My recommendation is to pay only the tax, and let the IRS bill you for the penalties and interest. There are two reasons for this,
1. Your estimate will always be off by some amount, meaning you will be waiting for a refund or owing a small additional amount. If you wait for the bill and pay what they say by the deadline they say, that will be the end of it.
2. When you get the bill, you can apply for a penalty abatement (reduction), either because this is the first time you owed a penalty, or because you had some good cause to be late. If the penalty is reduced, the interest on the taxes will also be recalculated. It's harder to ask for penalty relief if you already paid it.
https://www.irs.gov/payments/administrative-penalty-relief
