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$\mathsf{ZF + AD}$ proves that for all nontrivial forcings $\mathbb{P}$ on awellorderable set of cardinality less than $\Theta$, $1_{\mathbb{P}}\Vdash_{\mathbb{P}} \neg\mathsf{AD}$. $\mathsf{ZF + AD} + \Theta$ is regularproves that for all nontrivial forcing $\mathbb{P}$ which is a surjective imageof $\mathbb{R}$, $1_{\mathbb{P}} \Vdash_{\mathbb{P}} \neg\mathsf{AD}$. Inparticular, $\mathsf{ZF + AD + V = L(\mathbb{R})}$ proves that for everynontrivial forcing $\mathbb{P} \in L_\Theta(\mathbb{R})$, $1_{\mathbb{P}}\Vdash_{\mathbb{P}} \neg\mathsf{AD}$.

The Destruction of the Axiom of Determinacy by Forcings on $\mathbb{R}$ when $\Theta$ is Regular