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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).

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If Minecraft uses the real gravity parabola then you can probably make it at most 7 blocks horizontally at a height difference that would almost kill you from falling damage. –  Sadly Not Apr 5 '11 at 15:12
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@Sadly Not - Falling damage was answered / discussed here: gaming.stackexchange.com/questions/10218/… –  Raven Dreamer Apr 5 '11 at 15:16
    
Then you can put this into a nice 'will-I-die?' equation :) –  Sadly Not Apr 5 '11 at 15:20
    
We have a resident Minecraft code-diver (can't remember their name) that will probably sweep the floor once they find this question. –  Sadly Not Apr 5 '11 at 15:57

3 Answers 3

up vote 17 down vote accepted

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.

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So if this is framed in terms of how long a gap you can jump, the horizontal distance would be gap (blocks) - player hitbox? –  Nick T Apr 5 '11 at 16:14
    
I edited the equations and variables in your answer to make them a little easier to read; hope you don't mind @Sadly Not. –  Kevin Y Apr 5 '11 at 16:44
    
@Kevin Y: Not at all, I didn't know how to do in-line code blocks. –  Sadly Not Apr 5 '11 at 16:59
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Any information on sprinting available? –  Ids Oct 1 '12 at 11:17
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@Ids With sprinting you can make a 4 block jump. –  Timtech Nov 2 '13 at 23:07

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!

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This is incorrect - for flat surfaces, sprinting = 4 and walking = 2. –  Timtech Nov 2 '13 at 23:07

I believe if you sprint then you can jump 5 bocks (On a flat surface) and without sprinting, you can barely get 3

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Welcome to the site! Normally we try to add these kinds of answers as comments to other answers. You will be able to do that if you have enough reputation. Next time try suggesting an edit not an answer. It is an easier way of getting reputation. –  Ids Oct 1 '12 at 11:16
    
@lds: You make it sound like comments should be suggested as edits instead... –  The Annoying Pyro Feb 4 '13 at 11:48
    
If you do not have enough rep to add comments, I think it should. –  Ids Feb 6 '13 at 0:43

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