  Let $\varphi$ be a nonnegative integrable function on $(0,\infty)$. It is
well-known that the Hausdorff operator $\mathcal H_\varphi$ generated by
$\varphi$ is bounded on the real Hardy space $H^1(\mathbb R)$. The aim of this
paper is to give the exact norm of $\mathcal H_\varphi$. More precisely, we
prove that $$\|\mathcal H_\varphi\|_{H^1(\mathbb R)\to H^1(\mathbb R)}=
\int_0^\infty \varphi(t)dt.$$
