Is it better to try to calculate penalties on late payment? or better for the IRS to bill you for them?

If for example someone pays 1k of their 2k taxes by April 15th, but files an extension and pays the rest of their taxes due by October 15th when they file.

 

Is it better to try to calculate the penalties or let the IRS bill you for the penalties; also will this be a big increased audit risk to pay late and let the IRS bill you, or is this a pretty common thing where people pay late or owe penalties and things and get automatically billed?

 

Thanks!