> Protip: you can file an extension until October with no penalty.
Caveat: This is true ONLY if you are due a refund. If you owe tax you will be charged interest (and possibly penalties) for paying after the deadline[1].
Technically speaking, I believe you can still file in October, as long as you pay in April. So you can estimate (guesstimate) and pay, then calculate properly and file later, if that's advantageous somehow. If you pad your estimated payment so that you overpay, you should be safe from penalties, in the event that you can decently estimate up front but can't actually file a full return for some reason.
Caveat: This is true ONLY if you are due a refund. If you owe tax you will be charged interest (and possibly penalties) for paying after the deadline[1].
http://www.irs.gov/uac/Extensions-and-Payment-Options