You do not have to pay estimated tax if you meet all three of the following conditions:

You had no tax liability if your total tax was zero or you did not have to file an income tax return.

Your total tax on Form 1040 (PDF) is the amount listed on the line labeled "total tax" reduced by the amount of earned income credit, additional child tax credit, and credits from Form 4136 (PDF) and Form 8885 (PDF).  On Form 1040A (PDF), it is labeled "total tax" reduced by the amount of earned income credit and additional child tax credit. On Form 1040EZ (PDF), it is the amount labeled "tax" reduced by the amount of earned income credit.