Recipes call for cooking food over varying amounts of heat on the stove burners - medium, medium-high, low, etc. How can I compare what the person who wrote the recipe calls "medium" with what (I think) is "medium" on my stove?
With baking, it's easy because 400F in your oven is the same as 400F in my oven. But medium on your burner may be different from medium on my burner (or my burner may be labeled 1-10, and 5 may be different than your medium). Even on my own stove, the four burners are all different sizes and the flame on one is a different size than the flame on the rest, even if the knobs are all turned to 5. How can I ensure I'm using the right amount of heat on the burners?
Fortunately, temperatures don't usually need to be as precise in stovetop cooking as in baking. When you do need precise temperatures, you can stick a thermometer in the pan. This can be useful for tempering chocolate, scalding milk, deep frying, candy making, etc.
The real problem with stovetop heat settings is that the knob on your stove only controls one of many variables that affect the temperature of your ingredients. Other important variables include the materials used to make the pan, the thickness of those materials, the height to diameter ratio of the pan, how full the pan is, the water content of the ingredients, whether it's covered or not, agitation of the ingredients due to convection or stirring, etc. You really just need look, listen, and fiddle with the knob until it's right. It will get easier as you get used to your stove, pans, and recipes.
You can eliminate some of the guesswork by matching the burner size to the pan size. Also, most of the recipes I've used seem to have been written for gas stoves, which tend to deliver heat at a faster rate the electric versions. So, if you have an electric stove, plan on turning it up a bit higher than what the recipe calls for.
You could use a contact less thermometer to check your burner temperature.
But that would not help you deciding what is the temperature that a medium setting is.
The burner size exists mostly to fit different pan sizes; use a burner size as close as possible to your pan size to not loose efficiency.
Oh, and an oven temperature is never precise either; even if the display says 400F, the inside might be above or below, you need to use a thermometer to verify your oven temperature;
for example you might find that at lower temperature settings, your oven runs warmer (for example from 100F to 250F it runs lower than what is displayed, and after that, from 250 up to 500F it runs lower)
It is not a property of the stove (or the markings on it). Words like "medium heat" actually refer to the speed at which your food is cooking, and there are a lot of factors which contribute to that. Beyond the energy output of your burners, there is the type of stove (electric, gas, induction), the thermodynamic properties of your pan, the relation of pan size to burner size, how you preheated the pan, the amount of food you put in the pan, the quality of your raw ingredients, and other such stuff. So you cannot calculate it or compare it.
The only way to "calibrate" is to observe how your food is cooking. I can only give you very rough guidelines, since the words are not (and cannot) be defined precisely. "Slow heat" is the setting at which the food can be left alone for at least several minutes without much risk of burning. "High heat" is the setting at which you end up with a very crisp/charred outside and raw-ish middle. "Medium" is somewhere in the middle between the extremes.
Any of these will tend to correspond to a somewhat narrow range of stove settings, because when the same person cooks in the same kitchen, there is rarely too much variation in the other variables of the process (which make it so diverse in general). So you have to be able to recognize the current level of "heat" when you cook (I was tempted to say "by looking", but it actually also involves smell and hearing and sense of time). Once you see that your food is cooking at "medium", you can see which setting you are using, and after a few trys with your own stove you will know which setting to try the next time you cook.
There are ways to measure the energy output of your stove and a given combination of pan and cooking material.
A simple way would be to fill a pan with water at a specific temperature, and then graph the rate of temperature increase at given settings of the burner.
Different burners on your stove have different purposes as well. There is usually one or two larger burners that are for doing most cooking, and a smaller or lower-output burner for warming, and possibly and in-between burner as well for smaller pots.
However, while this information is interesting, it it essentially useless when it comes to what you appear to want: An empirical way to compare your own stove with the stove the recipe anticipates.
I've read plenty of recipes and not one of them has mentioned a specific model of stove.
Without knowing the relative measurements of a target stove your detailed information about your own stove means nothing. It is relative, and there is nothing to compare it to.
This is why most descriptions of stove-top cooking describe the appropriate outcome. This outcome is the standard you are trying to meet, the desired target: the time and temperature are just guidelines that should get you close.
Judging stovetop heat is difficult which is why many just learn the stove tops they uses.
I believe your asking about the heat output, in BTUs, of a burner. As electric stoves usually have a slower response, as the "coils" heat up or cool down I assume the coils are at their final temperature. I'm not sure on heat response on newer electric burners (induction or other technologies).
You can get a proxy of a BTU by using the same pan and a measure of "room temp" water (1/4 cup). Once the burner is at its full power place the pan and water on the burner and time how long it takes to boil. Note the time. Let the pan cool and replace the water. This can help you calibrate a small burner to a large burner on the same stove top. A little harder when calibrating your stove with a friends this way, unless they agree to perform the same test.
I did see, but can't find it now, one magazines temperature calibration using a similar process. Their stoves were set so that a Medium in their recipes, was 5 on their stoves, which would start to boil X cups of water a pan Y inch pan in Z minutes. I don't remember what magazine was and can't find a similar calibration.
I find this question really interesting. I don't really have a response so much as a related comment. SImply put, I don't understand why most ranges don't offer a linear flame response as you turn the dial up on a burner. They have "jumps" from low to medium-low, to medium-high, etc. The dials themselves turn smoothly, always, but the flame responds erratically. For example, on a numbered dial from 1-10, 1-3 might be low, and then suddenly at around 3.5 it jumps to medium low, where it remains until 5. Seems to me they should just have 4 buttons (low, med, etc..) instead of a dial that fools us into thinking we have fine control. I really want to get a range with a straight linear burner response, and no "presets." Not only is the information impossible to get from manufacturers, but retailers obviously can't leave ranges hooked up in their showrooms, so it's impossible to test them, too. I'm tired of trying to get the "sweet spots" between the damned presets that the manufacturer has decided is optimal for my cooking.