There is a lot of discourse surrounding cardio, weight training, and rest days. No two people will give you the same answer, and there is a lot of debate to be had. So should you be doing cardio on your rest days or not?
How important is a rest day in working out?
Firstly, the question of whether you should do cardio on rest days very much implies that you primarily train using weights, because if you were running or cycling as your primary training principle, you wouldn't consider doing even more cardio on your rest days. So let's assume you train 4 times a week lifting weights, which leaves 3 potential rest days a week. You may feel like not doing anything at all for 3 days a week will mean that you won't make as much as progress as if you were more active, but rest is just as important as hitting the gym! When you are lifting weights, you are actually tearing your muscles. It is only when you eat, sleep, and recover that your muscles are repairing and growing back bigger and stronger than before. Therefore, taking a rest day is very important in working out. If you continue to train when you are feeling very sore and achy, you could potentially injure yourself and do more damage than good.
How much should you rest between workouts?
This differs from person to person. If you have only recently started training or have started a new regime, your body will need longer to recover as it becomes accustomed to the stress and strain. The longer you have been doing a particular sport, the less rest you will need as muscle memory starts to kick in; it's important to mix up your training so that you continue to see results. As a general rule, you should not train a muscle group that is already aching. If your legs are sore, you could still do an upper body workout for example but it would not be wise to go for a long cycle or do a spin class. Listen to your body as that is always the most important thing.
So as for doing cardio on your rest days. That depends on your individual goals. If you primarily want to build muscle, you do not need to do cardio on your rest days. However, if you want to strip fat and keep your cardiovascular fitness up, it is recommended you do a light cardio session like a run or swim between weight sessions. You should always have at least one day a week where you do absolutely nothing though so that your body has a chance to keep up and fully recover.