Ok. I've been racking my brain; Not too long ago I read an article regarding fat loss, and it mentioned that working out when you're too tired can be counter-productive (as far as losing fat). For the life of me, I can't recall where I saw this....any input on the subject?
What kind of tired and what sort of work-out you are doing are important details. If you are tired from lack of sleep as ChuckC mentioned, you should focus more on quality of life choices first. Honestly, this has been the boat I've been in. Work had been physically demanding, my diet had slipped, and I was sleeping like hell because I was working crappy hours. Rather than push myself and go to the gym, I gave my body a chance to rest and recover by skipping the gym. I've taken steps to improve my quality life (namely switching jobs) so I'm hoping to get back to the gym regularly as my new schedule settles down. If you are in the same boat as I am, it's not a bad idea to skip a work-out, especially a cardio session. You could be causing a spike in cortisol, depending on your exercise of choice, and if you are lifting heavy weight form is of critical importance so you need to have proper focus. If you can't focus and maintain form because of fatigue, this may result in an injury and that will definitely curtain any fat loss. My advice is if you are in this boat is to take a day or two off if it's an isolated incident or make major changes if it's a regular issue and instead take a walk or do yoga, low intensity work that can help reduce stress rather increase it.
If you are simply "tired" on your way home or the gym, in that you don't want to do your prospective work-out, you have two options. 1)suck it up pussy :o) we all have days where we don't want to lift but once you get started, you'll be happy that you did. Or 2)give your work-out plans a lookover and see if it's something you're truly interested in and if they push you towards your desired goals. You may need to shake things up and try a different lifting strategy or type of lifting (swinging to kettlebells, for instance). Maybe have a few weeks where you focus on lifting or biking or rock climbing and then when you've had a few weeks away from the iron, you can come back to the gym with a renewed focus and vigor.
The CDC recently announced that shift work (re: Lack of sleep) is considered a known carcinogen. Adding undue stressors to a body with an already high cortisol level is an EXTREMELY counter-productive choice.
In order, you will get the most benefit from 1 - Sleep Regulation 2 - Diet Regulation 3 - High intensity Exercise.
However, you cannot out exercise a lack of sleep and a bad diet.
Firstly, as you have not defined what type of workout you're thinking about, I am going to assume that you mean a round of weight-lifting, simply because that what I think of when someone mentions a workout.
As far as fat-loss is concerned, I have not seen anything to say that training while tired is counter-productive. I have read that it can be counter-productive when it comes to gaining muscle. If you do a workout, the body will need energy to be able to perform. If you are eating right, bodyfat will be the preferred energy source.
I have seen articles that mention that reducing cortisol can be beneficial for fat loss. If the tiredness is from stress ( which would produce high cortisol), than fat loss may stall.
A more likely problem from training while tired is injury, especially if you are training with free weights. When you are tired, form breaks down more easily and poor form is a common cause of injury.
My recommendation about training while tired : Go light on the weights. Or go for low-intensity work, like a walk or an easy Yoga session. The most common Paleo thinking I have seen is low intensity work should be often (say, a daily walk) while high intensity work should be short and infrequent. (heavy lifting in the gym once or twice a week)
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