How many calories should a 25 year old woman be eating a day if she weights 270?

The normal recommended daily intake of calories is around 2000 calories for males and 1750 for females.

If you are trying to lose weight however, I would personally recommend doing 2 hours of cardio a week (preferably in 4 -30min sessions spread across the week or in 2, 1 hour sessions if your schedule is too hectic).

I would also recommend counting the calories you take and sticking to a diet of around 1500 calories a day. If you choose better healthy food, drink water or diet drinks instead of regular soft drinks, and avoid unhealthy food, I think you will find this diet very easy to follow.

Eating healthy, losing weight, and exercise are not only good for your body but good for your mind and self-confidence as well. Even if weight loss is not a primary goal, simply exercising will also increase your Basal Metabolic Rate, hypertrophy your muscles (make them bigger), tone your body, and make your required food intake higher so that if you wished to diet then it would be a lot easier and you would be in a healthier state.