Child under 3 years old need rail pass?

I will be travelling to Japan with my child. She's now below 3 years old, may i know if we need to pay train ticket or rail pass for her ?
Thank you & Regards,
Peggy

No the child needs no ticket and no JR Rail Pass. If the adults have a JR Rail Pass the adults can have free seat reservation, but " small child" will not get free seat reservation.
Details see under Definitions of Adult and Child : http://www.japanrail.com/JR_ticketrules.htm

Dear Peter

Thanks for your reply.
How about the bullet train..., i will be buying the Japan rail pass and will ride on bullet train from Osaka to Tokyo, so if i did not buy any pass for my child does that mean she won't get any seat at the bullet train?
Thanks & regards
Peggy

The rules state that if you plan on getting a reserved seat then she'll need either need a ticket/seat reservation or sit on your lap.

It doesn't get into unreserved seat so if you ride on the "Shinkansen" (aka bullet train) in the UNRESERVED section of the trains she probably would get her own seat since those are first come first serve seating.

Peggy,

Children under the age of 6 travel free of charge provided they do not occupy a seat. If you want a seat for your daughter, you will have to get a child railpass, which is half the cost of the adult pass.

Peggy, that is exactly the problem. With your adult JR Rail Pass you have the options: An unreserved seat at a hikari shinkansen from ShinOsaka to Tokyo ( you just hop on the next available train ) or a reserved seat in a specific train and this seat reservation is free for the adult, but in that case it may happen that the seat next to you is reserved, too and child has no own seat. So I would recommend that you take the non-reserved cars of the shinkansen. You can then sit the child on a seat next to you. As many hikari shinkansen start at ShinOsaka, so it is very likely you get seats in the non-reserved cars.
If this is your only train ride a single ticket ShinOsaka Tokyo is Yen 13300 while a 7 day JR Pass is Yen 28300.

Since i will be traveling by bullet train from Osaka to Tokyo and from Tokyo back to Osaka again, do u think its best for me to buy the Japan rail pass for my daughter so we do not have to worry about seats? and my last question is : is it allow to purchase railpass eventhough she has not 6 year old?Thank you.

Peggy,
frankly speaking: I would not buy a children rail pass. On non-holidays ( Golden week, Obon, New Year ) expect the hikari shinkansen in the unreserved cars to offer you two seats, one for you with your railpass and one for the child without ticket. I have never seen a conductor saying a word, if child is sitting at the moment he checks the tickets.

Thank you Peter for the reply.Thank you all for responding :)
Have a nice weekend, everybody !