© 2017 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the «https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. The measured (central) values of the Higgs and top quark masses indicate that the standard model (SM) effective potential develops an instability at high field values. The scale of this instability, determined as the Higgs field value at which the potential drops below the electroweak minimum, is about 1011 GeV. However, such a scale is unphysical as it is not gauge invariant and suffers from a gauge-fixing uncertainty of up to 2 orders of magnitude. Subjecting our system, the SM, to several probes of the instability (adding higher order operators to the potential, letting the vacuum decay through critical bubbles, heating up the system to very high temperature, and inflating it) and asking in each case physical questions, we are able to provide several gauge-invariant scales related with the Higgs potential instability.