I've been self-employed for just over 15 years now. What I've always done (and continue to do) is to send the IRS 20% of my gross business income each quarter. Then come tax filing time when I deal with all the deductible business expenses, I've always been well within $1000 of my tax liability. I typically get a refund. But in the 2-3 years I've actually owed the IRS, it's always been less than $500 - so no underpayment penalty. Also, with such a low amount owed I don't have to deal with "payment plans". I just write the check and press on with business.
While the IRS does provide "worksheets" that you can use to figure your quarterly tax, in my own experience it always comes to 19-23% of the gross business income. So that's why I just automatically pay 20% of the gross each quarter and don't waste time fretting over the math.
