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I spoke with a trainer a while back and after telling him my current weight and desired weight he suggested that I eat 3500 calories per day. I am 6'5 and at the time I was about 200lbs and I reached my goal of 220lbs. If I want to continue to gain weight (say I want to hit 240), do I need to increate my caloric intake or will I continue to gain wait by eating 3500 calories a day?
Was the 3500 calories a day designed to help me gain weight indefinitely, or just hit 220?
Most formulas estimate your caloric needs by age, height and weight. As your height and age don't change notably, the only variable is your weight.
To give you a feeling how your calories adjust with increasing weight I plotted the revised Harris-Benedict equation. I used your height (196cm) and assumed an age of 30, as you didn't mention you age. The age does not change too much, especially not for visualization purposes.
The equation only accounts for your basal metabolic rate. To reflect your exercise, I assumed moderate exercises (3–5 days per week), which adjusts the result multiplying it by 1.55.
When you weighed 200 pounds you needed approximately 3200kcal to maintain your weight. Now, as you are 220 pounds you need 3400kcal.
Continuing to eat 3500kcal would bring you (taking longer and longer) to about 230 pounds. To reach 240 pounds you would need to eat even more.
However, the math behind this makes certain assumptions (eg your body fat) and is only an approximation. Using a scale to help adjust your dietary needs is always better than simply relying on formulas.
If you want to get to 240, go back on your 3500 calorie a day diet. If your weight keeps going up, then you know you are still eating a surplus of calories. If your weight doesn't go up, then you need to eat more.
220 lbs will require more calories to maintain, and so you may not see much (if any) gain on the same diet that got you to this point. One of your better options is going to be letting the scale tell you whether you are eating enough or not.
Use myfitnesspal. When setting up your profile, tell it that you want to increase or maintain your weight depending on where you are now at. It will give you a total calorie budget for the day as well as a protein, sugar and fat budget in order to increase or maintain your weight. You get a greater calorie budget if you do more exercise that day.
Baarn's answer above is similar, but if you use myfitnesspal it will do the difficult calcuations for you, additionally allowing for exercise, and give you a good way of tracking the calories you get from food intake.
