  For any nonempty, compact and fiberwise convex set $K$ in $T^*\mathbb{R}^n$,
we prove an isomorphism between symplectic homology of $K$ and a certain
relative homology of loop spaces of $\mathbb{R}^n$. We also prove a formula
which computes symplectic homology capacity (which is a symplectic capacity
defined from symplectic homology) of $K$ using homology of loop spaces. As
applications, we prove (i) symplectic homology capacity of any convex body is
equal to its Ekeland-Hofer-Zehnder capacity, (ii) a certain subadditivity
property of the Hofer-Zehnder capacity, which is a generalization of a result
previously proved by Haim-Kislev.
