If I eat a very large meal, how long does my body take to convert the excess calories into fat?
There would be a lot of factors involved in this question; The rate of digestion, the rate absorption of GI tract, the rate of transfer from splanchnic circulation to the liver and other organs and the rate of metabolism of an individual in including different rates of different enzymes. But since OP is asking for "calorie to fat" we will limit it from glucose(since calorie is already a unit of energy)to fatty acids and Triglycerides.
During well-fed state or post-absorptive state, the body starts to either convert glucose into ATP/energy via glycolysis and citric acid cycle, into glycogen in liver or muscle or into fatty acids in the liver, kidney, adipose tissue etc.-excerpt from (NCBI)Food Intake and Starvation Induce Metabolic Changes
Let's start with the steps of conversion from glucose to fatty acids
The first step is Glycolysis - red circle. The second step is the Citric acid cycle or Kreb's cycle - green circle. The third step is Lipogenesis - blue circle.
Glucose is converted to pyruvate in the cell cytosol1. Pyruvate is converted to several substrates including citrate which is essential in lipogenesis in the cell mitochondria2. Lipogenesis is the process by which acetyl-CoA is converted to triglycerides, lipogenesis encompasses both the process of fatty acid synthesis and triglyceride synthesis, where fatty acids are esterified to glycerol3.
Rates of conversion
...ratios and rates varies widely depending on the nutritional status...
...high fat diet abolishes lipogenesis... The rate of lipogenesis from available carbohydrates seems to be regulated not only by the carbohydrate content of the diet; glucose utilization increases as the carbohydrate content increases or the fat content decreases.
When the glycogen stores are saturated, massive intakes of carbohydrate are disposed of by high carbohydrate-oxidation rates and substantial de novo lipid synthesis (150 g lipid/day using approximately 475 g carbs/day) without postabsorptive hyperglycemia.
Glycogen storage capacity in man is approximately 15 g/kg body weight and can accommodate a gain of approximately 500 g before net lipid synthesis contributes to increasing body fat mass.
It depends on several variables, nutrition, rate of metabolism of an individual, lifestyle and activity etc, but mainly the short term storage' glycogen stores' saturation. So as long as the glycogen stores are saturated, the body will start lipogenesis.
150 grams of fat per day from 475 grams of glucose/carbs
or 3.17 grams of glucose/carbs to produce 1 gram of fat
*when glycogen stores are saturated
*Some biochemistry textbooks say that 1 molecule of glucose yields between 36-38 ATPs. However, the amount of energy as ATP revolves around these numbers. According to Guyton, 1 ATP has ~12,000 calories (12 kcals). Thus 38 ATPs would have 456,000 calories or 456 kcals.
*de novo synthesis, meaning "new", from glucose to fat.