# Movement Formulas

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.