I'm quite suspicious that my electric stove runs hot. Recipes that suggest medium-high on my stove are incredibly, incredibly hot and you can feel 'high' radiating heat from across the kitchen.
As such, I've semi-recently purchased an IR thermometer - what pan surface temperature should low, medium-low,medium,medium-high, and high approximately register as?
They don't correspond to a temperature, they correspond to a rate of heat input.
The elements in your oven are connected to a thermostat with regulates their temperature, they are really constant heat/fixed temperature devices, like the heat in your home. The oven turns the elements on and off to regulate temperature, but the elements are only ever ON or OFF.
The stovetop elements, by contrast, are variable heat/variable temperature. There is no thermostat, but the elements can be variably adjusted between MAX and OFF. For every setting the temperature will just keep getting hotter and hotter (unless something is removing the heat, like cooking food) - the higher settings will just get hotter faster.
The important thing to know (for an electric range) is the wattage of the elements - most 8" elements are ~2500W, and most 6" elements are ~1500W. But there is a lot of variability. Additionally, if you are living in a home with 240V power but have recently lived in an apartment (which likely had 208V power, but 240V elements installed in the oven, even if you didn't realize it), your heater elements will seem much hotter than before. It is also possible that the oven maker or previous owner installed higher wattage elements (perhaps by installing elements intended for a 208V service in a home with 240V service, which would have the effect of "turbocharging" them a bit).
Temperature measured with an IR thermometer may not be useful for you to determine if your oven is hotter than usual, since an empty pan on Low will still reach 400+ degrees (it will just get there slower).
What might be more useful is to find out what setting people do certain cooking tasks at, and see if that is different than what works on your oven. You can also remove the elements and find the voltage/wattage stamped on the bottom - let us know what those values are and we may be able to tell you if they are abnormally high.
Personally, I sweat onions on 4/10, fry an egg at 6/10, simmer soup at 2/10, and maintain 1 gallon water at a consistent, but not vigorous boil at 8/10.
Here is what cook surface temperatures correspond to these labels:
High: 450° to 650°+
Medium-High: 375° to 449°
Medium: 325° to 374°
Medium-Low: 250° to 324°
Low: < 225° to 249°
On my electric stove, I've so far roughly figured out this system, using an IF thermometer, measuring a matte cooking surface:
High: 5 to 10 = 465° to 700°
Medium-High: 4.0 = 429°
Medium-Low: 2.8 = 272°
I'd say calibrate your own electric range, you should be able to find a reliable thermometer for under $20. Use a flat pan, preferably enameled steel, put some oil in it with a high smoke point, and measure away. Careful not to damage your pan, of course.
It's possible that the common quick-boil feature serves to distort the heat output - I do know someone with a gas stove where the highest setting is quick-boil, and there's a similar temperature distortion (where the simmer setting is much hotter than it should be, etc).
Rather than empty pan temperature, I suggest adding a quantity (like 2 cups) of water and measuring the time from off to boil. As other posters have indicated, stoves vary in power (heat input over time) without respect to temperature. By the way, electric ovens usually come in constant power (except those with "preheat" and "clean" settings -- which use the broil as well as bake element) and a thermostat (which is a switch activated by a temperature sensor) to turn the element on and off. (the knob for the burner eyes also has a thermostat, but it's not connected to the eye -- it uses a tiny heater inside the switch assembly to open and close a bi- metal switch -- it's turning on and off all the time. They use these because they're relatively cheap.)
Assuming that your electric stove elements are "overheating," you can simply not use the "high" setting. Electrical heating elements have negative temperature coefficients -- resistance (and power) goes down as the temperature of the element goes up. Also, as the element gets brighter, more energy is radiated and less is conducted, which means that a lot more energy is required for not much change in temperature once the element starts glowing brightly (you feel the radiant energy from across the room). When heating elements fail, they just stop working -- they won't catch fire or explode.
The biggest problem of too much power is that food gets too hot on the bottom of pots and pans. The food then sticks, cooks unevenly, or is overcooked. The best solution for that is to get to know your stove really well. The IR thermometer is great, but it's great for measuring the temperature of your food and hot oil. The temperature of the bottom of an empty pan is pretty useless information. Also, most IR thermometers have an upper limit of 400f or less. Since most foods char at less than 400f, they're great for food.
In my experience, burners vary in calibration pretty significantly. As Sam Ley has pointed out some electric burners may even be installed with the wrong voltage settings, causing them to operate outside of their calibrations.
What I've done for low, medium and high settings in recipes is to develop my own sense of what's low, medium and high. This can be as precise or rough, but universal.
An example of precise would be using an IR thermometer to read pan temps after a fixed time on the stove, which sounds like what you're after. I've only used my IR gun for bbq cooking, since I wanted to make sure I was getting the best possible sear on my steaks.
An example of rough and universal is what I do for stove top--use the smoke point of a common oil, i.e. canola oil, as an indicator of how much heat the stove can deliver in a fixed time.
My personal experience has been that medium-high and high on many recipes means canola oil is slightly smoking and quickly smoking, respectively. Medium would boil a few drops of water in under 5 seconds, whereas low would be where a few drops of water just barely sizzle, if at all. All this is on a medium-thickness saucepan, not cast iron or a cheap, thin skillet (i.e. 5 dollar pan from Ikea)
The advantage of the rough and universal method is that it can be applied to calibrate when switching cooking environments. I've used it while cooking at friends' houses and in vacation homes.
If the stove does not use any thermostatic mechanism, there is a way to find out what wattage the hobplates are actually running at: Make sure your home is as "electrically quiet" (nothing turned on that doesn't need to be) as it can be, then run the hobplate with a big pot of water on it for a given time, and check your electricity meter for what is being consumed - if, eg, you get 0,6 kWh after running half an hour, the plate is effectively running at 1200W.
Quicker way: IF you can access a few cm of the actual wires going to the stove (no need to be able to make an electrical contact!), get or borrow a clamp current meter, measure current and multiply by voltage to get wattage.
I have found that, using an IR thermometer to read pan bottom temperature after 5 minutes of heating (the temperature is no longer rising), that high corresponds to 375 degrees F, medium high to 330 degrees, medium to 300 degrees, and low to about 275 degrees.
Electric frying pans go up to 400 degs. Judging from that, the pots and pans on your range don't need to be heated above 400 or 500 degs, for any cooking task. (If the heating element on your range is glowing light red, it's between 800 and 900 degs.)
Looking at Sam's comment on top, I must disagree. A newer stove will have different electrical components the the VERY old stove in my apartment, but both are shooting for the same thing. The idea that one setting simply determines the rate of climb to a max wattage is incorrect. The elements in the oven are switched on and off at a rate that is determined by the set temperature, and the set temperature is what determines the rate of temperature rise in the food. I am going to make a guess here and say it may not go completely off, but rather partially off so you don't have any sharp current spikes, but I would have to look at the electrical schematic to be better informed about that. Now as far as the stove is concerned, on an older one such as mine, everything is purely resistive. In other words it is nothing more than a matter of limiting the current going through the heating element. When the burner is set to low, less current. When the burner is set to high, more current flows through the element. Since the burner element is a fixed resistance, the different setting choices, low, high etc., will have a produce higher or lower temperature being emitted from the element. And just like the oven,food will cook more quickly if the temperature is higher. As anyone who has accidentally left a burner set at low overnight like, ahem, me, can tell you that it never reaches the cherry red that a burner set on high will after only a few minutes. This was a very wordy way of saying yes, the stove setting is going to give you different maximum temperatures for the element. It would be easier to contact the manufacturer of your stove, and they will be able to give you an approximate answer to your question. You can expect resistance values to change somewhat with age.
Well I'm not sure what temp they can reach but I do know they can reach a temp high enough to melt down lead and leads melting point is around 620° f
