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Although you may burn a higher percentage of fat calories when walking, you will burn more total calories, and more total fat calories, by running the same amount of time. Running burns slightly more calories for the same distance covered, although walking will take longer. Still, if you don't like to run, don't like the impact, or are not in shape to run very far, you will burn more calories and fat by walking because you will be able to do significantly more of it.