In the Tell-Tale Heart, the narrator claims he isn't insane. There are things he uses to back his argument, but some of them aren't very convincing. I think the narrator is insane.
First, he doesn't like the eye this old man has. His solution: Kill the old man. Why is that not crazy? Second, it took him a whole hour to put his head through the door. "Ha! would a madman have been so wise as this." Once he killed the man, he chopped him up and hid him under the floorboards. Then, he started hearing sounds and when it was too much to bear he called the officers villains and told them to rip up the floorboards. "Villains!" I shrieked, "dissemble no more! I admit the deed! --tear up the planks! here, here! --It is the beating of his hideous heart!"
I don't think he was very calm. Especially near the end. He is definitely insane.