Question in title.
Do there exist any devices that can tell you how many calories you are buring off through the day?
Well, there are formulas that kinda guesstimate your expenditure. Here’s a fairly good one. But they can be really inaccurate. Some universities and health clubs offer a procedure that supposedly can measure your resting caloric expenditure, i.e. calories expending while doing nothing. Don’t know about the accuracy tho’. From there you would have to figure out how much activity you do during the day and add on…
Good-quality heart rate monitors will calculate your calorie usage (like this one, as an example).
There are big individual variations in active metabolism due to differences in muscle mass and aerobic fitness. The heart rate monitors can give you a rough estimate of your caloric expenditure, but nothing terribly accurate.
One other thing you should keep in mind is the difference between gross and net caloric expenditure. The gross caloric expenditure is the total amount you burn, and that’s what’s measured whenever you get a figure. But to figure out your daily total, you need your net caloric expenditure, which is the amount of calories you burned doing an activity minus the number of calories you would’ve burned doing nothing. If you just add your gross caloric expenditure to your RMR, you’re systematically overcounting.