There is no fast hard "requirement" to pay quarterly taxes. But it's a good idea to do so. Otherwise, at tax filing time if your tax liability exceeds certain limits then in addition to paying the tax due at tax filing time, you will also be assessed an underpayment penalty for not having paid enough quarterly taxes during the tax year.
Generally, I send the IRS a flat 20% of my gross business income each quarter. Then, come tax filing time I'll always be well within the limits and no underpayment penalties are assessed.
Generally, I end up getting some of my quarterly payments refunded. But in the two years I owed the IRS, it was less than $1000 and therefore no underpayment penalty was assessed.
