We've established that the speed of jogging already puts that activity as vigorous exercise so do you need to go any faster? The answer is that if you find the jogging speed easy, then yes. Go faster and as fast as you can so as not to lose your breath or become so exhausted from a relatively short run.
Running too fast as though you're racing every time is not good training. This will only cause injuries, even on a treadmill. However if you can successfully run faster than jogging and you feel comfortable doing it. You clearly have a good fitness base already. Or you're built for this type of exercise.
So for a running speed it would be more than the jogging speed so 7.5 km/h (5.3 mph) and higher. You may see people running faster in a gym but they are likely to be experienced runners. Also you don't necessarily know how long they've been running at that pace for! If you're running at this pace you'll soon get passed a couch to 5k if you needed to use one at all.
How fast should you go
If you're a beginner then despite everything said above about speed, how fast you should go depends on how you feel while running. A great way to tell is using your heart rate but since not everyone has heart rate monitors and the ones on treadmills aren't very accurate. You can tell by the rate you're breathing at and how much you could say while exercising.
If you can speak a sentence while exercising then you're comfortably running/jogging and you can stay at that pace. If you can only say a word or two before breathing again then you are probably going too fast. If you're exhausted after running only 10 or 20 minutes and you're not doing speed work or training for a race then you're going too fast.
Your speed can change as you get used to exercise. You will soon be breathing easier after completing a couch to 5k. Still use that speed button carefully. You can also increase your speed by doing speed work exercises which are good for treadmills. These are usually done by experienced runners and plans can be found online. However fast you go make sure you enjoy it and push yourself to achieve more and you'll be successful.
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