My understanding is if a person is trying to do a back door contribution by contributing to a non-dedctible IRA then converting to a Roth, they have factor in all their IRAs when figuring out the taxable part, is that correct? In other words, say a person has $5500 in a traditional IRA from a previous year contribution but in the current year they make a $5500 non-deductible contribution to a TIRA and then convert it to a Roth, it would not be a “tax free” conversion because they would have to factor in the $5500 from the previous year. So it would be $2750 tax free conversion and $2750 taxed as ordinary income. Do I have that right?

And is this discussed anywhere in Pub 590?

Thank you.