双曲线扇形是指在一个笛卡儿坐标平面 之上，双曲线与从原点出发的两条射线相交处的两点和之间的面积。

一个标准位置的双曲线扇形有及。

处于标准位置的双曲线扇形的面积是 。

证明：

黄色部分的面积相等于三角形的面积加上双曲线底下从 到 的面积，再减去白色三角形的面积。所以，黄色部分的面积为：

处于标准位置的双曲线扇形与正值的双曲角相对应。

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy = 1 (or the corresponding region when this hyperbola is rescaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola).