Movement speed

Movement speed is one of the player's stats and affects how quickly they can travel around. Many features can affect movement speed, such as Movement Accessories, Wings, Mounts, Minecarts and Liquids, along with certain Buffs, Debuffs, Armor and other hazards such as Ice Blocks and Cobwebs. Movement speed can be broken down into horizontal movement, which is the most affected component by most sources, and vertical movement, which is mostly affected by Wings and Movement Accessories.
== Horizontal movement ==
All characters start with a horizontal movement speed of , or (shown by the Stopwatch). While moving, the character will automatically climb any one-block high ledge or hill, and horizontal movement speed is not impeded by doing so (climbing over a pyramid is just as fast as tunneling through it). These values are ignoring the small amount of time it takes to accelerate from a standing position. 
 Horizontal movement speed is capped at 1.6 × base speed, or +60%.
* Hooks reel in the player at a constant speed regardless of speed boosting accessories. The more movement speed boosts a player has, the less noticeable the speed boost a hook provided is.
* Sprinting accessories increase the player's max speed to a fixed value. Using other movement boosts with any of the accessories only increases one's acceleration.
Object 	Effect(% increase) 	Velocity(miles/hour) 	Velocity(tiles/sec) 	Velocity(pixels/tick)
Base 	Base 	Base 	Base 	Base
Nothing from below 	0% 	15 	11.36 	3
Armor 	Armor 	Armor 	Armor 	Armor
: Full set 	×1.15 	×1.15 	×1.15 	×1.15
: Full set while in stealth 	×0.3 	×0.3 	×0.3 	×0.3
Accessories 	Accessories 	Accessories 	Accessories 	Accessories
 	×1.15 	×1.15 	×1.15 	×1.15
(on Ice) 	×1.25 	×1.25 	×1.25 	×1.25
(in use) 	×1.5 	×1.5 	×1.5 	×1.5
(on Sand) 	×1.75 	×1.75 	×1.75 	×1.75
Buffs 	Buffs 	Buffs 	Buffs 	Buffs
×1.1 	×1.1 	×1.1 	×1.1 	
At first Happy! applies +10% speed bonus and then it multiplies the velocity of the player (combined with all previous bonuses and multipliers) by 1.1	At first Happy! applies +10% speed bonus and then it multiplies the velocity of the player (combined with all previous bonuses and multipliers) by 1.1	At first Happy! applies +10% speed bonus and then it multiplies the velocity of the player (combined with all previous bonuses and multipliers) by 1.1	At first Happy! applies +10% speed bonus and then it multiplies the velocity of the player (combined with all previous bonuses and multipliers) by 1.1	At first Happy! applies +10% speed bonus and then it multiplies the velocity of the player (combined with all previous bonuses and multipliers) by 1.1
Blocks 	Blocks 	Blocks 	Blocks 	Blocks
 	×3.5 	×3.5 	×3.5 	×3.5
Debuffs 	Debuffs 	Debuffs 	Debuffs 	Debuffs
 	×0.75 	×0.75 	×0.75 	×0.75
 	×0.5 	×0.5 	×0.5 	×0.5
 	×0.5 	×0.5 	×0.5 	×0.5
 	×0.33 	×0.33 	×0.33 	×0.33
 	×0.33 	×0.33 	×0.33 	×0.33
Modifiers 	Modifiers 	Modifiers 	Modifiers 	Modifiers
* Modifiers are only applicable to accessories. Five accessories may have these modifiers, meaning +20% horizontal speed possible. Only one of these modifiers may be applied at a time. (See: Reforging)
* Movement speed bonuses are capped at 160% of the regular speed.
If you place two minecart tracks side by side and use a hammer to set them both to the 3rd setting, and hold in one direction while in a minecart, you can go up to an unrecorded speed.
== Vertical movement ==
=== Upward movement ===
There are two quantities that play a role when dealing with vertical upward movement: jump duration and jump speed. Together, they describe jump reach, the maximum number of tiles that a character can ascend with a jump. All characters have a base jump duration of 15 and a base jump speed of 5.01, granting them a base jump reach of tiles.
A jump in Terraria consists of two phases: First, the character steadily ascends with a fixed velocity, and then slows down their ascension rate until coming to a stop when reaching the peak of the jump.
* The first phase lasts for ticks, i.e. 16 ticks (0.267 seconds) for default characters, though releasing the key will terminate it prematurely – hence, in order to acquire the maximum possible jump reach, the key must be held for the entire duration of the first phase. The velocity during this phase is equal to jump speed (in pixels/tick) minus gravity (0.4 by default, below the Space layer), i.e. 17.2875 tiles/second for default characters; it is acquired instantly when starting the jump and it is not altered until the first phase is completed.
* The second phase begins when jump duration has been exhausted: The character is now normally only subject to gravity, which will linearly reduce their velocity. The phase is terminated when the character's velocity becomes zero and they have reached the peak of their jump.
It can be seen that while jump duration affects for how long the character surmounts gravity and moves upward, jump speed dictates the character's velocity during their ascent.
With this information, jump reach for any given combination of jump duration, jump speed, and gravity can be calculated:
\text{jump reach} = (\text{jump duration}+1) * (\text{jump speed}-\text{gravity}) + \frac{\text{gravity}}{2} * (\frac{\text{jump speed}}{\text{gravity}}-1)^2 
The two summands here represent the two phases of the jump, as described above.
The base jump reach of all characters can be determined by inserting the default values into the formula:
\text{base jump reach} = (15+1) * (5.01-0.4) + \frac{0.4}{2} * (\frac{5.01}{0.4}-1)^2 \approx 100.33 \approx 100⅓
The result value is in pixels; dividing it by 16 gives the number of tiles:
\text{base jump reach}_{\text{tiles}} = \frac{100.33}{16} \approx 6.27 \approx 6¼
==== Boosts ====
The following table lists all items that have an effect on jump duration and/or jump speed. Items that are listed in the same row do not stack with each other.
Items 	Jumpduration	Jumpspeed	Resultingjump reachAssuming gravity is default and no boosts other than the one of the respective row are in effect (use the formula above for multiple boosts). The increase in percent is referring to the increase from base jump reach ( tiles).
Balloons 	20 	6.51 	tiles (+)
 	 	+2.4 	tiles (+)
 	+1 	+1.8 	tiles (+)
() 	+2 	+0.2 	tiles (+)
 	+5 	 	tiles (+)
Being atop	-90% 	-80% 	tiles ()
 	-80% 	-50% 	tiles ()
The maximum possible jump reach is (+ in total), attainable by equipping one of the accessories from each row above (e.g. a Shiny Red Balloon, the Soaring Insignia, a Frog Leg, the Moon Lord Legs, a Moon Charm, and a Step Stool), at night and while using the Step Stool.
==== Multiple jumps ====
Usually, a character may only perform a single jump and will need to stand on a surface again before pressing the button causes the character to ascend again. However, certain items grant the ability to perform another jump mid-air which is functionally identical to the regular jump described above. These items set an own jump duration for their respective jump.
=== Downward movement ===
Characters falling downward constantly accelerate with 1.5 tiles/second², but falling speed is capped at 37.5 tiles/second (or ). However, both of these values may be modified by certain items, buffs, and environmental factors.
== Medium movement ==
There are currently 4 mediums in the game other than air: Water, Lava, Cobwebs, and Honey. They all have slowing effects on movement compared to that of air. All wings also reduce fall speed compared to that of air.
The Fishron Wings will make the player's movement ignore all liquids. Players can only move in Shimmer after equipping the .
Medium(s) 	Multiplier	Horizontal speed	Horizontal speed	Horizontal speed
Medium(s) 	Multiplier	 	Tiles/sec 	
No Medium 	None 	 	 	
Water, lava, and	×0.5 	 	 	
Honey 	×0.25 	 	 	
Cobweb 	×0.0635 	 	 	
== Maximizing speed ==
=== Horizontal speed ===
On the , the maximum horizontal speed possible is , achieved by using the following items/buffs:
=== Vertical speed ===
On the , the maximum stable ascend speed (i.e. the speed remains the same when ascending) possible is , achieved by using the following items:
For the maximum instantaneous speed, use the same loadout as above, and mount the after reaching maximum speed. This will further increase the speed to about briefly. However, by using the Inner Tube, the player can achieve infinite speed theoretically.
The maximum falling speed is , achieved by holding a .
== References ==