In this equation, the amount of water to produce grains that can generate energy required by a person for daily activities for a year (X = D kcal/ [(1,000 kcal/day/per capita per year) /100t per capita per year]) is obtained first. Then, based on the person's consumption rate of fresh water (U), the required amount of water (X/U) is calculated. Lastly, taking into account the loss of grains (L), the required amount of water [(X/U)/(1-L)] is obtained.
Thus, by adding the amount of fresh water required for domestic use (37m3)(12) to the obtained value of Wr, the amount of fresh water needed for a person for food and daily life for a year is obtained. Finally, the maximum allowable population under a particular condition of water resources is obtained as：
where Wa = An amount of replaceable fresh water human beings can utilize.
Cohen calculates the maximum allowable populations on combinations of the following assumptions.
1] U is either 20% (a relatively realistic level)(13) or 100% (the greatest maximum value available but an unrealistic level).
2] D is either 2,350kcal (the average intake of energy)(14) or 10,000kcal (the average consumption in the US)
3] L is either 10% (quite efficient but unrealistic) or 40% (the world average level)
4] Wa is 41,000km3 (the total amount the world's utilizable fresh water), 14,000km3 (the estimated ceiling of the amount of fresh water actually used), or 9,000 km3 (the estimated floor value of the same)
