There was a scientific study that actually got women to handle and pick measured cylinder objects of different sizes that they would want as their life long partner's penis size and one they'd want in a one night stand.
Citation: Prause N, Park J, Leung S, Miller G (2015) Women's Preferences for Penis Size: A New Research Method Using Selection among 3D Models. PLoS ONE 10(9): e0133079. doi:10.1371/journal.pone.0133079
The average penis size is 5.17 inches/13.2 cm long and 4.56 inches/11.6 cm in girth (circumference around the penis). This was done by the biggest most up to date study that only took into consideration measurements that were performed by the medical examiner instead of the volunteer self reporting them. It included over 15,000 men.
Citation:
BJU Int. 2015 Jun;115(6):978-86. doi: 10.1111/bju.13010. Epub 2015 Mar 2.
Now to the results:
For a one time partner, the average girl picked a length of 6.4 inches/16.3 cm and a girth( or circumference) of 5.0 inches/12.7 cm. For a life long partner they preferred a length of 6.3 inches/16.0 cm and a girth(circumference) of 4.8 inches/12.2 cm. On average girls prefer above average length and slightly above average girth, so its bigger than average, but not much bigger.
Now thats the "average" girl. There's girls that like it bigger and there's girls that like it smaller. There's girls for everybody. Also just having the ideal size isn't going to cause great sex by itself. You still have to consider the other factors and fulfill their needs. And if you're under sized, try to make up for it with great oral skills etc.
Now we know the average size women prefer. And i hope this answers all the penis size questions on this topic. Have a great night :)
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