Does this work or am I getting the rules wrong

So I've been looking into movement and I THINK I found a way to get a speed of 1440 feet of movement in a single round. In order to do this you will need. An 18th level tabaxi monk , the boots of speed, and a haste spell. 

Step1. the turn before this feet of movement can happen you must click the heels of the boots of speed together activating there effect which double your movement

Step2. now have your spell caster use haste on you doubling you movement once again

Step3. it's now your turn now using feline agility to double your movement AGAIN

Step4. using one ki point activate step of the wind to dash as a bonus action

Step5. Finally dash with your main action 

So does this actually work or have I messed up on some of these work

I haven't done the math, but I see little issue with an 18 level feline monk with a magical speed item and a speed spell to be able to run 400 m in 6 seconds. It's practically peak fantasy capacity, if we take out Time Stop.

...I wonder if there are Olympic Games in Faerun or the multiversal neighborhood... >.>

Math 60*2=120 (boots of speed) 120*2 = 240 (haste) 240*2=480 (feline agility) then 480 * 3 for both dashes and 1440 feet

Yes, that works.

https://www.dandwiki.com/wiki/Pushing_the_Speed_Limit_(5e_Optimized_Character_Build)

Quote from BDaddLy >>

https://www.dandwiki.com/wiki/Pushing_the_Speed_Limit_(5e_Optimized_Character_Build)

As a level 18 monk tabaxi, your speed is 60 ft. With [feat]Mobile[/feat] (because why the heck not? It's awesome for monks), it would be 70 ft.

Haste, the boots of speed, and tabaxi's Feline Grace all say you double your speed.

Each one of those would double your speed (a specific character stat) to 120 ft or 140 ft with Mobile feat. It would need to state it doubles your movement or something like that before you could stack on all those multipliers.

For support, Mike Mearl's doesn't think it all ought to stack.

Mearls has great insight into the rules as intended, but his tweets don't hold water when talking about the rules as they were written. His tweets aren't official rulings and he's wrong too often. Maybe these things shouldn't stack, but there's no rule that prevents it, unlike the rules for proficiency bonus or resistance/vulnerability. See also this tweet from Crawford:

"While the haste spell is active, it doubles your current speed. If your speed changes, haste doubles whatever your new speed is."

In practice you'll rarely have enough of these speed boosts to create a gameplay issue. I doubt anyone would seriously consider giving Boots of Speed or Haste to a Tabaxi Monk when there's other characters that could benefit much more.

Haste gives you an extra action to dash with so wouldn’t is be 60*4 for 4 moves a turn and then double it for the boots, haste, and the cat ability? Then throw on Mobile and make your speed 70. Or you can do it with an aracokra and have a flying speed of 90 but only double it twice. 

I would interpret any thing that doubles your speed to set your current speed = your base speed x2.  They tried to let people stack multiplication in 3e and found it was stupid.  So in 5e they stopped that crap.   Things that work on your base always work on your base (do not stack), things that are addons add on to the total and stack.  That means Boots of speed, haste and Feline Agility all in use together only double your speed from 60 to 120.

My interpretation of that build is;

Tabaxi, base speed = 30.   Monk, 18th level clearly increases base speed from 30 +30- to 60.

Any of Feline Agility, Haste or Boots of speed, can double your base speed from 60 to 120.   But all together they just do that.

So speed is 120 using just your movement.  Using your action to dash = +120 ft = 240 ft.

Using Haste to get an extra action, which you use to dash = +120=360 ft

Using 1 ki point to dash as a bonus action, +120 ft=  480 ft.

So now you have upped your speed to 120 from a normal speed of 30, and then used a move, an action, an extra action, and a bonus action, all to move. 

If you also has 2 levels of Fighter, you can action surge on top of that, adding another 120 ft = 600 ft.

In real life, you can jump off a cliff and in 6 seconds, fall 579 feet.  But in D&D5e, they rounded down and set it to 500 ft per round.

Why would you need to move so far in one round? You still attack once and I doubt you could see something that far away to attack, but if course you might get the first strike on their best caster in their rear.

If you give up a few levels of Monk for a few levels of Barbarian you can actually squeeze extra 5 feet into your base movement as well because of Fast Movement:

Fast Movement

Starting at 5th level, your speed increases by 10 feet while you aren’t wearing heavy armor.

A Monk 15/Barbarian 5 with Mobile feat ends up with base Movement of 75 feet. With Boots of Speed that’s 150 feet, and Haste that’s 300 feet, and Feline Agility that goes to 600 feet*4 (move, dash, BA dash, Haste Action Dash) that’s 2400 feet of movement in one round, or just shy of 273 mi/hr.

because sometimes you just don't care about fighting the dragon, but you really want the thing they're guarding.  Moving 1320 feet (220 fps, 150mph) in a round you can come screaming in from 600 feet away, snatch something, and be 720 feet away at the end of your turn.

(numbers based on just being a level 8 tabaxi monk with mobile, boots, haste, step of the wind, feline agility)

If your DM didn't want you to do it, they shouldn't have let you have those boots~~

sure, a DM can rule whatever they want.  I don't think anyone's asking about homebrewing rules though.

I mean you are running at an incredible 163 mph (or 263 kph), which is a little over twice the speed of a cheetah at full speed (75 mph). It's fast, but for fantasy standards it's not absurb imo.

if you take totem warrior the benefited movement from the becomes +25 rather than +15

Not really. Being able to go fast can be useful, but you still have only one action, reaction, bonus action and move action. There are builds that can make use of this speed (Ashardalon's Stride, spirit guardians, etc), but mostly anything over 100 ft per round is superfluous. Being superfast is cool, but you won't be able to maintain it for long distances and thus teleportation is better in nearly every way. Being superfast is like being proficient in all skills: it sounds cool but won't be as useful as you think. You can't make the rest of your party superfast, so you're going to get isolated. You still act in turns and your movement speed doesn't avoid attacks or mitigate damage. I've thought about this a lot. The only time more movement speed is broken is the warrior of elements monk and their flight ability at level 11. you can get over 100ft flight speed for 10 min with a single focus point. And that's not including step of the wind. Does boots of speed double that speed? Because now we are talking...

Quote from Obscureinfo >>

Not really. Being able to go fast can be useful, but you still have only one action, reaction, bonus action and move action.

First, there is no move action and you can potentially have 4 actions in one turn (normal action, Haste action, Action Surge action, and Wild Magic 53-56 result action), maybe more.

Second, movement happens on your turn and certain actions (such as Dash) or non-actions (such as Feline Agility) directly or indirectly affect your movement available. However, you can break up that movement before and after your actions and bonus action for the turn.

Quote from Obscureinfo >>

Does boots of speed double that speed? Because now we are talking...

Yes. See Changes to Your Speeds.

Quote from Obscureinfo >>

Being superfast is like being proficient in all skills: it sounds cool but won't be as useful as you think. You can't make the rest of your party superfast, so you're going to get isolated. You still act in turns and your movement speed doesn't avoid attacks or mitigate damage. I've thought about this a lot. The only time more movement speed is broken is the warrior of elements monk and their flight ability at level 11.

Superfast flying speed is cool and all but dealing tens of thousands of damage by comboing grapple with Prismatic Wall is more broken. As for movement, flying or otherwise, the most I was able to get was 5,660 feet in one turn (a little over 1 mile / 1.7 km in one turn), but I didn't try to work in a Wild Magic action. If I interpreted certain rules differently, I may have been able to further increase the number.

Discounting that, having a ridiculous speed can be more effective depending on your allies. Let's say, for example, an 18th level Hasted Tabaxi Monk with Boots of Speed, is fighting alongside a Battlemaster Fighter. The Tabaxi has a speed of 240 feet. If the Fighter hits (perhaps with a longbow) and uses Maneuvering Attack, the Tabaxi can now move 120 feet (half their speed) as a Reaction. This can place them in melee range to wreak some havoc on their next turn.

Spike Growth is a popular combo with grappling so instead of using Maneuvering Strike to get a monk into position, a Battlemaster could use it to provide additional opportunity for dragging across the spikes.

College of Dance Bards have a similar ability, but it is much more restricted. There may be other methods to provide the monk with off-turn movement that I am not thinking of. 

Quote from SmiteMakesRight_3_5 >>

Quote from Obscureinfo >>

Not really. Being able to go fast can be useful, but you still have only one action, reaction, bonus action and move action.

First, there is no move action and you can potentially have 4 actions in one turn (normal action, Haste action, Action Surge action, and Wild Magic 53-56 result action), maybe more.

 The most I've found would be in a wild magic zone, rolling a twenty, and rolling the extra action with the wild magic table (Not that likely). One action

Base action

Haste action

Normal wild magic action

Action surge action

And, technically, potions of speed stack with Haste (As they say that you gain the effect of haste, not cast the spell, meaning that it stacks)

Which is four actions

Quote from Tana___ >>

And, technically, potions of speed stack with Haste (As they say that you gain the effect of haste, not cast the spell, meaning that it stacks)

That is dubious and I think Combining Spell Effects is clearly intended to apply preventing them from stacking.

However, keep in mind that the effect is triggered off of casting a spell with a spell slot, so that could be a Bonus Action spell, such as Expeditious Retreat. (It could also be to cast Haste or Prismatic Wall in order to get an extra Dash!)

Still, four actions plus a Bonus Action is, pun intended, wild.