We're not sure if this has ever been measured due to the fact that it all depends on why a swan is swimming, walking or running and the fact that usually, if they are not captive (pinioned and unable to fly), will just fly if the need arises.

We can say that a human would be able to keep up with a strolling (slow walking) swan. If the swan starts to pick-up pace, then the human would need to keep a fast pace walk or slow run. In this case, the swan usually is scared enough to resort to flying or going into the water so that the human cannot readily chase. This limits the measurement of how fast they really run or walk since they are usually running away instead of toward someone.

As far as swimming, the same concept exists. If the swan is taking a slow swim around the pond rather than "busking", the speed is going to be rather slow. If the swan is doing what is called "busking", the head lies further back on the neck and the feet are thrust forward so that a small wake is produced (swan is usually in a territorial mode and rather defensive), the speed of the swan is rather fast and we would theorize that the speed would be around
2-5 mph.

Swan flying mesurements have been taken and it is presumed that swans can fly approximately 50 mph. Sorry we could not be more specific, but the measurements for swan walking, running and swimming have not been significantly studied or documented. The Regal Swan