If you feel you will owe any estimated tax payments, it's better to pay them sooner rather than later. Remember that the estimated taxes on your independent contractor work is based on the "net" income that is your total income minus your expenses so it might not be as much as you anticipate. Also, if you had enough taxes withheld from your salaried position to compensate for the net profit from your contract work, you might be okay.
The self-employment tax rate of 15.3% plus your ordinary income tax rate (which depends on you taxable income and filing status). The following article has easy to read tables for this amount
http://taxfoundation.org/article/2017-tax-brackets
