A calorimeter is used.
Take some base ingredient, like fat, and place it in a sealed chamber. Submerge it in water, and then burn the ingredient. We can than measure the temperature of the water and how much it changed while the ingredient was burning, and then using some math know how much energy was in that ingredient.
Do this to a variety of ingredients, and now we can determine for any given food the number of calories. Carbs and proteins provide 4 calories per gram, fat 9.
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