Fourier's law is exact and inconvenient: nobody wants to carry a conductivity and a thickness around a job site. So the trade turns the two into ONE number and calls it the R-value. $R = \dfrac{L}{k}$ — read aloud R equals L over k. $R$ is the layer's area-specific thermal resistance in m²·K/W, $L$ is its thickness in metres, and $k$ is its thermal conductivity in W/(m·K). Metric labels call that number RSI; an RSI-3.5 batt is the R-20 batt of the North American aisle, and the twin lesson in imperial units is coming.

There is a second R in this chapter and the two must never be confused. $R = \dfrac{L}{kA}$, in K/W, is the resistance of a PARTICULAR slab, area and all — that is the one you use when you want watts out the far end. The R-value above is the same quantity with the area divided out, which is why an insulation label can quote it without knowing what building you are in. Watch the unit and you will never mix them: m²·K/W is per square metre, K/W is the whole slab.

Thicker is better, leakier is worse, and both live in one fraction. Twice the thickness of the same board is exactly twice the R — insulation is one of the few things in engineering that scales that politely. And once again: $L$ enters in metres, so 100 mm of board is 0.100 m. Millimetres straight into that fraction give an RSI in the thousands, and a wall that good has never been built.