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Hi there your question has been up for a while...are your still around to chat?
So I am assuming your 11 year old has not yet been through puberty or started at all...other signs are like body hair, odor, acne, voice changes, growth in height...
Once he hits puberty his penis will grow after he notes testes growth which tends to come first.
1/2 inch stretched is the length of his penis currently? This is about less than 2cm which is quite small. Generally the penis does not grow a whole lot before puberty after a baby leaves toddlerhood....but a penis this small qualifies for the definition of a micropenis or microphallus as in a newborn measurements of < 2-2.5 cm qualify.... Did his doctor or anyone notice at all at birth or mention anything to you along the last 11 years? When you brought up this concern at the office at routine visits what did they tell you?
You may have meant 1 and 1/2 inches....if so this is small side of normal and thus wouldn't qualify for the definition of a microphallus.
IF your son qualifies for the diagnosis of microphallus he should visit a pediatric endocrinologist as there should be a medical evaluation to rule out hormonal deficiencies, etc....that could be important to know about now. There can be some response to testosterone shots for example if there is not adequate production by his body,
I would say that you should look into this now as he is going to be going through puberty soon if he has not already started and this is when he would get the most out of treatment. It is also possible if he is overweight that the true length of his penis is obscured by a large pubic fat pad....this will in effect hide the base of the penis (and can be a lot!!) and make it appear to be smaller than it is. This is very common nowadays and these boys have no problem endocrinologically and will develop normally but will obviously benefit greatly from a more normalized body mass index.
To answer your question initially there is no supplement to increase penile growth....but this may be a medical problem that needs treatment. Please reassure him that you will work on this problem and that he need not concentrate on the size of his penis. He will most likely grow once he hits puberty thus reassure him that things will get better...in the meantime he can avoid changing around others etc...which he probably already does and not worry too much. Helping him be strong and active can help him focus on other areas of his body.
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