Carbon inequality is often quantified based on economic inequality. Therefore it is critical to use appropriate income, wealth or consumption concepts to measure carbon inequality. Equivalence scales of income is a concept from welfare economics that is frequently applied to carbon footprint accounting and carbon inequality assessments. Here we argue that this is a mistake based on a methodological misunderstanding that overestimates carbon footprints, particularly in lower-income groups and low-income countries, and underestimates carbon inequalities - which in turn has implications for climate justice. We also quantify empirical differences between methods across a range of countries and suggest alternative approaches.