Is it possible to fit a 26" fork to a 29er bike frame

Update: Fixed bad calculation for the BB drop, thanks to @mattnz.

Physically, it may be possible to fit the fork alone. But the resulting bicycle will be dangerous to ride, for at least two reasons.

1. The wheels with 26" rims vs 29" rims are at least (622 - 559)/2 = 31.5 mm or 1¼ inch lower, meaning everything will be lower, including the bottom bracket and the pedals in their lowest position. This means you will have much greater chance to scratch the road or trail when pedaling. Even if it won't touch the ground when you ride the straight line, at cornering the whole bike leans, and pedals go even lower. An unexpected pedal-to-ground contact, especially when cornering, can kick the rider out of the saddle.

2. What size of wheel will you put at the back? If it would be a 29" one, the bike will look very odd, a "reverse mullet" of sorts. Besides the looks, a bigger wheel at the back will increase the steering angle, which in general corresponds to more sensitive steering. The bottom bracket will still become lower, although at lesser extent. The bike will be twitchy to control. If it would be a 26" wheel at the back to match the front wheel, see the lower bottom bracket argument above. Plus, if you have a frame for rim brakes, they won't work because they are designed for a specific diameter of the rim.

Using 26" wheels in a frame designed around 29" ones is really not recommended unless you can run all the numbers yourself for the specific frame and are confident that it will work, and you understand how the resulting bicycle geometry changes affect ride characteristics. As an example, for frames designed around 27.5" wheels, some people did use 26" wheels with them. But then one needed extra wide/high tires to compensate for the rim diameter difference. Wider tires are less likely to fit into the frame/fork without rubbing, so there are limits to this as well.

The difference between 29" and 26" wheel is just too big for this trick to work on regular bicycle frames. Some fatbike frames allow even that, e.g. one of my bikes accepts both wheels with 26"×4.8" and 29"×3", as confirmed by its manufacturer. But that is fairy unusual.

Firsts-off:

On a practical side for reusing old components on a new frame, you need to make sure all the standards match:

• Fork steering tube
• bottom bracket width / size /desing
• rear wheel dropout (width/design)
• seat tube dia (and seat tube length)
• cable endpoints,
• front derailleur mount
• rear disk brake mount (or Canti/Vbrake -Sockets)
• mounts for lights / mudgard / bike stand etc..

Next - these standards change over time, especially in the last 10..12 years there was quite a development and fragmentation of standards. If you have old components, and you manage to find a new, shiny, good frame that accomodates all those old standards, then you're stuck with them and it will be hard to find good new components that fit those old standards.

Last not least - economic aspects: usually buying all the components of a bike will be a lot more expensive than buying the whole bike (in my experience it was factor of at least 2x).

Side Note on riding characteristics: Using a shorter fork is not only lowering the bike, it's also lowering the front more than the rear. This rotates the bike frame, and increases the steering angle by ~approx 1.5deg per inch shorter fork. That in turn reduces the steering offset & has an effect on bike stability.

How much? will it still work? that depends largely on how the bike was in the first place, and how much stability decrease you're comfortable with. In an extreme case you could get to an unstable bike: one where you wouldn't be able to take the hands of the handlebar. On the other side: the difference in fork length beteween 26" and 29" bikes is approx 1 inch, and eg in an MTB suspension forks travel a lot more without problem.

Bottom line: it would be significant work with ~uncertain outcome, and likely not saving much money