The question of amino acids intake is inextricably interwoven with protein intake in general. According to our primary source (p. 144), for adults, the protein requirement equals 0.8 g per kg of body mass per day. For a man of the reference weight (p. 17), it means 56 g of protein per day which is also the reference value for men over 18 years old.
The 'g per kg' approach is consistent with the 'macros' approach from the source (p. 145), according to which energy from protein should constitute at least 10pct of total calories. If we plug the reference weight and height in the EER (Estimated Energy Requirement) equation from the source (p. 82), we'll see that those 56 grams of protein per day do translate to roughly 10pct of total calories in the base-case scenario (PA = 1.00). Let's keep these findings in mind: 0.8 g of proteins per kg of body mass per day corresponds to 10pct of total calories (it hints at how your need will be calculated).
It should be mentioned, however, that the requirements are based primarily on the nitrogen balance approach, and authors admit that "athletes should consume a higher–than–normal protein intake to maintain optimum physical performance." (p. 150). Nowadays, the vast majority of fitness experts recommend adhering to 20pct of the protein in total calorie intake, and the percentage grows as we age. Since all requirements for amino acids in our guidance are seemingly calculated on the "0.8 g per kg per day = 10pct of total calories" basis, any changes in this ratio should impact your estimated need accordingly.
By default, the website sets the protein ratio at 20%, meaning initial values for amino acids from the source's summary tables will be multiplied by two. Registered users are allowed to define their own ratios for macros on the Metrics page, and their needs will be recalculated accordingly. For example, if they go for 25pct of protein intake (or 2 g per kg of body mass), initial RDA values for amino acids will be multiplied by 2.5, if it is 13pct – by 1.3, and so on.
Next, these values are multiplied by the user's weight (as they should), which in cases of an anonymous user or a user without metrics, is 60 kg. After establishing the base, those values go through the routine explained in the section on your need.