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:
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
Second assumption, that
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
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
Falling damage is calculated as
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 believe if you sprint then you can jump 5 bocks (On a flat surface) and without sprinting, you can barely get 3
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!
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).