Hand Drill New Chuck Problem

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I have an old hand drill that I used to drill holes in wood. Over time the chuck broke and I couldn't find an original replacement.
Over a month ago I decided to buy a new chuck. I ordered one that seemed to be able to fit into the hand drill.
Today I received it (long wait indeed). The chuck looks really great even better than the dead one.
When I tried to screw it on, it went only few threads and stopped.
The new chuck thread is 1/2-20UNF so I am guessing my drill has a threading of 1/2-20 UNC or 13mm (metric size) and this is why it wouldn't go any further.
In the end I found a working solution using an accessory that I ordered together with chuck. It has a square opening but it went inside the drill and I fixed it with adhesive tape. Well it works now but I would like to know if there is a better option.
What I need is a coupler or adapter that has different thread pitch on both sides.
Can anyone think of a better solution, without the need to order a custom design?

[thecoalman]

There is 1/2 13, 1/2 20 and rarely 1/2 28, the second number is the thread count per inch. If you have existing 1/2 bolt with known thread count you can just see if the threads line up with the threaded shaft on the drill.

Note 1/2 inch is almost identical size to 13mm, the threads should not line up but there is a few sizes/pitch where they are very close.

Once you determine what sizes you have they have "thread adapters". This is not the one you need but something like this. They also make them to adapt metric to standard.

https://www.aliexpress.us/item/3256804920391294.html?src=google&gatewayAdapt=glo2usa

[Subtitles]

There is 1/2 13, 1/2 20 and rarely 1/2 28, the second number is the thread count per inch. If you have existing 1/2 bolt with known thread count you can just see if the threads line up with the threaded shaft on the drill.

Note 1/2 inch is almost identical size to 13mm, the threads should not line up but there is a few sizes/pitch where they are very close.

Once you determine what sizes you have they have "thread adapters". This is not the one you need but something like this. They also make them to adapt metric to standard.

https://www.aliexpress.us/item/3256804920391294.html?src=google&gatewayAdapt=glo2usa

Thank you very much for the explanation and the link.
This kind of adapter is what I am looking for but I think I need Male 1/2-20 UNF to Female 1/2-20 UNC adapter because I don't think my hand drill has 28 threads per inch but I could be wrong. Anyway I will do a bit more searching.

Edit: Apparently there is no 1/2-20 UNC only 1/2-13 UNC. I probably have 1/2-28 UNEF thread. I am used to the metric system and the imperial system is kind of confusing, but I am learning.

[thecoalman]

I am used to the metric system and the imperial system is kind of confusing, but I am learning.

Here in the US we have this mix of uses so you get exposed to both. I was a bike mechanic in my late teens which is mostly metric and it was also a hardware store so I'm familiar with both. I never used the letter designations for standard, just the thread count.

Quick tip on grades/class. Metric class 8.8 is equivalent to standard grade 5, metric class 10.9 is equivalent to standard grade 8. Anything not marked is class 4 for metric or grade 2 for standard. I'm assuming the metric classes were made to be the same as standard hence the reason for decimal.

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I took few images and enlarged them so that I would be able to count the number of threads per Inch on my hand drill.
As seen from the photo, I counted 20 threads per inch which means this drill was made to metric standards and not imperial, because 1/2 Inch UNC can only have 13 threads and it can't be 1/2-20 UNF because the chuck wouldn't screw onto the drill. I am guessing that the diameter is NOT 1/2 Inch (13mm) BUT possibly M12 with standard pitch of 1.25mm which makes it 20 threads per inch, as seen in the image.
Unfortunately the adapter 1/2-20 UNF to 1/2-28 UNEF is not going to help, as I need 20 threads on the drill side and not 28 threads.
In the meantime I made a better attachment of the drill accessory and used a tie wrap to keep it hopefully in place until I find a better solution.

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I finally got the drill to work relatively stable.
Ordered flanged rod coupling size 7mm and 14mm (unfortunately they didn't have 1/2 Inch size which is 12.7mm or 13mm only 14mm). So I had to wrap the drill shaft with masking tape to increase the diameter to 14mm.
The couplings come with set screws and they have a really good grip on the parts.
The images show the installation process. The drill works fine but it is not 100% straight. Nothing serious, at least now I can drill away without the chuck coming out of the drill shaft.