Movement Formulas

Movement formulas applied to a 3b jump.

The player's movement can be accurately calculated with sequences.

The following formulas come from analyzing the game's source code.

Note that these formulas are not exact, due to how floats are computed.
When used for calculations, only the first 4-6 decimals should be considered accurate.
For a completely accurate simulation, you would need to replicate the source code.

• Vertical Movement (recursive formulas)
• Horizontal Movement (recursive formulas)
• Non-recursive formulas

Note:
Minecraft's coordinate system is oriented differently: 0° points towards "positive Z", and 90° points towards "negative X".
We choose to work in the standard coordinate system to make calculations more intuitive.