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 11.36 blocks/sec, or 15 mph (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%.


 * The hook tools, the Grappling Hook, Ivy Whip, Dual Hook, Spooky Hook, Bat Hook, Web Slinger, Skeletron Hand, and gem hooks like the Diamond Hook, reel in the player at a constant speed regardless of speed boosting accessories. The more passive speed boosts a player has, the less noticeable using a hook is to move quickly.
 * The Hermes Boots, Spectre Boots, Lightning Boots, Frostspark Boots, and the Terraspark Boots build up to a fixed speed of max speed. Using movement boosts with one of the four boots only speeds up the boots' effect. Max possible speed vertically is 235 mph.


 * 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.
 * The maximum running speed the player can achieve is 235 mph on an Asphalt Block, done by wearing the Orichalcum Helmet, Gi, and Valhalla Knight's Greaves alongside the following set of Accessories with the Quick Modifier on Master Mode: Terraspark Boots, Frostspark Boots, Lightning Boots, Anklet of the Wind, Aglet, Soaring Insignia, and Moon Charm (or any of its upgrades). It must be nighttime to activate the Moon Charm's Werewolf buff, and the player must additionally be under the effects of Happy!, Exquisitely Stuffed, Swiftness, and Panic!. These effects are granted by a nearby Sunflower, certain food items, Swiftness Potion, and the Panic Necklace (or its upgrades), respectively. The Panic Necklace must be unequipped for one of the other accessories after the buff is applied. This represents a 1553.33% movement speed and is far beyond any other attainable movement speed, beating even the terminal falling velocity from a Portal Gun (which is 179 mph).

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 jump duration + 1 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:

$$\text{base jump reach} = (15+1) * (5.01-0.4)  +   \frac{0.4}{2} * (\frac{5.01}{0.4}-1)^2   \approx   100.33$$

The result value is in pixels; dividing it by 16 gives the number of tiles:

$$\text{base jump reach}_{\text{tiles}} = \frac{100.33}{16} \approx 6.27 $$

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.

The maximum possible jump reach is tiles (plus another 1.625 tiles from standing atop the Step Stool; + 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 Amphibian Boots, 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.


 * Note that the Fishron Wings dropped by Duke Fishron increase movement speed in all liquids.