a. 90% Rule
If you pay taxes on at least 90% of the year's income through estimated tax payments and withholdings, the IRS will spare you with any interest charges.
b. Safe-harbor Rule
Here is a better news - if you pay a certain percentage of your prior year's tax bill over 4 quarters, then no matter what your final tax bill will be for the year, the IRS will accept those estimated tax payments and will not be punitive.
The percentage varies based on your income - if you earn more than $150,000, you need to pay 110% of prior year's tax; if you earn less than $150,000, then you just need to pay at least 100% of prior year's tax bill and you will be fine.
What if your income declines big this year? For example, you sold a rental property last year and had a big gain, but it won't happen again this year? You could still pay 110% of last year's tax bill (if you earn more than $150,000) and get a refund, although this means you are extending a free loan to Uncle Sam!
c. Increase Withholding
There is another way - if you have salaried income and a few quarters later realize you have been underpaying your estimated taxes, you can ask your employer to increase your withholding from your salary for the rest of the year to back-pay the underpaid taxes in previous quarters, this is an accepted practice by IRS, but the risk is you might attract IRS attention for chronic underpayment and an audit.
In Summary
Paying estimated taxes each quarter accurately is a daunting task, but it's doable through a few simple actions. Please consult your tax advisor for specific questions.