This article explains how Food Production is calculated.
Farms
Farms are City Improvements that generate Food. The amount of Food they generate is dependent upon the amount of Land in the City, as well as the total number of Farms. Each City can have up to 20 Farms.
Improvement Specialization Bonus
Resource producing improvements get bonus production for having additional of the same improvement in the same City. Farms get bonus production up to 50% if a City has the maximum number of Farms, 20.
The bonus calculation is:
Improvement Specialization Bonus = 1 + ((0.5 * (Farms - 1)) / (20 - 1))
Base Production
The other factor of Food production is the amount of Land in the City. The Food Production Rate is equal to the total amount of Land in the City divided by 500.
Food Production Rate = City's Land / 500
Mass Irrigation National Project
The Mass Irrigation National Project increases the base Food Production Rate. With the Mass Irrigation National Project the Food Production Rate is equal to the total amount of Land in the City divided by 400.
Food Production Rate (w/ Mass Irrigation) = City's Land / 400
Antarctica Penalty
If a nation is located in Antarctica, it suffers from a permanent -50% food production penalty.
Food Production Rate (Antarctica) = [City's Land / 500] * 0.5
Food Production Rate (Antarctica, w/ Mass Irrigation) = [City's Land / 400] * 0.5
Production Before Modifiers
Base Food Production (per city) = Round(Farms * Improvement Specialization Bonus * Food Production Rate,2)
Food Production Modifiers
There are a number of potential further modifiers to Food Production applied after the Base Food Production Rate is calculated, including the Improvement Specialization Bonus.
Seasonal Modifier
The Food Production rate is increased or decreased depending on the nation's continent and the time of year (Orbis Date.) If a nation is not experiencing Summer or Winter, the Seasonal Modifier = 1. Antarctica never experiences Summer or Winter.
Summer Bonus
The summer bonus is a 20% increase in Food Production for nations in North America, Europe, and Asia during the months of June, July, and August, or for nations in South America, Australia, and Africa during the months of December, January, and February.
Food Production = Base Food Production * 1.2
Winter Penalty
The winter penalty is a 20% decrease in Food Production for nations in North America, Europe, and Asia during the months of December, January, and February or for nations in South America, Australia, and Africa during the months of June, July, and August.
Food Production = Base Food Production * 0.8
Radiation Penalty
The presence of Radiation decreases Food Production. This penalty is applied after the Seasonal Modifier.
Radiation Index = Nation's Continent's Radiation + Global Radiation
Radiation Penalty = Radiation Index / (-1000)
Food Production = Base Food Production * (1 + Radiation Penalty)
Final Food Production Formula
Food Production = MAX(Base Food Production * Seasonal Modifier * (1 + Radiation Penalty), 0)
Food Production cannot be negative.
Running Out of Food
If your nation runs out of food, your gross income receives a 33% decrease penalty effect. Your nation's Approval Rating will drop by 0.5 per turn.