In this paper an uncertainty inequality for Hankel transforms is obtained.Let $\nu > 0$ be fixed. We set \[ d\mu _\nu (x) = c_\nu ^{ - 1} x^{2v} dx,\quad c_\nu = 2^{{{\nu - 1} / 2}} \Gamma (\nu + \frac{1}{2}),\] and \[ {\bf J}_\nu (x) = c_\nu x^{ - \nu + {1 / 2}} J_{\nu - {1 / 2}} (x),\] where $J_{\nu - {1 / 2}} (x)$ is a Bessel function of the first kind of order $\nu - \frac{1}{2}$. We define \[ f^ \wedge (t;\nu ) = \int_0^\infty {f(x)J_\nu (xt)d\mu _\nu (x)} .\]A probability frequency function with respect to $d\mu _\nu $, is defined as a nonnegative function in $L_\nu ^1 (0,\infty )$ with norm one, and the generalized variance of a probability frequency function $F(x)$ is defined by \[ V_\nu [F] = \int_0^\infty {x^2 F(x)d\mu _\nu (x)} .\] Let $f(x)$ belong to $L_\nu ^2 (0,\infty )$ with norm one. By Parseval’s equality $| {f(x)} |^2 $ and $| {f^\wedge (x;v)} |^2 $ can be considered as probability frequency functions. The uncertainty inequality \[ V_\nu \left[ {| {f(x)} |^2 } ]V_\nu [ {| {f^ \wedge (x;...