Velocity Math and Vectors

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.

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📊 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)

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🧮 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):

$$V_{\text{bps}} = |v_y| \times 20.0$$

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🔄 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)

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🔗 Related Pages

• F3 Debug Integration
• Dynamic HUD Formatting
• Ground Rest Fixes