on our part. Plus, the noise/ our neighbors. It's all a balancing act and your specific location and details have to be accounted for.