Quarterly taxes for 2018 begin with the first payment on 4/17/18. If you are required to file them, an extension to file your 2017 return does not extend the time to pay the taxes due on your return, nor the estimated tax payment. There is no extension for the quarterly taxes.
You can compute the amount using the IRS vouchers in this link 2018 1040-ES
The penalty for underpaying 2017 taxes will be computed when you file your return. You can see how the penalty is calculated here Underpayment penalty
