Fairly frequently, I see a gap in Minecraft that I think I can make, so I go for it...and lose a couple hearts because I didn't. How far can you jump horizontally (or horizontally + 1-3 blocks down), so I know if I'm bad or just ill-equipped (in game).
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.
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.
I have done an experiment and these are my results:
Without sprinting, the farthest you can get is 3 blocks if the entire surface is flat. Or if you are jumping up, the max is 2 blocks in length, 1 block in height.
If you are sprinting, the farthest you can reach on a flat platform is 5 blocks in length, but if you are jumping up 1 block in height, the max length is 4 blocks.
Hope you enjoy this!
This hasn't been posted on in awhile, but here is my answer, coming from a person who pretty much only plays Minecraft Parkour:
3 block is not possible without sprinting, however 2 and up 1 is possible with no sprinting.
As for with sprinting, a 3 block onto a trapdoor 2 blocks higher (A 3 up 1.18750) is possible. And a 4 block with 8 layers of snow (4 up 0.8750) is said to be possible, however I can only do 7 (4 up 0.750). If you have HH (Headhitter, or 2 block ceiling) and 2 blocks of momentum, you can make a 5 block or 4 up 1.
Lastly, with speed II, it is possible to do a 5 block and a 4 up 1 if you have momentum.
And just one more thing, you jump 1.20 blocks high without jump boost.
Something odd I have found is that you can jump a 3 block diagonal which should be equal to about 4.2 blocks. These seems to bring up the only viable reason being that the game registers the diagonal in Minecraft with a different formula then that of a non diagonal jump, or that the 4 blocks jumping forward is incorrect. I have not yet tested this with partially eaten sides of a cake however which is the easiest way to test the inbetween .5 jumps, or using cords. Lastly I would like to ask if this is a mechanic in the game intentionally designed where it will sort of give you the extra .2 blocks (app).
You can make a flat 5 block jump.
I have made a 4x3 jump before in game with no ice/slime/HH/potions/vertical momentum ie a flat 4x3 jump. 4x3 means I am jumping diagonally from the corner of one block to the corner of another block which are 4 blocks of air apart in one direction and 3 blocks of air apart in the other. The gap between these corners is exactly 5 blocks.
I believe the explanation is that since the player has a 0.6x0.6 hit box, you can jump off a block with some of your hit box hanging over the edge of the take-off block and land with only part of your hit box on the landing block. So, the actual distance the player moves is less than 5 blocks.
Despite this, since the distance between the corners of a 4x3 jump is exactly the same as the distance between the edges of a straight 5 block gap, in my opinion, this counts as a 5 block jump.
As a side note, I have not seen anyone make a flat, straight 5 block jump. I don't know why this is. If I had to guess I would say it is because you can overhang your hit box more on the corner of a block than the edge.