I'm just an average person who questions the validity of my treadmill's claims about how many calories I've burned after an hour's worth of a cardio workout. How can I get a more accurate measurement based on pre and post workout conditions? I suspect the most accurate approach is to use rather sophisticated/expensive equipment (i.e. things I don't have/can't afford), but I'm also curious if there is a low cost/low tech approach to measure calories burned without relying solely on a heuristic formula?
This is actually quite a difficult problem.
Measuring the work done by a specific exercise output, eg treadmill, cycling, rowing machine etc is easy enough. However this only measures what you might call 'shaft horsepower' and ignores any effort that doesn't go directly into the output being measured.
This also ignores the efficiency of the underlying metabolic processes ie how much food you use up to produce a specific amount of mechanical work and it is certainly reasonable to assume that the amount of energy consumed to perform a specific amount of work will vary somewhat from person to person.
In terms of setting up an experiment the big difficulty is setting meaningful system boundaries such that you can measure energy input and output, especially since the human body has several different mechanisms for storing energy. For example a sensible way to measure the rate of metabolism is to measure the amount of carbon dioxide you exhale as that is a direct product of respiration and really you need to measure everything which goes in and out of the body during a period of exercise.
Weighting yourself doesn't help much either on its own as your mass can vary a lot due to fluctuations in water and waste products which aren't directly related to energy consumption and you will certainly lose a certain amount of water mass due to sweating and exhalation during exercise.
Having said that even knowing exactly how many calories you have used doesn't tell the whole story as you don't necessarily know how much usable energy is actually absorbed from a given quantity of food and unless you are eating precisely measured and processed food calorie counts are an average at best.
Really, measuring output work from an exercise machine is as good as you are realistically going to get without very specialist equipment, as that is at least measuring something specific and well defined and if nothing else you do know that you have expended at least that amount of energy.