Of the three exercises -- running, swimming and walking -- the one that burns the most calories is determined by the time and intensity you do them as well as well as your weight, muscle mass and metabolism. Other factors that enter in are how much time you have to exercise on any given day as well as which type of exercise you enjoy and would be more likely to do. Even though running for 20 minutes burns more calories than walking for the same amount of time, if you dislike running and avoid doing it, you would be better off to walk and get some exercise rather than none at all.
There is a lot of variation in the number of calories burned running, depending on your weight and the speed at which you run. According to the Nutristrategy website, a 130-lb. person running for an hour at 5 mph, or a 12-minute mile, would burn 472 calories. That same person running at 10.9 mph, or a 5.5-minute mile, would burn 1062 calories in an hour. A person weighing 205 lbs. would burn 745 calories in an hour running at 12-minute mile pace, while that same person would burn 1675 calories running a 5.5-minute mile. There are many steps in between, as well as different values for cross country running and running up stairs.
Swimming, either freestyle at a fast pace or breaststroke, burns 590 calories hourly done by a 130-lb. person. For a 205-lb. person either exercise burns 931 calories. Slow freestyle swimming or backstroke burns 413 calories per hour by a 130-lb. person and 651 calories by someone weighing 205 lbs. Treading water at a fast pace burns 590 calories for someone weighing 130 lbs., and 931 for someone weighing 205 lbs. Swimming leisurely burns 354 calories per hour for a 130-lb. person; 558 for someone weighing 205.
Walking slowly at 2 mph burns 148 calories per hour for a 130-lb. person; 233 for someone weighing 205 lbs.. A moderate walking pace of 3 mph burns 195 calories per hour for a 130-lb. person and 307 for a 205-lb. person. Walking the dog burns 177 calories per hour for someone weighing 130 lbs. and 279 for someone weighing 205 lbs. Rapid walking at 5 mph burns 472 calories at 130-lbs.and 745 at 205 lbs.
Both running and swimming burn more calories per hour than walking, unless you are walking at a very brisk pace of 5 mph. There are pluses and minuses for each activity. Walking does not burn as many calories but may be more pleasurable for some people. You may not have easy access to a swimming pool but swimming is easy on the joints. Running burns a lot of calories but is hard on the joints. The best advice is to pick an activity you enjoy and stick with it.