Example sentences
shāng商diàn店zài在yòu右biān边。
The shop is on the right.
qǐng请wǎng往yòu右biān边zǒu走。
Please walk to the right.
About this word
右 is the right hand, 边 is a side or an edge, so 右边 is the right-hand side. 边 is what turns a direction into a place you can be at, and it does that job across the whole language: 左边, 上边, 下边, 前边, 后边, 里边, 外边, 旁边. It goes neutral here, yòubian. Northern speech also has 右边儿, and the 边 drops away when the direction is obvious, as in 往右走.
The story behind the character
右
右 is 又, a right hand, with 口 added underneath. In the oracle bones the hand by itself was enough, that was the character for right. The 口 is a later addition, tacked on to keep the meanings apart. Xu Shen read the pair as 助也, hand plus mouth means help. 右边, the right side, still has the hand in it.
边
边 is 辶 (walking) with 力 on the right in its simplified form. The traditional 邊 carried a larger sound element on the right. Xu Shen defined it as 行垂崖也: walking along the edge of a cliff. So the side of a thing is, at root, the edge you do not want to step too close to.