Note that Amtrak has substantially higher fatalities than elsewhere. European trains have 0.85 fatalities per billion KM (source). If my math is right, that's 1.37 per million freedom units.

So yes, still worse than airplanes, but Amtrak sucks. That's what happens when suffering from years of neglect and sharing rail with coal haulers.

I knew flying was the safest form but seeing it in actual numbers in mind-boggling. 0.27 fatal accidents per MILLION flights. Damn.

Whilst you are right, even fatal train accidents generally lead to far fewer casualties than fatal plane crashes, because a 'fatal plane crash' quite often means everybody in the plane dies, whereas a 'fatal train crash' may merely be 1-2 wagons being crashed, multiple deaths occuring, but still having a majority of the passengers surviving the crash.

Besides that, your amount of Amtrak accidents per 1m train miles also includes non-fatal accidents, and even accidents without any injuries.

Besides that, planes are a lot faster, so whilst the fatality rate per 'unit of distance of your choice' are far lower for planes (0.05 (plane) VS 0.6 deaths per 1 billion kilometers, thus making trains seem 12x more deadly), your odds of dying per 'amount of time spent traveling' are almost equal, but slightly higher for planes (30.8 (plane) VS 30 (train) deaths per 1 billiion hours spent traveling by mode of transport)

So yeah, it depends on your perspective, but looking at time spent air travel would be more dangerous than travelling by train - counteracted by the fact that people generally spend way more time in their lives commuting by train, rather than by plane

Source

People riding normal trains is lower, though.

If you go by deaths per passenger miles, I imagine cruise ships are crushing it too. 3000-5000 people per ship, and there are ~100 or so ships that size (conservatively, could be slightly higher), travelling say, 1500 nautical miles per week (again that's very conservative), 52 weeks a year. Puts you in the neighbourhood of 27-30 billion passenger miles per year (much more if you include the crew of said ships), with astonishingly few deaths. (We're talking deaths due to the fact that they travelled by ship, as opposed to people who roll up and have a heart attack or choke or something.) Big cruise ships don't sink, as a rule.*

*unless you're showing off and run one up on the rocks in Italy for example. And technically still didn't "sink."

There are three kind of accident statistics: per mile, per trip and per hours travelled. All meaningful in the right context. Airlines like to emphasize per mile statistics because it favours them. Comparing forms of travel using the other two methods shows different results.