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The most common method of calculating calories is by burning it until the substance reaches 1C(1.8F) for every 1 gram of food. To calculate fiber and carbs and such, you simply see how much carbon, hydrogen, and oxygen atoms the substance has for 1g of the substance. Fiber is similar to carbs, since it's a type of carb that is not digested by the body (lack of enzymes that cannot metabolize the fiber), instead soluble fiber attaches to water particles and other small particles, and insoluble fiber attaches to bigger particles like proteins and fatty acids and such.
Calories are not essential. Food burnt by heat acts differently than when it is digested by your body. One Calorie of 'raw veggies' reacts different in your body than one calorie of starch.