Suppose that $h$ is a Gaussian free field (GFF) on a planar domain. Fix $\kappa \in (0,4)$. The SLE light cone $L(\theta )$ of $h$ with opening angle $\theta \in [0,\pi ]$ is the set of points reachable from a given boundary point by angle-varying flow lines of the (formal) vector field $eih/\chi$, $\chi =2\kappa -\kappa 2$, with angles in $[-\theta 2,\theta 2]$. We derive the Hausdorff dimension of $L(\theta )$.

If $\theta =0$ then $L(\theta )$ is an ordinary SLE curve (with ); if $\theta =\pi$ then $L(\theta )$ is the range of an SLE curve ($\kappa \prime =16/\kappa >4$). In these extremes, this leads to a new proof of the Hausdorff dimension formula for SLE.

We also consider SLE processes, which were originally only defined for $\rho >-2$, but which can also be defined for $\rho \le -2$ using Lévy compensation. The range of an SLE is qualitatively different when $\rho \le -2$. In particular, these curves are self-intersecting for and double points are dense, while ordinary SLE is simple. It was previously shown (Miller-Sheffield, 2016) that certain SLE curves agree in law with certain light cones. Combining this with other known results, we obtain a general formula for the Hausdorff dimension of SLE for all values of $\rho$.

Finally, we show that the Hausdorff dimension of the so-called SLE fan is the same as that of ordinary SLE.