Found this site that enable us to calculate the calorie burn depending on miles hiked,elevation gain,body and backpack weight.
I am not sure how precise and scientific the calculator is but entering some numbers it seems legitimate to me.
For example a 160 pounds hiker in a 20 miles round trip with 2000 feet elevation gain with a 30 pounds backpack burns 4679 calories.
http://hikingscience.blogspot.ca/p/c...burned_22.html
If this has been discussed before ,sorry.