Mathematically determine the length and width of board required to make a box

Lets first define the variables 

Let $t$ be the thickness of the wood.
Let $k$ be the kerf thickness of the saw blade (the amount of wood removed by the saw blade).
Let $L_{\text{min}}$, $W_{\text{min}}$, and $H_{\text{max}}$ be the minimum inner length, width, and maximum inner height of the box, respectively.


Next we Calculate Outer Dimensions

The outer length ($L_{\text{outer}}$), outer width ($W_{\text{outer}}$), and outer height ($H_{\text{outer}}$) of the box can be calculated by adding twice the thickness of the wood to the inner dimensions. Additionally, if the cutting process affects these dimensions, you would add twice the kerf thickness for cuts impacting each dimension.


Outer Length
\[L_{\text{outer}} = L_{\text{min}} + 2t + 2k\]

Outer Width:
\[W_{\text{outer}} = W_{\text{min}} + 2t + 2k\]

Outer Height:
\[H_{\text{outer}} = H_{\text{max}} + 2t.\]
(Assuming the kerf affects only the length and width when constructing the box.)


Explanation:


The addition of $2t$ accounts for the wood thickness on both sides of each dimension.
The addition of $2k$ accounts for the wood removed by the saw along both cuts impacting each dimensional plane. Note that $k$ is added per cut impacting the dimension, so if both lengthwise and widthwise cuts are made (and assuming cuts are made at both ends of the wood pieces), it contributes to both dimensions.