The diminishing returns of insulation thickness is a legend referenced by many builders and architects which is actually incorrect. It is often paired with financial payback calculations that don’t consider the full range of insulation benefits.
The legend states that any amount of insulation added after R-10,20,30,40… (pick your number) is a waste of money or unnecessary, or simply doesn’t make sense. I’ll explain why that is not the case.
Note: I originally wrote this as a comment to this blog post and decide to share it here with additional details and context.
Why R-values and U-values Get Confusing
Materials transfer heat at a constant rate that is proportional to the width and the temperature difference between both sides of the material. It is expressed as W/(mK) and a typical (and conservative) value for a blown-in cellulose, wood fibre or mineral wool is 0.04W/(mK).
Dividing this number by the width of the material we derive the rate of heat transfer per area of the material which is the U-value or W/(m2K). The inverse of that is the resistance to the heat conductivity or the R-value or m2K/W.
It appears as if each additional layer of insulation does “less” to reduce the rate of heat transfer (U-value) while the R-value increases linearly. This is the source of confusion.
However, the ratio of insulation added relative to the total amount of insulation is actually the same as the change in the rate of heat transfer or the U-value:
|Thickness, m||Thickness Change||U-value Change|
|0.2||+50% (0.1/0.2)||-50% (0.2/0.4)|
|0.3||+33% (0.1/0.3)||-33% (0.066/0.20)|
|0.4||+25% (0.1/0.4)||-25% (0.033/0.133)|
|0.5||+20% (0.1/0.5)||-20% (0.02/0.10)|
This is similar to how a 50% drop in stock market requires an 100% increase afterwards to get to the original value. The reference point is what matters and creates the perceived difference.
Doubling the width of insulation at every step also halves the U-value but normally the increments are constant so the rate of change appears to slow down.
How Much Insulation is Enough?
After adding enough insulation for basic things like thermal comfort and avoiding condensation risk, it boils down to the cost of energy and its sustainability over the lifetime of the building.
The passive house limits of 15kWh/m2 of energy per year or 10W/m2 of heating/cooling load are great guidelines based on the maximum amount of heat that can be transported with the ventilation air. It is also low enough to require paying attention to thermal bridges and air tightness. Importantly, that amount of energy is easily available from photovoltaics during the summer and can be cheaply extracted from the ground via heat pumps during the winter.