Nuts are extremely healthy, as they're packed full of nutrients and antioxidants. In fact, they have been linked to a wide range of health benefits, including protection against heart disease and diabetes. However, they're also high in fat and calories, causing many people to avoid nuts out of fear that they are fattening. Nuts are high in calories. This is because a large part of them is fat, which is a concentrated source of energy. One gram of fat contains 9 calories, while one gram of carbs or protein contains just 4 calories.