If you are looking for the absolute humidity (mass of water per volume of air), this excerpt from my undergrad tesis will help you

Once you know the absolute humidity, you can adapt the same formula to calculate the relative humidity of a parcel of outside air (of now known content of water), that is taken inside a building where its temperature risen to a new value. But it in unclear if that's what you want.

You can easily achieve that assuming that there is no sources of water vapour inside, so the absolute humidity (mass of water per volume of air), remains constant. This excerpt from my undergrad tesis will explain the formula for absolute humidity

Once you know the absolute humidity, you can adapt the same formula to calculate the relative humidity of a parcel of outside air (of now known content of water), that is taken from outside to inside a building where its temperature risen to a new value. If we add subscripts "e" to exterior temperature and relative humidity and "i" for interior ones. Most of the constants can be dropped and the interior relative humidity would be given by

If you are looking for the absolute humidity (mass of water per volume of air), this excerpt from my undergrad tesis will help you

Once you know the absolute humidity, you can adapt the same formula to calculate the relative humidity of a parcel of outside air (of now know content of water), that is taken inside a building where its temperature risen to a new value. But it in unclear if that's what you want.

If you are looking for the absolute humidity (mass of water per volume of air), this excerpt from my undergrad tesis will help you

Once you know the absolute humidity, you can adapt the same formula to calculate the relative humidity of a parcel of outside air (of now known content of water), that is taken inside a building where its temperature risen to a new value. But it in unclear if that's what you want.