Making a low frequency inductor design?
The equation is probably OK lower frequencies

Suppose you have a 2 inch diameter, 6 inch long coil, with 33 loops.  The first equation would predict an inductance of

\$L= \frac{d^2 \cdot n^2}{(18d+40l)}\$ 

\$L= \frac{2^2 \cdot 33^2}{18 \cdot 2 + 40 \cdot 6} \approx15.8 \mu H \$ 

Using the second formula, 2 inch diameter is about 0.0508 m (radius 0.0254 m) and 6 inch length is about 0.1524 m

\$L = \frac{\mu_0 \cdot N^2 \cdot A}{l} = \frac{4\pi 10^{-7} \cdot 33^2 \cdot \pi \cdot 0.0254^2}{0.1524} \approx 18.2 \mu H\$

How tight is your design tolerance?  Do you need it to be really close to 16 uH?  If so, you can tune it by stretching (lower) or compressing (higher) to the extent the wire is flexible.  You can also increase effective inductance by adding a small capacitor in parallel.