Circular saw blades


I have a DeWalt DC390 18v cordless circular saw. This takes 165mm diameter blades on a 20mm arbour. I can't find any blade finer than 30 tooth to fit this saw. I have seen a Trend 48 tooth blade that has the same size arbour (20mm) but is 160mm diameter (5mm less).
I have 2 questions. The first of course is if I fit the smaller Trend blade, will it be dangerous? Secondly, will it give me the fine cut that the blade is designed for?
Whilst on this subject, am I right in thinking that the smaller the blade diameter, the fewer teeth are needed for finer cuts? For example, the trend described above has 48 teeth around its circumference. This gives 0.095 teeth per centimetre of circumference. On a 300 mm diameter blade, to get 0.095 teeth per cm you would need 90 teeth around the circumference. Which is a "fine" or even "extra fine" cut if you read the adverts. Is this sort of conversion the right thing to do?
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I have inherited a very old circular saw, without any instruction manual. I need to order a new blade, but I am not sure of the size. Are the blade sizes based on the diameter measured across the blade from tooth to tooth, or from gap to gap? Thanks.
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Gary C asks:

Tip to tip. You'll also need to know the diameter of the arbor hole. You might also want to get one or more specialized blades for your saw...fine cut, rip, etc.
Charlie Self
We thought, because we had power, we had wisdom. Stephen Vincent Benet
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No problem fitting a smaller blade to a saw. It is done all the time. The only real potential difficulty may be if you are cutting something that is at the depth limit of the exposed saw blade.
As for a number of teet to smoothness relationship, Like any relationship, it depends. I am no expert, but for the sawing I do, it probably is true. But there are a bazillion different saw blades out there now with many different design philosophies.
I think it really boils down to if you are comfortable with a particulat manufacturer and saw blade. Find something that you like. If in doubt, cut some scrap and see.
Another big factor is durability. I have purchases many steel blades for fine cutting on a job basis. It only has to last one job. And if there is much cutting, I may get two or more "one job" blades. It was quick and fast.
But other blades I buy I want more durability and the ability to resharpen.
So the great qualifier, it depends.
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No. It will not be dangerous except for the fact that the blade guard may not cover the teeth on the upper side of the saw.

No. That is not correct thinking. You can simulate more teeth by feeding the saw slower. In addition to fewer teeth you will also have a slower tooth tip speed because of the smaller diameter and this will compound the problem. Feed slower to help off set this effect. More teeth tend to make finer cuts because each tooth takes a smaller bite out of the wood. If you slow down the tip speed the teeth will tend to take bigger bites and typically will give you a rougher cut.
For example,

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