The question should be more general than how much energy does it take to kill and elk. After all people have killed polar bears and tigers with 22lr so a 22lr should be able to kill an elk. The question you should ask is what is the recommended cartridges for elk hunting.

You don't get many opportunities at an elk so you should use a cartridge that maximizes you chances for success. You need to have penetration from what every angle you happen to see him and out to 300 yards or so. You also want something that will drop the elk relatively close to where its shot. Having it run 5 miles or more and dying in the brush is not a good thing.

The generally accepted best cartridge for elk is the 338 mag. It will do all that you need for elk. The general big game cartridges - 270, 308, 7mm mag, 3006, 300 win will do ok though it would be best if you use controlled expansion bullets for better penetration.



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