What's the actual safe distance to keep from wildlife at national parks like Yellowstone?

With another bison scare trending, what are the real rules for how close you can get to wild animals at places like Yellowstone?

At Yellowstone specifically, the National Park Service requires staying at least 25 yards (about 23 meters) away from large animals — bison, elk, deer, bighorn sheep, moose, and coyotes — and at least 100 yards (about 91 meters) away from bears and wolves. These aren't arbitrary numbers: bison alone have injured more visitors than any other animal in the park's history, precisely because they look docile grazing near a trail but can move explosively fast (up to 35 mph) and will charge with little warning if they feel crowded. The general safety principle that applies everywhere, not just Yellowstone: if an animal changes its behavior because of your presence — stops eating, lifts its head, turns to face you, or moves toward you — you're already too close, and the right move is to calmly back away the way you came, not to continue past it or make a wide loop closer to get around it. Never approach wildlife for a photo, and keep in mind that boardwalks and trails don't guarantee safe distance on their own if an animal is grazing right next to them, as several recent incidents have shown.