R Value
This graph shows the speed of escaping energy on the left. Squint so you can see the decimal point. The highest value is point 3 with zero at the bottom of the graph. The R-value is shown across the bottom of the graph.
Look at the graph and notice two things.
One. The speed of escaping energy is slowed a lot for each little bit of insulation until you reach R 14 where it turns the corner.
Two. From R 28 onward, there is very little improvement.
If you were to improve attic insulation from R-7 to R-21, for example, you could cut you energy losses through the ceiling by 65%.
Going from 1/7 versus to 1/21 U-value (or from 0.14 to 0.05) is a 65% improvement.
In most homes about 35% of the heat is lost out the roof, the rest gets out through the walls, windows and by air leaks. Therefore, the overall energy bill for the heating season would be reduced by about 23% (a 65% improvement of 35% of the heating bill.)
In this example, three times as much insulation saves less than one quarter of the heating bill.
The myth persists that, if R-11 insulation in your house saves heat and money, R-22 insulation saves twice as much. However, the energy and money you save by adding more insulation diminishes quickly.
Look at the graph again. Starting with an R-value of 3.5, every doubling of units in R-value cuts the speed of heat loss through the wall or ceiling by about half. The R-value points shown on the graph are selected because they are double the previous number.
As the thickness (R-value) gets higher, the speed of heat escaping through the ceiling soon becomes tiny. It reaches a thickness where adding more insulation costs more than it is worth.