More comment by OG. The original value of N or Standard Penetration Test considered the way the value was obtained. A spinning cat-head (capstan) with one wrap of a rope hauled up a 140 pound weight and dropped it 30 inches, with number of blows in 12 inches of penetration counted. More modern methods are more efficient and so the blow count is lower than by the original method. Most of the formulas from some years back were based on the original methods. Depending on how the method was done, you may or may not need the correction.
A quick search for bearing capacity methods and formulas assuming a given degree of settlement of a footing was made on Google and some 21 different papers are discussed by this very complete summary of the subject. Some of them are shown in SY's ist above.
I think one has to evaluate whether or not his footings are rectangular, near square or long when using any of these. I'd think most are for rectangular, in which case settlement is likely less than for the same width long footings. You don't just use that that width (B) in any such determination.
Finally, with several places where width is used in the formula, or other awkward use, likely it is necessary for you to develop a chart relating loads (column, or load per unit length) versus width of footing, with lines of equal settlement then plotted. The use of that chart by the footing design engineer then avoids them making any calculations using any of the many methods available. Where ever you can find that the method was used was field checked to see how well it works, then that might be more useful than blindly adopting any method. In the case of the Hough original charts, a study by California DOT with some of their jobs showed it was quite accurate, unless the water table was shallow, in which case it under-predictged settlement. From what I know, I don[t think one can automatically apply any of these to a mat or raft foundation. In that case get samples and get actual compression related data and run the calculations.
Don't forget to have grain size tests done for sand, because uniform graded sand N values are very misleadingly low.