After searching wikipedia and other sites I failed to find a handy formula for calculating GDP using the production method, similar to the one below. Perhaps someone could suggest which of the below listed ones are the best/most common. I look forward to your feedback
Expenditure:
GDP (Y) = C + I + G + NX, (NX = X - M)
GDP = C + I + G + (X-M)
Income:
GDP = COE + GOS + GMI + TP & M – SP &
2.GDP=R+I+P+SA+W

The reason you’re having trouble finding a formula might be that the formula is so simple and straightforward that people don’t consider writing it out.
Another term for the “production method” of calculating GDP is the “value-added method”. Unlike the expenditure method where you look at the value of all final goods sales – excluding intermediate goods – what you need to do in this case is count the value-added of every step in the chain. A formula would look like:
Value of sales MINUS cost of inputs
You would add up this figure for every economic entity in the economy. See the following for an example: (note: PowerPoint presentation). Or for a longer description of the value-added approach, you can look at this (long) article from the UN about the “production approach”. (Note: PDF file.) Keep in mind that the UN is using the System of National Accounts definitions, whereas the US relies on NIPA definitions which are slightly different.