Velocity Math & Vectors
This page details the mathematical formulas, vector mechanics, and tick-to-second conversions used by Speedometer to compute player and entity movement speed.
📊 Mathematical Mechanics Infobox
| Property | Formula / Value |
|---|---|
| Vanilla Tick Rate | $20.0\text{ ticks} = 1.0\text{ second}$ |
| Native Speed Source | entity.getKnownSpeed() ($\text{Vec3}$) |
| Total 3D Speed ($S$) | $S = \sqrt{v_x^2 + v_y^2 + v_z^2} \times 20.0$ |
| Horizontal Speed ($H$) | $H = \sqrt{v_x^2 + v_z^2} \times 20.0$ |
| Vertical Speed ($V$) | $V = |
| Unit of Measurement | Blocks per Second ($\text{b/s}$) |
| Display Precision | Floating point formatted to 2 decimals (%.2f) |
🧮 Mathematical Formulas
Minecraft calculates entity movement internally per tick. Let $\vec{v} = (v_x, v_y, v_z)$ represent the velocity vector returned by entity.getKnownSpeed() in units of $\text{blocks/tick}$.
1. Total 3D Velocity Conversion
To convert total 3D velocity from $\text{blocks/tick}$ to $\text{blocks/second}$ ($\text{b/s}$):
$$S_{\text{bps}} = |\vec{v}| \times 20.0 = \sqrt{v_x^2 + v_y^2 + v_z^2} \times 20.0$$
2. Horizontal Velocity ($H$)
Ground speed across the Cartesian $X$ and $Z$ axes (ignoring elevation changes):
$$H_{\text{bps}} = \sqrt{v_x^2 + v_z^2} \times 20.0$$
3. Vertical Velocity ($V$)
Vertical speed along the $Y$ axis (climbing, falling, flying, or jumping):
$$V_{\text{bps}} = |v_y| \times 20.0$$
🔄 Tick-to-Second Conversion Matrix
Below are sample velocity values comparing raw vanilla $\text{blocks/tick}$ with Speedometer's $\text{blocks/second}$ output:
| Movement Action | Raw Velocity ($\text{blocks/tick}$) | Horizontal ($H$) | Vertical ($V$) | Speedometer Output ($\text{b/s}$) |
|---|---|---|---|---|
| Walking | $0.215\text{ b/t}$ | $4.30\text{ b/s}$ | $0.00\text{ b/s}$ | Speed: 4.30 b/s (H: 4.30, V: 0.00) |
| Sprinting | $0.280\text{ b/t}$ | $5.60\text{ b/s}$ | $0.00\text{ b/s}$ | Speed: 5.60 b/s (H: 5.60, V: 0.00) |
| Sprinting + Jumping | $0.340\text{ b/t}$ | $6.20\text{ b/s}$ | $2.42\text{ b/s}$ | Speed: 6.66 b/s (H: 6.20, V: 2.42) |
| Boat (Blue Ice) | $3.500\text{ b/t}$ | $70.00\text{ b/s}$ | $0.00\text{ b/s}$ | Speed: 70.00 b/s (H: 70.00, V: 0.00) |
| Elytra Terminal Dive | $2.500\text{ b/t}$ | $30.00\text{ b/s}$ | $40.00\text{ b/s}$ | Speed: 50.00 b/s (H: 30.00, V: 40.00) |