We define essential dimension for finite étale covers as the minimal dimension of a space W to which the cover compresses over a dense open, recalling both the scheme-theoretic and rigid-analytic versions. We then introduce perfectoid essential dimension: the same compression problem, but allowing W to be perfectoid and measuring its dimension in the spectral sense. The main theorem is tilting invariance: for a finite étale cover Y→X of perfectoid spaces, ed(Y/X)=ed(Y♭/X♭), using the tilting equivalence on perfectoid spaces and finite étale sites together with compatibility properties of base change and dimension.