January 1st is an obvious start to the calendar year, not the fiscal year.
In the UK the fiscal year begins in early April, and while different countries do have different starts to the fiscal year, few of them (not, for example, UK or USA) start on January 1st.
That's the US government's fiscal year. It's also one of the biggest reasons you can convince them to let them use that fiscal year (if you do a lot of government business, like a military contractor).
January 1st is the default fiscal method for all taxpayers in the US. Business entities can choose to use their fiscal year as their tax year when they incorporate/charter. Individuals can also choose a non-calendar year tax year, but only before they file their first tax return.
All US taxpayers can change their tax year by petitioning the IRS for a change of taxable year; this is usually granted without hassle for businesses (i.e, C-Corporations), but almost never for individuals.
Ours are set quarterly, usually to the prior quarter's prices, but more when the work load demands fewer hours. Usually contracts (which run for a <year) lock-in the rate for the quarter they're made.