We prove that for any compact set E ⊂ R 2 E\subset \mathbb {R}^2 , dim H ⁡ ( E ) > 1 \dim _{\mathcal {H}}(E)>1 , there exists x ∈ E x\in E such that the Hausdorff dimension of the pinned distance set Δ x ( E ) = { | x − y | : y ∈ E } \begin{equation*} \Delta _x(E)=\{|x-y|: y \in E\} \end{equation*} is no less than min { 4 3 dim H ⁡ ( E ) − 2 3 , 1 } \min \left \{\frac {4}{3}\dim _{\mathcal {H}}(E)-\frac {2}{3}, 1\right \} . This answers a question recently raised by Guth, Iosevich, Ou, and Wang, as well as improves results of Keleti and Shmerkin.