how many calories do we need to gain weight a day?

easy:

monitor daily calories with precision. easiest way to do this is eat exactly the same thing everyday in measured portions.

measure weight daily with precision. easiest way to do this is to weigh-in everyday at exactly the same time, right after waking is best, and keep a running average, say seven days, to account for daily variations.

if weight is steady or dropping, slightly increase calories by an arbitrary amount, say 5%.

if weight is increasing too quickly, slightly decrease calories by an arbitrary amount, say 2.5%.

the number of accurately measured calories that results in your appropriate weight gain per time period, is what you need to gain the weight you want to gain!

long story short: it is highly individual and requires individual record keeping and some tweaking to figure out...

Generally speaking, an extra 500 cals per day over (or under) your maintenance level will result in an estimated 1# wt gain (or loss) per wk.

However, of course, indivdual results will differ.

Gaining weight in general just means being in a surplus and there isn’t an optimal amount per se.

Gaining muscle however is a different ball game and isn’t really about surplus calories. Muscle gain is more to do with stimulating muscle protein synthesis and the key components to that are hitting the leucine threshold every 2 or 3 hours with your protein feeds.

In terms of calories, you want to be eating whatever a) allows you your protein/leucine requirements and b) enough food to fuel your workouts to get the maximum out of them.