If you perform the conversion any time in calendar year 2017, the taxes will be calculated and paid on your 2017 tax return which is due April 15, 2018. To avoid a penalty for underpaying your taxes during the year, the amount you pay into the system (combination of withholding and estimated payments) should be at least equal to 110% of your tax liability (line 63) from this year. Your withholding may already cover it, or you may need to make an additional estimated payment. If you need to make an estimated payment to bring your yearly payments up to the needed amount, the deadline would be September 15 for a conversion that happens between now and August 30. You can make a payment at www.irs.gov/payments, make sure to select "2017 form 1040-ES" as the reason.
