As we continue to explore the possibility of building a house that doesn’t require a heating and cooling system, the next step is to get to know the current standard for adding insulation for energy efficiency. This is a topic that involves a bit of math. In this post, I’ll walk you through the equations that are used to determine how much insulation to add. In the next post on insulation I’ll go through two simple examples of working out how much insulation to add.

### Payback Period

The typical plan for adding insulation for energy efficiency is to add to the point where you are able to cover the costs of the added material with the money that you will be saving in heating and cooling costs. The time it takes to recoup the money for energy efficiency upgrades is called the **payback period**. For the insulation of a residential building the average payback period that most people are interested in waiting is between 4 and 5 years. So, in order to figure out the payback period we need to consider the R-value of the insulation, and the cost of heating and cooling the house per year.

### Calculating the R-Value

As you may remember from my last post on insulation, the R-Value is a numerical value given to insulation that tells you how much the insulation is going to resist the flow of heat. Determining the R-Value of an insulation material depends on a number of different factors:

- Initial indoor temperature (Ti)
- Outdoor temperature (To)
- time (t)
- surface area of the building (A)
- The heat loss indoors (dQ)

And the equation looks like this:

R = (Ti – To) * A *t / dQ

The good news about R-Value calculations is that you usually don’t have to do them. Since the measurements to complete the calculation are done in a lab setting in a controlled environment, the insulation manufacturer provides that information for you when you choose your material.

### Calculating the Payback Period

In order to calculate the payback period of adding insulation, we need to take into account the insulation and the heat system. The payback period depends on the following features:

- R-value of the initial insulation (Ri)
- R-value of the final insulation (Rf)
- Cost of insulation (Ci)
- Efficiency of the heat system (E)
- Cost of energy (Ce)
- Number of days that require heat per year (t)

And the equation looks like this:

P = (Ci * Ri * Rf * E) / (Ce * (R2 – R1) * t)

You can find more information on calculating the payback period of adding insulation here.

I know looking at all these equations can be intimidating if you are interested in figuring out how much insulation to add to your house to meet the 4 – 5 year payback period. But hopefully after I work through a couple examples in my next post on insulation, it will seem manageable. Maybe you’ll even be inspired to add insulation to your own house to make it more energy efficient.