Calculus means that It can’t be resolved as a matter of arithmetic .

This entire book is written in a style which is very figurative, very complex, and very beautiful. Kevin Powers uses the English language in a very unique way and that makes it both very beautiful but also difficult even for native speakers to understand. I like Brian's explanation: I think that Powers is contrasting grief and forgiveness. Grief is represented by the empty seats on the plane. It is very obvious who is missing, there is a visual pattern to the grief. But there is no pattern to forgiveness, no mathematical "calculus" that can represent it.

This is a very complex sentence. I would like to add that as a whole, the paragraph has a strong implication that forgiveness can't be "patterned," that it does not have an underlying logic, and can only be determined on a case by case basis. In other words, forgiveness can't be patterned like that way the dead can be counted. Here, the long sentence about the dead casts a strong sense that the author is bemoaning how the soldiers are treated as disposable goods. Still, this passage is VERY HARD to understand, and others may disagree with my interpretation. This is because the author is trying harder to be poetic than to be precise.

Calculus = a count of something. Here, it means the number of soldiers who died in the war, which interpretation seems to be corroborated by the "empty seats between (the boys on a chartered plane)."

Sorry, but no. Calculus here does not mean mathematics. That is a different meaning. I agree entirely the passage is a little difficult. . Calculus also has a meaning of a solidified mass, a solid essence of something. I do not use this word this way, myself, so I am not an expert.