Many years ago some guy decided to leave a legacy behind. His goal was to confuse the heck out of us. But with a little patience I will try to clear the muddy water on our way to understanding R-values. R-values are a measure of thermal resistance, or the ability to insulate. You will most commonly find R-values on insulating materials at your local building supply store. R-values range from 1 (for a single-pane window) to 7.2/inch (for polyisocyanurate foil-faced panels) or as high as 10 for high-tech silica aerogel and 30 for vacuum insulated panels. But what does R-value mean? Well, here comes the confusing part: R=ft²-°F-h/Btu (I am using the non-SI definition here because it is most common in the US). What?

Basically, R-value is the amount of energy lost, in BTU per hour, through a square foot of surface, based on the temperature difference between the inside and outside. To really wrap your head around it let’s look at an example… Let’s say we have a hallway that leads to the south pole, where it’s quite cold. We could just run the heater at full blast to try and keep the cold back, but energy is expensive. The other option is to block off this hallway with an insulated wall. Let’s say the cross section of the hallway is 20 ft², it is 0F at the South Pole today, and we want to keep our end of the hallway at 70F. I think I would like to install a three-inch thick wall of the polyisocyanurate foil-faced panels, with an R value of 21.6.
With a little bit of algebra we can get the R=ft²-°F-h/Btu equation to say Btu/h=ft²-°F/R. Plugging in 20 ft², 70°F (70°F – 0°F), and 21.6R, we get 64.8 Btu/h. This answer assumes that the remaining walls of the hallway are hyper-insulated but it tells us how much heat will still be lost through the new wall.
I will do one more example, using an enclosed space with both insulating panels and a glass window to find the overall heat-loss. This result will be useful for next week’s AskPablo.
Let’s say we have a box that is 1x1m, 25cm high and has a 1x1m double-pane window on the front. What will be our heat-loss at various temperature levels (assuming a constant 50°F exterior temperature)? Let’s assume that we are using the 3 inch thick polyisocyanurate foil-faced panels again, which would have a combined surface area of 20,000 cm², or 21.53 ft². The double-pane glass has an R-value of 2 and an area of 10.765 ft². To calculate heat-loss for a composite wall (made up of different materials) we can use this equation: Btu/h=(AreaWall/RWall + AreaWindow/RWindow) x °F. The part of the equation in parenthesis comes out to 6.38. To get BTU/h for any temperature difference, we simply need to multiply it by this factor. If the temperature inside the box is 50F, there is no heat loss; at 60°F the heat loss is 63.8 Btu/h; at 70°F the heat loss is 127.6 Btu/h; and so on.
For those metric fans out there, 63.8Btu/h is equal to 18.7 Watts. So for every 10°F rise in interior temperature we would need to turn on one 20W bulb to maintain that temperature. Neat!
Pablo Päster, MBA
Sustainability Engineer
Pablo(dot)Paster(at)gmail(dot)com

### 6 responses

1. Pablo says:

Max,
From Wikipedia (http://en.wikipedia.org/wiki/R-value_%28insulation%29):
The SI units for thermal resistance are K·m²/W
and
The conversion between the two is 1 ft²·°F·h/Btu ≈ 0.1761 K·m²/W, or 1 K·m²/W ≈ 5.67446 ft²·°F·h/Btu.
For the second part of your question (from my article above): “To calculate heat-loss for a composite wall (made up of different materials) we can use this equation: Btu/h=(AreaWall/RWall + AreaWindow/RWindow) x °F.” So, for your example, we would calculate (30/4 + 10/2) x °F = 12.5 x °F.
Pablo

2. Max says:

Ah, never understood that quite well. Guess you don’t happen to have the SI variety of the formula handy? Overhere we calc in celcius, meters and watt/hour.
How do you sum different R values to get average room isolation? Like 10 ft2 windows with R=2 and 30 ft2 walls with R=4 would give a total R of ???

3. Max says:

Hi Pablo,
Thanks for the pointer to wikipedia. I’ll have a go at doing some calculations to become familiar with it.
Conversion between SI and BTU may be handy as well to compare with the many international publications.
And sorry for not reading the last part of your article well, I guess my eyes moved on while my brain was still with the previous formulae…
Max

4. Jiltedcitizen says:

You should just make a dummy section and say higher is better. And R values for new construction differ from state to state and probably county to county. I think standard where I live is R-30 for attic, and R-18 for walls or R-13 can’t remember.

5. Flynn Cowan says:

pablo i need to convert 0.38btu and 0.30btu into an r value can you help me, im from australia so i only deal with the metric system.

6. Alan says:

Pablo,
Could you validate or correct a calculation I’m trying to do?
I’d like to know if 3″ thick polyiso will insulate a pipe exposed outdoors, 3 feet long and 3/4″ in diameter. The pipe at sundown holds water heated to at least 90 degrees F. The overnight winter temperature (near Boston, MA) can get as low as 20 F.
3 ft of 3/4″ pipe = 16 cubic inches = .06926 gallons = 0.5769 pounds.
BTUs available before the pipe freezes =
(90 – 32) * .5769 = 33.5 BTUs.
I calculate the surface of the polyiso box around the pipe as 3 foot long x 12 inches around = 3 sq. foot.
BTU/h lost during the night =
BTU/h = 3 * (90 – 20) / 21.6 = 9.6 BTU/h
From this I reckon the pipes will freeze in
33.5 / 9.6 hours = 3.5 hours.
Can this be right?
Thanks.