How far can I jump?
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).
Solution 1:
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.
Solution 2:
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!
Solution 3:
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.