# Longest Jumps

Momentum is assumed to use flat ground, 45° strafe, and an optimal half angle.

Formula to convert a jump's distance (from block form to meters):

${\displaystyle Dist(d_x,d_z) = \sqrt{max(0,d_x-0.6)^2 + max(0,d_z-0.6)^2}}$

Reminder: 1 pixel = 1/16th of a block = 0.0625b.

Example: a configuration of (X:64 Z:32) can be mapped to a 4x2 gap.

• List of all pixel configurations, ordered by distance up to 16b.
• Python code used to find the top longest configurations for a given distance.
• Python program to find constructible setups for a given configuration.
• Fortunately, all configurations can be built in 1.8 (but not in every direction)

Configurations listed below are given in terms of pixels, along with their margin (between their distance and the max jump distance for that tier).

Quite often, the true margin is bit smaller because half angles are less efficient for diagonal jumps.

## Longest Jump per Tier with Flat Momentum

Tier Height Range Max Distance Longest Jump (px) Margin Verification
5 +1.171 to +1.249 2.6861854m 51 x 21 0.002380
4 +1.016 to +1.170 3.0210507m 57 x 19 0.000858
3 +0.786 to +1.015 3.3517794m 62 x 21 0.000171 3.875 x 1.3125 + 1
2 +0.481 to +0.785 3.6787438m 60 x 40 0.000089 3.75 x 2.5 + 0.75
1 +0.105 to +0.480 4.0022827m 60 x 49 0.003982
0 −0.343 to +0.104 4.3227043m 65 x 51 0.000198 4.0625 x 3.1875
-1 −0.860 to −0.344 4.6402892m 82 x 26 0.000650
-2 −1.445 to −0.861 4.9552927m 81 x 44 0.001869
-3 −2.097 to −1.446 5.2679471m 83 x 51 0.001040
-4 −2.814 to −2.098 5.5784640m 87 x54 0.001544
-5 −3.595 to −2.815 5.8870355m 100 x 36 0.001035
...
-104 at most -255.190 34.6872685m 550 x 136 0.000663 34.375 x 8.5 - 255.25

Notes:

• Tier -104 is debatable, because there are 4 longer jumps that are technically within the margin, but couldn't be performed because they are too diagonal (therefore half angles aren't as effective)
• A lot more jumps can be built if we consider walled jumps, some of which would be longer than the ones listed.