If you are following Atkins your total calorie goal is 1500-1800 for women for induction or phase 1, so it depends on what you are considering your calorie goal.
That being said I lost for the first month counting carbs, then stalled out and started to lose energy on net 20g of carbs trying to stay with a net 1200 calories.
Now I'm tweeking by adding more calories and a few more healthy carbs.
Also even on Atkins you will lose only 1-2 pounds a week after the initial water loss if you don't have alot of weight to lose in the first place.

I have another question with the calories issue on Induction. I know the 1500-1800 calorie goal, but was just wondering how you decide when to increase or decrease. I am closer to my goal weight - 13 lbs to be exact, so I know it's harder at this point after losing weight. I also work out at least an hour a day - between walking, running intervals, cycling, lifting weights, and videos - it's my therapy. So, just asking someone else's opinion other than the calculator. Thanks!

I'm keto, not just low carb. If you're hungry, I'd eat more calories from fat. Cook in bacon grease or coconut oil. Add heavy cream to tea or coffee, Pick fattier cuts of meat, leave skin on chicken..

Two years ago I stuck to 1400 calories, ran three times a week, was sadly often starving and didn't lose anything - inches or in weight. I was starving even on days I didn't run.

I'm at 1400 as a goal now, but 20 carbs a day. At 65% fat calories I'm sated for once. Many ketoers I know start not counting calories. Eat till full. Eventually they need to cut the number down or watch it at least when closer to their goal. I was about 40 pounds from mine, so I've watched my calorie count, but if hungry, I eat more. Hasn't hurt my progress. 29 pounds down January 6th till yesterday, 11ish to go.

Cutting carbs must also lead to lowering of calorie intake if weight loss is to occur. For some people, they can go from obese to lean simply by cutting carbs and not paying attention to calories. For many (most), there is a point where we plateau and need to start restricting calories as well in order to keep losing.

I plateaued about 5 lbs above goal weight eating ad libitum calories with only carb restriction. However I'm also 15% body fat, so it wasn't too shabby to get where I got without counting calories. I do think maintenance is much easier than actually creating a caloric deficit when only restricting carbs. So cut calories to lose and once you hit goal weight, see if you can maintain by only restricting carbs.