Spur Gear Ratio: Optimal Ratio Explained

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An optimal spur gear ratio is defined as the ratio that best suits the specific application requirements, typically ranging from 1:1 to 1:6. The ideal pitch line velocity for spur gears can reach up to 25 m/s. A gear with a normal pressure angle of 20 degrees should have a minimum of 18 teeth to ensure proper function. The preferred number of teeth for spur gears spans from 12 to 250, with specific integers recommended to promote even wear. Selecting the correct p/q ratio, where p and q are coprime, is crucial for achieving optimal performance and longevity.
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Single stage spur gears ratio
What is an optimal spur gear ratio?
 
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The ratio that best meets the needs of the application. A good search term is the word optimal.

That answers the wrong question, then you need to more carefully word your question.
 
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About 6.5 to 1
 
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https://roymech.org/Useful_Tables/Drive/Gears.html#Design said:
A single spur gear is generally selected to have a ratio range of between 1:1 and 1:6 with a pitch line velocity up to 25 m/s. [...] The minimum number of teeth on a gear with a normal pressure angle of 20 desgrees is 18.

The preferred number of teeth are as follows
12 13 14 15 16 18 20 22 24 25 28 30 32 34 38 40 45 50 54 60
64 70 72 75 80 84 90 96 100 120 140 150 180 200 220 250
 
The p/q ratio should involve integers p and q that do not share common factors, so the gears will wear evenly, with a "hunting tooth".
 

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