You won't end up being double taxed. The money in your Traditional IRA can be grouped into three categories:
- Deductible contributions
- Non-deductible contributions
If you convert the entire balance of your Traditional IRA to Roth, you'll pay regular income tax on the value of #1 and #3, but not #2. Unfortunately you can't choose to only convert #2 to Roth; there is something called the pro rata rule that says whenever you do a conversion, it must come proportionally from the pre-tax and after-tax components. See Form 8606 for more details.
A few side notes:
- Are part of your non-deductible contributions from 2017 and/or 2018? If so, and your income is below the limits, you can do what's called a recharacterization to Roth. You would contact your brokerage to do this, and it'd be like you contributed to a Roth in the first place (a proportional amount of the account's earnings would be moved along with the contribution). This would be advantageous because a Roth IRA is almost always superior to non-deductible Traditional IRA.
- Are you sure you want to do a Roth conversion? As mentioned above, you'll pay regular income tax on all but the after-tax amounts. That's basically undoing the benefit of the pre-tax deduction you received. If it's a substantial amount of money, you could push part of it into a higher income tax bracket. If you really want to convert, you might consider if it makes sense to stretch it over several years to lessen the tax impact.