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Let's say for the sake of the argument that a person would burn 100 calories per hour sitting on a chair. That person does an hour of exercise on a machine at the gym and the display states that 600 calories have been burned.

Ignoring any inaccuracies in the way the machine does the calculation, does that mean the person has actually burned 600 calories by using the machine, or that they have really burned only 500 (since they would have burned 100 anyway "for free" without the machine's help)?

If the answer is that it varies between machines then I'd like to know what is most common (if such an answer is possible).

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Most calculators that you see in commercial fitness machines and similar include the BMR in the calculation. It's basically the difference between gross and net calorie.

Gross calories are all calories burned during an exercise session (Which is what most calculators report), and net calories, which are the calories burned separate from your BMR.

Unfortunately, most devices won't tell you which they are reporting, you'd have to see if the manufacturer has it on their website or do some research, but to be on the safe side if you can't find out, assume that it is gross calories so that you don't potentially go over your calorie budget.

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You may be able to discover this on a non-motorised machine e.g. a bike by starting a workout but not actually performing any work, check the rate at which energy is accumulated over time.

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