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Dean Anderson, Certified Personal Trainer
I think that the ideal would be to do these two forms of exercise on different days (or one in the morning and one in the evening), so that you can devote maximum effort and get the maximum benefit from each. Any time you do one followed by the other, the second one will suffer at least a little (although you may gradually improve your overall endurance this way).
If that’s not possible, then it comes down to a question of priorities and goals–for that day, and overall. If you’re trying to build muscle mass, doing cardio right after strength training is not usually a good idea, because the more depleted your muscle fuel (glycogen) becomes, the more protein you’re body will use as fuel. After an hour of fairly intense exercise, protein may provide up to 10% of the fuel used, compared to the 1-2% it normally provides. That’s the opposite of what you want for muscle building. To increase strength, you want your body to shift into "repair and rebuild" (anabolic) mode as soon as possible after your strength workout, and the best way to make that happen is to eat instead of doing cardio. A light cardio workout before lifting would be better. But don’t try to do a strenuous strength workout after you’ve already tired yourself out with cardio–that’s not safe.
If you’re mainly trying to lose fat and maintain the muscle you’ve got, then doing cardio after strength training can be a good strategy. The percentage of energy contributed by fat goes up considerably after an hour of exercise, and since strength training uses mostly glucose for energy, doing that first will also increase the amount of fat your body uses for the cardio. However, it’s also true that as more fat is being used to fuel the exercise, the less work you’ll be able to put out, and the fewer total calories you’ll burn. Your cardio will probably be less intense and/or shorter than it would otherwise be, and this may cancel out the amount of extra fat actually burned.
Jen Mueller, Certified Personal Trainer
You'll find a lot of different opinions when it comes to this question. I don't know that there is a lot of reliable research to substantiate doing one or the other first, so I think it comes down to individual goals and preference. If your goal is to build muscle mass and strength, you'd probably want to do your weight training first. If your goal is to gain cardiovascular endurance, you'd want to do your cardio workout first. Here's an example. When I train for a marathon, my primary focus is increasing my mileage. Weight training is going to help prevent injury and increase strength, but what matters most is the running and increasing my distance. So in that case, I always do cardio first.