The international process for tackling climate change endured several backslashes since the signing of the Paris Agreement in 2015. Issues around the respective responsibilities are not fully solved yet. The underlying question of how to share efforts in order to reach a Zero Net Emissions state remains largely unclear and the INDCs process has still to deliver a pathway for decarbonization. In the last years, the concept of global carbon budget has emerged as one of the most direct ways to materialize the constraint from the climate. It mainly relies on the idea that only a limited quantity of carbon dioxide can be released in the atmosphere if we want to stay below the 2°C temperature change threshold above pre-industrial levels and, if possible, below +1.5°C, as agreed at the Paris Conference in 2015. By comparing what is in our carbon budget to what is done to reduce the carbon footprint of societies, we calculate a distance to the climate constraint. Expressed in euro this distance, called the “climate debt”, measure how much we avoid paying by delaying climate change mitigation. Using different rules for sharing the burden, acknowledging there is no negotiated nor consensual way to share it, we calculate this climate debt for main EU countries. The first step of the following work is to compute a carbon budget for both the European Union and member countries mixing population based sharing (egalitarian) for EU and rest of world budget and emission based sharing (grandfathering) for EU countries. In a second step, we determine how many years are left before these budgets are depleted at the regional and national levels, which requires assumptions on the future emissions trend. Combining these trends with assumptions on the abatement cost of remaining carbon dioxide emissions after the depletion date allows us to evaluate the “climate debt”. More precisely, the “climate debt” is the amount of money that will have to be invested or paid by countries for them not to exceed their carbon budget. This work led us to three key policy insights. First, there are few years left for major European countries before exhausting their carbon budget under the +2°C target. As for the +1.5°C target, carbon budgets are exhausted for EU main countries, which are thus running excessive climate deficits. Secondly, the carbon debt should be considered as one of the major issues of the decades to come since in the baseline scenario it represents about 50% of the EU GDP to stay below +2°C (120% for staying below +1.5°C). Thirdly, the results of the estimation of this carbon debt are subject to numerous moral, ethical and technical assumptions that should motivate further and urgent investigations on this subject, critical to climate change mitigation, from both state bodies and independent research institutes.