Carbs don't really work like calories.
With calories, you work out your basal metabolic weight, eat less than you burn, and (in theory) you lose weight.
With carbs, you find out how much carby food your body can tolerate (it varies a lot from person to person). It can be anywhere from 20g a day, or less to 100s of grams. Others can tolerate more. But the thing we have in common is that we lose weight best when we eat less than our personal carb threshold.
Atkins came up with a good way of finding it. He said drop to less than 20g carbs a day for 2 weeks. If you lose weight, great. Then go up to 25g for a week. Still losing? Go to 30 g. And so on. The point you stop losing, is your personal carb tolerance.
You can do the same with blood glucose. So that is a quicker way to spot your carb tolerances. If your bg stays at normal levels you are below your personal carb tolerance. Drugs may help with this.
The weight loss comes as a complex interaction of hormones, calories, and protein/fat intake. When we drop carbs, we have to eat something - basically fat and protein. And since they are more satisfying and filling than carbs, if we eat lots of non-carby veg, and protein and fat, we often end up eating less and being less hungry than when we filled up with carbs. Which leads to weight loss.
Hope that helps.