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# Calculating Surface temperatures of a thermal insulator

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I'm interested in knowing the surface temperature of both sides of a double-pane or triple-pane window.

Given the R-value of the window, and the air temps outside and inside, how can I calculate the temperature of both surfaces of the window?

I plan to use this formula to help prevent condensation from occuring on either side when the house is too cold in the summer or too humid in the winter.

I've also noticed, in winter at least, that condensation only occurs on the bottom edge of the window. I'm not sure if that's because the gasses between the panes settle out and are less isulative at the bottom, or because something about the bottom of the frame is less insulative than the sides or top.

I don't think the same is true in the summer. I think in the summer, dew forms uniformly or around the center of the glass.

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The "R value" of insulation is its thermal resistance. It tells you how much of a temperature difference is required to transfer a certain amount of heat power per unit area. The R-value you see on insulation in stores, at least here in North America, is in some arcane units, like °F per BTU per hour per square foot.

So, knowing the R-value of the window and the temperature difference between inside and outside will tell you how much heat power is moving thru the window. That doesn't directly tell you what the inside surface temperature of the window will be. For that you need to know the coupling from the inside surface of the window to the ambient air. That times the heat power you know is flowing thru the window will tell you the temperature difference of the window surface from the inside ambient temperature.

There is probably no easy way to know this second window surface to ambient inside air R-value. Of course that has nothing to do with the window anymore, just the fact that it's flat and vertical. Someone has probably done such measurements already and published them.

You can probably get a reasonably good idea of this yourself. Stick something very thin and black on the inside of the window, then use an infrared thermometer to measure its temperature. The reason to make it thin is so that it adds little insulation to the window. The reason to make it black is so that the assumptions built into the infrared thermometer are met, which is that it's looking at black body radiators.

The reason the bottoms of your windows frost up first is due to convection. The window is colder than ambient. That means the layer of air right against the window is will be flowing down. The boundary layer of that falling air will be cooled more as it flows past the window, so will be coldest at bottom.

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