There is no carrot in it. Chai tow means white radish, and the cake is radish and rice flour steamed into a block, which is about 130 calories per 100g before frying. 200g of that is 260 calories. Then it goes onto a griddle with a big ladle of oil, one and a half eggs, chye poh and garlic. The eggs add 110, the oil about 90, and the seasonings 35. That is the 493 figure from KKH, with 35g of fat, which is more fat than a plate of char kway teow.
Black versus white is a 180 calorie decision. White is fried in oil and egg, about 403. Black is the same plate with sweet dark soy sauce poured on and caramelised, about 585. The sweet soy is sugar syrup, and the stall pours a lot of it to get the colour. If you like black, ask for less sauce and you land somewhere near 500.
The crispy style, where the stall presses the cake flat and fries it until the edges are brown, takes on more oil than the soft style. Crispy white can reach the black number. The soft, wetter style with more egg and less time on the griddle is usually the lighter plate, even though it looks messier.