Depends... are we talking airburst arty rounds, ground burst, or nukes? I wouldn't really say there is a safe distance from nuke CEP, considering the damage fall-out would cause. But as far as artillery, my guess would be that when engineering a shell to detonate, they test how far from the detonation point a fragment is still lethal. (Then add 5-10m, I would say,...heh heh heh)

You can't calculate safe distance using CEP and here's why. Let's say we have a guided 105mm round and a guided 155mm round. Both have a CEP of 20 meters. Which one has the larger lethal radius? Does that have anything to do with CEP?

Ok, I have reread my question and it indeed does not make much sense. CEP denotes the circle where half the bombs/shells/whatever fall within and half fall outside the circle on average. What I wanted to ask is how to use this to calculate the maximum circular error - where all the shells/bombs/whatever fall within the circle. This data does not seem to be given for most weapon stats on various websites...

Well, and it depends on the circumstances. Are you in a forest ? Are you standing ? Laying in a trench ? The Artillery pieces, especially the anti-equipment grenades from a mortar will probably kill you 50 meters away if you are standing on a field without cover.

Well, those factors you mentioned would affect the safe distance, but they should not really alter the maximum circular error of fire - though, of course, that too could be effected by wind and other environmental conditions but than again the same could be said for CEP, yet CEP is still stated (I guess they must assume a certain type of weather for that). BTW: Nasty German Idiot, this is unrelated to the discussion in this thread, but I recall you managed to provide the Syrian Order of Battle on the Syria board. I don's suppose you have something similar (including the composition and equipment of mechanized and armoured divisions like you gave for Syria) for Iran and Pakistan? That would be very helpful...

As far as I know you use a normal distribution squared, there is on to the third. I can never remember which one of them is called Maxwell and which one Taylor. Basically you say that the distance from center is normally distributed both in azimuth and in range. And that combined gives a squared normal distribution. I don't know if anybody has done any serious research into whether it is normally distributed - it would certainly take a lot of shells to find out. Never mind: The normal distribution curve has a point of inflexion where approx. half the area under the curve is between +/- one sigma away from the average. It is a practical tool.

Well, if it is the normal distribution, than what is the standard deviation? CEP only gives us the mean...

To the best of my recollection: In a normal distribution about 50% is between mean +/- the standard deviation.

nope, it's about 68,3% between -1 and 1; 95,5% between -2 and 2; and 99,73% between -3 and 3

"nope, it's about 68,3% between -1 and 1; 95,5% between -2 and 2; and 99,73% between -3 and " Yes, but we do not know the value of the standard deviation in the first place, so we cannot calculate anything.