Attack speed

There is no attack speed field in Terraria. What the game tracks is use time, counted in ticks, and every line of text about increased attack speed is really a divisor sitting inside that value. Lower use time means a faster weapon, so a weapon at 10 ticks acts three times as often as one at 30.

Weapon modifiers can speed up almost anything you can hold. Accessories cannot. Every accessory and armor bonus that touches speed is specifically melee speed, which is why ranged, magic and summon get their rate of fire from weapon choice and reforging alone.

The awkward part is that for many melee weapons, extra melee speed does not raise damage per second at all. It changes something else, and which something depends entirely on the weapon type. Before you build for it, find your weapon in this list.

• Swords that fire projectiles: the swing animation shortens and the projectile travels faster and further, which mostly buys you reach. Fire rate improves a little and the amount varies per weapon. One group shoots on every swing without exception, including Blade of Grass, Night's Edge, Excalibur, Terra Blade and The Horseman's Blade, and for those the speed does convert cleanly into damage.
• Weapons that are nothing but a projectile, such as Vampire Knives, Scourge of the Corruptor and Daybreak: the projectile simply moves faster. You get no extra hits, only easier hits at range.
• Yoyos: the yoyo moves faster and its string gets longer, but the hit rate is fixed. The multiplier on both is 4 divided by the quantity 1 plus 3 divided by your melee speed, so doubling melee speed buys roughly sixty percent more string. That applies on top of any string upgrade, and it matters most early, when a yoyo is too short to reach a boss from anywhere safe.
• Flails: velocity only, thrown or launched. They reach out further and return sooner, a real gain against flying targets even though the swing rate never changes.
• Spears: these genuinely attack faster. The reach gain is too small to notice. Spears that emit projectiles, like Chlorophyte Partisan, North Pole and Gungnir, fire them faster as well.
• Boomerangs: more velocity and more distance covered, same rate of throwing.
• Whips deal summon damage but scale off melee speed, and for them the bonus is a straight increase in swings per second.

A short list takes nothing at all from melee speed: Terragrim, Arkhalis, the jousting lances, Starlight, Sleepy Octopod, Solar Eruption and Zenith. Zenith even reacts backwards on screen, summoning fewer swords per attack as your melee speed climbs, though the damage it deals is unaffected.

A few take only a fraction of the bonus. Bladed Glove receives half, Terra Blade three quarters, Psycho Knife a third, and Fetid Baghnakhs a quarter, which is deliberate given how fast it swings already. Reforging those for speed pays a lot less than the tooltip percentage suggests.

Enemies run their own hit cooldowns, and past a point your extra swings land inside a window where the target cannot be damaged. Projectiles that do not pierce are exempt from this, but anything that pierces or explodes is subject to it. The usual window is ten ticks, a sixth of a second, with per-projectile exceptions running from five ticks up to twenty. Once your attack interval drops under the target's cooldown, more speed is buying animation and nothing else.

Mining is a separate system. Melee speed does nothing for a pickaxe or an axe. Only mining specific bonuses and the tool's own modifier apply there, and the fastest tool modifier is Light rather than any of the weapon speed rolls.

Stacked to the limit, melee speed lands a little over +158 percent, built from a Monk cap, a Shinobi Infiltrator torso, Solar Flare Leggings, a well fed buff, Tipsy, and the five glove line accessories all reforged for speed. Expert and Master add slots and push it higher. Getting there costs your entire accessory budget.

For most characters the question is simpler than the ceiling. Check what your weapon does with the bonus first. If you are swinging a yoyo, a flail or a boomerang, speed gear is buying reach and safety, which may be exactly what a fight needs. If you are using a spear, a whip, or one of the swords that shoots on every swing, it is buying damage. If you are holding Zenith or Solar Eruption, spend the slot on something else.