# Calculating the distance when shooting at a flying foe [duplicate]

Lets say that a foe is 30' away and 20' up in the air.

Using trigonometry, that gives a distance of 30^2 + 20^2 = 1300 sqrt(1300) = 36.06 ...but I don't believe Pathfinder expects folks to use trig to figure out range increments.

Is there a rule that covers this? I can't find it but my impression was that one actually just takes the larger of the two values (so if someone is 100' away and on one dimension and 50' away on another, it's still just a range of 100').

• I'd never heard the "take the highest" rule before; that's pretty good! At worst it underestimates the distance by 30%, but that seems a small loss compared to how much time it takes to calculate in practice. Jan 21, 2015 at 17:57
• "Take the highest" is the rule in D&D 4e. It's very simple to use, but it does some really weird things, too. (For one, you now shoot Firecubes instead of Fireballs, because "anything within 30ft" is a cubic area)
– Erik
Jan 21, 2015 at 19:47
• Funny thing with the math is that is works for spells, but it kind of fails for moving objects that travel in an arc. My longbow may have a 1000ft range but it can't reach things 1000ft in the air. So beyond just the Pythagorean theorem, you need to calculate arcs :) Jan 22, 2015 at 2:33

I can't find the exact rule on the Pathfinder SRD, but there's a link to a topic here that describes it: http://paizo.com/threads/rzs2n3i9?Question-about-diagonal-movement

And this is the rule in the D20SRD, which I'm pretty confident is the same: http://www.d20srd.org/srd/combat/movementPositionAndDistance.htm

You might find the exact rule in your rulebook somewhere (but I don't have one to check, unfortunately)

It essentially comes down to this:

## Diagonal movement

Every other square of diagonal movement is counted double. So the first square is 5ft, the second is 10ft, the third is 5ft, etc. This approaches the actual diagonal reasonably over short distances.

So in your example, the distance would be 10ft going straight (30ft-20ft) and then 20ft going in a pure diagonal (the lowest of the two) with every other square counting double; ie the distance multiplied by 1.5x, which gives 30ft of diagonal movement for a total of 40ft travelled.

The rule you remember of "take the highest" is from 4th Edition D&D.

(As you can see the final result comes within 5ft of the trig answer, so it's accurate enough for game purposes)

• According to the rules for fly this approximation is not used for (partial) vertical movement - your speed is simply halved while ascending and unchanged while descending (moving downards is 'free' when going diagonally). I think those rules make a better approximation for any missile that obeys the laws of physics, although things like Fireballs (and area calculations) might still be better served with straight up Pythagoras or an approximation like this one. Aug 5, 2016 at 17:11