A cockring can make your cock harder by restricting the flow of blood out of your penis and this can make it harder, they can even help you to keep your cock hard for longer than usual.
If it is too small then it will cut off blood flow which isn't good for your penis and if you get one that's too big then it won't do its job properly as it won't restrict blood flow out of the penis.
You need to measure around the penis at the point where you want the cock ring to sit. Most guys have the cock ring placed at the base of the penis.
You measure the diameter of the erect phallus, around both shaft and testicles using a sewing tape measure or equivalent, then divide this figure by 3.14 (Pi) to get a first idea of the diameter you need.
Your 23cm would give a cockring with a diameter about 7cm; which is quite unusual...
From my favorite gay sexshop
IEM - Fournisseur de Fantasmes here in Paris the largest one is 6cm! Most common being between 4.5 and 5.5cm!
For the first time, the silicone version, for its flexible and comfortable to wear side, will be the most recommended.
After that it depends on how tight you want it...
For me 4.5cm is the minimum,can be too tight when really horny
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I feel better with 5cm
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