How far can I jump?
Read the long explanation of my answer below, but here is a chart that summarizes how big of a gap you can jump along with how far you must fall to make the jump and the damage you will take (without mitigation). You must make a full running jump for this chart to apply:
Gap Width (Blocks) Blocks fallen below jump level Damage taken from fall
2 none none
3 2½ 1
4 7½ 3½
5 14½ 7
6 23½ 11½ (death)
So without falling damage mitigation you can make a jump over a gap that is at most 5 blocks wide, after falling about 14 blocks down from the point where you make a running jump.
I will test this in-game at a later time to make sure this is realistic.
So this answer only works given a number of assumptions hold.
First assumption, Minecraft models gravity using a parabolic equation of the form y = a(x - h)^2 + k
, where x
is the size of the gap you want to jump and y
is the height difference you will be after clearing the gap (negative indicates you are below the point you jumped). a
is a tunable parameter that describes the rate at which you will fall (related to the constant of gravity). k
is the highest you can jump from the ground in Minecraft and h
is the horizontal distance you will have cleared while jumping that high after running forward.
Second assumption, that k
(the height you can jump from the ground) is 1½ blocks and h
(the horizontal distance you will have cleared at that height) is 1 block.
Third assumption, that horizontal momentum is preserved. Basically this means that you will travel at the same speed horizontally throughout the jump.
These three assumptions give the equation y = -(x - 1)^2 + 1½
.
So let's say you want to jump a gap that is 2 blocks wide. To see how far down you must fall before making that jump, plug x = 2
into the equation and you get y = ½
. This corresponds with being able to safely jump a gap that is 2 blocks wide with a running jump, and you will reach a block on the other side of the gap while being a little higher than ground level.
Falling damage is calculated as (number of blocks fallen x ½) - 1½
. So, let's say you want to jump a gap that is 5 blocks wide. Plug x = 5
into the equation and you get y = -14½
. This means you will reach jump a gap that is 5 blocks wide after falling 14½ blocks and taking about 7 hearts of damage.
Sprinting Added
You can jump significantly further with sprinting; at least three blocks horizontally. This answer assumes no sprinting but I will try to update it ASAP.