There is no simple algorithm to calculate calory needs. It depends on many conditions, such as the intensity of the trek, the temperature and humidity, your metabolism, what you are wearing etc.
My typical calory usage (70kg weight) in mountains measured in Crna Gora in August, route between 20 and 30 GOTs (1 GOT is 1 km distance or 100 m elevation) was between 4500 and 6000 kcal. A woman, 50kg, has in the same time calory usage between 3000 and 3500 kcal.
My collegue is writing a doctor thesis based on such measurements, and I will encourage her to publish the results. But the amounts above are, according to her, typical.