I have noticed how the Monk class gets increased movement, well I took it on myself to discover the literally fastest you can go in D&D including spells and potions. 

Here is what I found

35 base feet per turn from Wood Elf

Extra 30 feet from Monk Class

Extra 10 feet from Mobile Feat

Extra 30 feet from Boon of Speed

Total base: 105 feet

Double from Dash (Bonus Action from Boon of Speed) = 210 feet

Double from Boots of Speed = 420 feet

Double from Potion of Speed's Haste = 840 feet

Now this requires level 20 with Epic Boon and those two items, but if you are at level 20, you better have access to a Potion of Speed and Boots of Speed

This total of 840 feet is over 6 seconds so that is 140 feet per second. Now, this converted to meters per second is 42.672 meters per second, which is also 95.4545 mph or 153.619 kph.

Usain bolt, however, made the world record at about 28 mph in a 100m sprint. My monk can defeat Usain in less than a heartbeat. At 105 feet per turn with 17.5 feet per second, you go about 5.334 m/s, 11.93182 mph, or 19.2024 kph. Dashing gives 205 feet per turn with 35 feet per second, 10.668 m/s, 23.8636 mph, or 38.4048. Just adding that second boost of the Boots of Speed or the Potion of Speed, my monk leaves Usain in the dust. Sure this is steroids at its finest, but it is still pretty freaking amazing at the fact that my monk can match the speed of cars on the Autobahn, though only for a minute.

This means that in 1 hour, my monk can travel:

1.5909 miles after the first minute, rest for 6 seconds, then continue at half speed for another 7.0795495 miles with the Boots of Speed active for the rest of the 10 minutes. After that, the dash alone will provide another 19.88633 miles.

Totaling about 28.5567

Now that is a Marathon runner. I now understand why the first marathon runner died from exhaustion.

Now just imagin if Usain Bolt had the magic items and Boon!  That is a fun build though, fun fact your monk can run across water even without the Unarmored movement feature.

The monk can also spend Ki to triple move in a turn, thus it would be...

Base - 105ft

Dash - 210ft

Ki Dash - 315ft

Boots of Speed - 630ft

Potion of speed - 1260ft

1260ft/6sec

210ft/sec

756,000ft/hr

143.18 mph or 230.43 kph

Then if you multi-class into barbarian (and you are allowed to go past lvl 20) then your base speed is increased by and additional 10ft thus..

The max speed is 156.81 mph or 251 kph

The thing is that their Dash does not stack with the normal dash, it just allows you to make the Dash Action as a bonus action instead of an action so that additional double does not apply.

If we use the Tabaxi we can go even faster

normal move level 20 monk/5th level barbarian with mobile= 110 ft

Dash 220 ft

feline agility 440 ft

boots of speed 880 ft 

potion of speed 1,760 ft

1760ft/6sec  293.33ft/sec  200 mph or 182.27 Kph

Quote from UsurperofNessus >>

The thing is that their Dash does not stack with the normal dash, it just allows you to make the Dash Action as a bonus action instead of an action so that additional double does not apply.

Well then, double that top number then and we have quite the fast elf monk. Good to know about that.

so the 15th monk/5th barbarian Tabaxi with mobile and boon of speed 95 ft

the dash 190 ft

ki dash 380 ft 

feline agility 760 ft

boots of speed 1520 ft 

potion of speed 3,040 ft then all the conversions and we get 345.45 mph  or 555.95 kph

So I recalculated with the triple dash also dash doubles each time as the book states that it is calculated to last after any previous modifier has been added. so that means that double dash does not add your speed, it doubles its current level.

Wood Elf(this just gives an increased base amount while Tabaxi is only viable in combat), Mobile, Boon of Speed, with lv 15 Monk and lv 5 Barbarian is 110 feet per turn.

110x2=220 (Boots of Speed)

220x2=440 (Haste from Speed Potion)

440x2=880 (First Double from Dash)

880x2=1760 (Second Double from Bonus Action Dash, this dash has only 20 uses so it can run for 2 minutes)

This just reduces down two levels when the first two doubles wear off. The order of the doubles doesn't matter at all since no other additional modifier is added.

1760/6=293 1/3 feet per second

this in mph is oddly at exactly 200 mph

In kph its 321.869

In m/s it's 89.408

Kiss my ass Usain Bolt.

Yes, Tabaxi gets double this in a turn of combat, but that is only viable on every other turn.

At this speed for 1 minute you can travel (based on mph) 3.33 miles

Next Minute and six seconds you can travel another 1.528 miles

then in the next 8 minutes, you travel 6.67 miles

finally, after the final 50 minutes, you travel 20.83

Totaling in 1 hour, you can run 32.36 miles

That is quite the upgrade

For comparison sack here is the Tabaxi's 1-hour coverage assuming that every turn they are in battle

add 1 more double, but minus 5 to the total.

Tabaxi amounts

105x2=210 (First Dash)

210x2=420 (Ki Dash (lasts 2 minutes, extended to 4 minutes given tabaxi ability))

420x2=840 (Boots of Speed (lasts 10 minutes)

840x2=1680 (Potion of Haste (lasts 1 minute with 6 seconds doing nothing after)

1680x2=3360 (Double in combat, only makes you move every other turn)

381.818 mph for the first minute traveling a total of 3.18 miles (You don't need to worry about potion of speed because of the tabaxi ability

Then on your next 3 minutes at 190.909 mph, you travel an additional 4.77 miles

The next 6 minutes are then at 95.4545 mph meaning that you travel another 4.77 miles oddly

The final 50 minutes will as well entail traveling at a speed of 47.7273 going a total of 19.89 miles

This totals out at 32.61 miles, just over the wood elf, but that requires being in combat the whole hours and not moving every other turn (6 seconds)

In conclusion, the wood elf can do it more efficiently and I would pick over the tabaxi any day.

There is also another method where you choose instead to be a lv 18 Monk and level 2 Rogue to get the Cunning Action every turn instead of only for 2 minutes.

This works differently as it extends the time to sprint that double to the whole hour, but takes down the speed some. Lets see what it is at for the Wood Elf. I will not calculate the Tabaxi for this one for time sake.

105x2=210 (Boots of Speed)

210x2=420 (Haste from Speed Potion)

420x2=840 (First Double from Dash)

840x2=1680 (Second Double from Bonus Action Dash)

Now to transfer it:

190.909 mph for 1 minute gives 3.18 miles

95.4545 for 8 minutes and 54 seconds gives 14.16 miles

47.7273 for the final 50 minutes gives 39.77 miles

Totaling at 57.11 miles which mean that the level 18 monk and level 2 rogue is the way to go with that unlimited double dash.

However, like the tabaxi ability, this dash is limited to only during combat. So this method only works if you are constantly in combat. I will still prefer the lv15 Monk and lv 5 Barbarian as it can go without needing to be in combat. Now, if this ability is not limited to combat, then it would be the fastest ability giving the Monk/Rogue a Velocity of 57.11 mph making it able to run on the highway and keep up.

How hard would that hit? 

It makes me want to just have two monks fighting on the countryside as a random travelling encounter.  Speeding through fields at 60 MPH... 

Yeah, this is anime level speeds with two individuals just duking it out as Monks lv 18 and Rogues lv 2 making them just duel at such high speeds. They can really make some distance while fighting.

Now we just need a few wizards in the background making random fireballs for special effects, get them to cast jump on each combatant, give both monks glowing gloves and get a bard to play some battle music.

Then we've got an epic battle.

Quote from Charlie_Charleston_III_of_Griten >>

Now we just need a few wizards in the background making random fireballs for special effects, get them to cast jump on each combatant, give both monks glowing gloves and get a bard to play some battle music.

Then we've got an epic battle.

that's super op