Roth Conversion

So, generally taxes are not due until the tax deadline of the following year, though your question indicates that you have estimated tax liability.   

So let's start here Who must pay estimated tax : 

Individuals, including sole proprietors, partners, and S corporation shareholders, generally have to make estimated tax payments if they expect to owe tax of $1,000 or more when their return is filed.

Your question really is important if you are annualizing your income for purposes of the estimated tax penalty.   If you need to do this you want to make the estimated tax payment in the quarter that you did the conversion to minimize the estimated tax penalty.  If you spit it across two quarters or more your penalty will be higher.

I would also suggest potentially adjusting your Form W-4 for your new employer to account for some or all of the taxes for the remainder of the year, which could lessen or eliminate the need for estimated tax payments.

Thank you so much for your question  @Garychen 

Be well and safe!

Marc T.

Turbo Tax Expert

27 Years of Experience Helping Clients