Let $k$ be a field, and let ${\mathcal{C}}$ be a $k$-linear, Hom-finite triangulated category with split idempotents. In this paper, we show that under suitable circumstances, the Grothendieck group of ${\mathcal{C}}$, denoted by $K_{0}({\mathcal{C}})$, can be expressed as a quotient of the split Grothendieck group of a higher cluster tilting subcategory of ${\mathcal{C}}$. The results we prove are higher versions of results on Grothendieck groups of triangulated categories by Xiao and Zhu and by Palu. Assume that $n\geqslant 2$ is an integer; ${\mathcal{C}}$ has a Serre functor $\mathbb{S}$ and an $n$-cluster tilting subcategory ${\mathcal{T}}$ such that $\operatorname{Ind}{\mathcal{T}}$ is locally bounded. Then, for every indecomposable $M$ in ${\mathcal{T}}$, there is an Auslander–Reiten $(n+2)$-angle in ${\mathcal{T}}$ of the form $\mathbb{S}\unicode[STIX]{x1D6F4}^{-n}(M)\rightarrow T_{n-1}\rightarrow \cdots \rightarrow T_{0}\rightarrow M$ and
$$\begin{eqnarray}K_{0}({\mathcal{C}})\cong K_{0}^{\text{sp}}({\mathcal{T}})\left/\left\langle -[M]+(-1)^{n}[\mathbb{S}\unicode[STIX]{x1D6F4}^{-n}(M)]+\left.\mathop{\sum }_{i=0}^{n-1}(-1)^{i}[T_{i}]\right|M\in \operatorname{Ind}{\mathcal{T}}\right\rangle .\right.\end{eqnarray}$$ Assume now that
$d$ is a positive integer and
${\mathcal{C}}$ has a
$d$-cluster tilting subcategory
${\mathcal{S}}$ closed under
$d$-suspension. Then,
${\mathcal{S}}$ is a so-called
$(d+2)$-angulated category whose Grothendieck group
$K_{0}({\mathcal{S}})$ can be defined as a certain quotient of
$K_{0}^{\text{sp}}({\mathcal{S}})$. We will show
$$\begin{eqnarray}K_{0}({\mathcal{C}})\cong K_{0}({\mathcal{S}}).\end{eqnarray}$$ Moreover, assume that
$n=2d$, that all the above assumptions hold, and that
${\mathcal{T}}\subseteq {\mathcal{S}}$. Then our results can be combined to express
$K_{0}({\mathcal{S}})$ as a quotient of
$K_{0}^{\text{sp}}({\mathcal{T}})$.