You've found yourself in a dangerous situation. You're being cornered and threatened by somebody with a crowbar. You're armed, but he's 30 feet away. Where do you reasonably draw the line?
The totality of the circumstances will determine the exact distance in various cases, but there is a general rule of thumb that serves as a helpful baseline, known as the "21-foot rule." This 'rule' states that (generally) when an armed threat is 21 feet away or closer, they'll be able to make lethal contact with you before you could access, aim, and use your firearm to stop the threat reliably.
This concept was identified, explored, tested, and published by Dennis Tueller, a Salt Lake City Police Officer in the 1980's.
First, let's look at how long it would take you to draw your firearm, aim, and pull the trigger to stop the threat. From the holster to firing at the target, the average time was found to be about 1.5 seconds. You may quicker, or you may slower, just keep in mind that if you're slower (or don't carry with a round in the chamber), you'll need even more time/distance to reliably protect yourself.
Tueller then tested to see how much distance 'bad guy' actors could cover in these 1.5 seconds. You may think in just 1.5 seconds, someone could only lunge forward a few steps, but you'd be wrong. More than half the time, actors were able to cover 21 feet (7 Yards!) and 'slash' or 'stab' the officer before they could draw and fire to protect themselves.
This is assuming the armed threat has made itself known over 21 feet away, or you're very alert to your environment and sense it. If that's not the case, say you're commonly absorbed into your phone, then your reaction time will take much longer than 1.5 seconds.
The distance within which you cannot reliably react in time to protect yourself, is also known as your 'reactionary gap.' This should be your "personal bubble". When it comes to armed (knife/crowbar/etc) threats as discussed above, that's about 21 feet. When it comes to unarmed threats, your reactionary gap is about arm's length in distance. Punches for example, launched at you from 2 feet away are very likely to hit you, no matter how quick you think you are. In contrast, punches launched at you from 4 or 5 feet away, are very unlikely to land, since you have plenty of reaction time/distance. When people are in your Danger Zone, their Actions will always be faster than your Reactions.
It's fun to test this as well, partner with a friend and see if they can block your pokes within arm's reach, or outside of arm's reach.
Whenever around others in public, especially in dangerous situations, always mind your surroundings, as well as this 'personal bubble' of yours. Keep strangers out of your danger zone and thank me later.