I have an old Giant MTB frame. It's got typical oversized aluminum tubing but with roadbike-esque triangle shapes. It's disc-brake compatible and I want to turn it into a commuter bike.
The rear end has a radius limit of 343 mm. I currently don't have the resources nor the opportunity to test-fit. The theoretical tire radius seems to fit just fine, but actual tires may deviate or vary slightly, hence my crowd-sourcing question.
An old MTB will have used 26" wheels (559mm rims), you want to put 700c (662mm) rims on it with smaller tires.
We can work out wheel approximate diameters. Assuming tire height above the rim is about the same as its nominal width and the MTB frame will take a 50mm tire.
559/2 + 50 = 329mm
622/2 + 28 = 339mm (+10mm)
The 700c tire might fit but bear in mind you are also raising your bottom bracket 10mm, which will raise your position on the bike and affect handling to some extent. The larger diameter wheel will also effectively increase the gear ratios.
Note that a 27.5" / 650b (584mm rim) with a 32mm tire comes out to the same diameter as the 559 with a 50mm tire.
584/2 + 32 = 320mm
Finding 27.5" wheels with rims narrow enough to take a 32mm tire make be tricky though.
is it a MTB frame for a 29" wheel originally? then "probably" But if its a smaller wheel size then your chance of success will drop.
You also need to check the OLD of your frame vs your proposed wheels - a road bike wheel is probably 100mm at the front and 135mm at the back, your frame could be one of the weirder MTB sizes depending on its age.
Disk brakes are what make this a possibility - if you had rim brakes it would be quite unlikely. Since you're probably going to thinner tyres, again its more possible.
Do try a test fit before you get too far down the spending-money path! Even if you just borrow some wheels for a static "fit" test, and leave all the transmission fiddling for later.
@GregoryLeo another side-thought is gearing changes.
Some assumptions - the bike is a 48/38/28 triple, with an 11-32 cassette (number of gears is irrelevant here) and I've assumed a 559-54 tyre, so ~54mm wide.
48 38 28 tooth chainring
11 113.2 89.6 66.0
12 103.8 82.1 60.5
14 88.9 70.4 51.9
16 77.8 61.6 45.4
18 69.2 54.8 40.4 <-- gear-inches, where bigger numbers
21 59.3 46.9 34.6 are "harder" and smaller numbers
26 47.9 37.9 27.9 are "easier"
32 38.9 30.8 22.7
^
Cassette gear
If you increase the wheel size to 622-32 and keep everything else the same:
48 38 28 tooth chainring
11 117.8 93.3 68.7
12 108.0 85.5 63.0
14 92.6 73.3 54.0
16 81.0 64.1 47.3
18 72.0 57.0 42.0
21 61.7 48.9 36.0
26 49.8 39.5 29.1
32 40.5 32.1 23.6
^
Cassette gear
So your tailwind gear of 48-11 would be 4.1% further down the road on the bigger wheels for each pedal stroke. Likewise, your grannie hillclimbing gear of 28-32 would be 4.0% harder than on the MTB wheels.
The upshot is all your gears move roughly halfway to the next gear.
Personally I think any gearing changes will be offset by the lower rolling resistance of road tyres and better aerodynamics, but if you depend on the lowest grannie for anything then it won't be quite as low as it was.
Tables calculated with https://www.sheldonbrown.com/gear-calc.html thanks to Saint Sheldon. This gear calculator doesn't offer a 28mm tyre option in 622, so I chose the slightly higher of the two MTB tyre sizes to offset that.
I think you'll find that most mountain and road bicycle wheels with mounted tires have the same outer radius (approximately). A road bike has 622-28 tires, for an outer diameter of 678mm. A mountain bike has something like 559-60 tires, for an outer diameter of 679mm.
The rim size is smaller on the mountain bike only to allow mounting a larger tire size without making the outer radius excessively large.
However, what makes your plan fail is the brakes, if you have rim brakes. Mountain bikes usually have V brakes; some older variants may have cantilever brakes. There may not be enough adjustment possibility in the brakes to move the brake pads to track a 622mm rim -- and even if there is, the mechanical advantage of the brakes would change. For example, a V brake where the pads are moved upwards has larger travel and smaller mechanical advantage. Thus, stopping the bike would be difficult with excessively small mechanical advantage.
I don't see anything that would make the plan fail if you use disc brakes. For rim brakes, you need to use 559-28 tires instead of 622-28 tires.
However, fitting narrow high performance tires won't make a mountain bike into a road bike. You also need drop bars. This may prove to be difficult. I have a long time ago converted a V braked hybrid bike (622mm rims) with cheap suspension fork into a drop bar bike.
I run 700c x 25 in a GT Aggressor 1 frame. They work a treat. Although you do need disc brakes.
