Paying estimated taxes avoids an underpayment penalty, so to determine whether or not you need to pay estimated taxes, you need to look at what triggers the penalty.
An IRS article on Estimated Taxes states this:
If you didn’t pay enough tax throughout the year, either through withholding or by making estimated tax payments, you may have to pay a penalty for underpayment of estimated tax. Generally, most taxpayers will avoid this penalty if they owe less than $1,000 in tax after subtracting their withholdings and credits, or if they paid at least 90% of the tax for the current year, or 100% of the tax shown on the return for the prior year, whichever is smaller.
This spells out three criteria, and meeting any of these will avoid the penalty. First, if you do your 2019 tax return next year and find that you owe less than $1000 or you owe less than 10% of your total tax with your return, you will not owe a penalty. However, if you aren't sure what your total tax will be for 2019, you can ensure that you won't owe the underpayment penalty by making sure that your tax payments before your 2019 return equal at least what your total tax was for 2018 (or at least 110% of 2018's total tax, for high income earners).
Publication 505 has more details about the estimated tax requirements, including this helpful flow chart:
If you find that you might be subject to the underpayment penalty next year unless you pay more during the year, you can avoid sending in estimated taxes if you are employed by simply requesting that your employer withhold more tax from your paycheck by filling out a new W-4 form.
