Mounting evidence indicates that climate tipping points can have large, potentially irreversible, impacts on the earth system and human societies. Yet, climate change metrics applied in current sustainability assessment methods generally do not consider these tipping points, with the use of arbitrarily determined time horizons and assumptions that the climate impact of a product or service is independent of emission timing. Here, we propose a new method for calculating climate tipping characterization factors for greenhouse gases (carbon dioxide, methane, and nitrous oxide) at midpoint. It covers 13 projected tipping points, incorporates the effect that the crossing of a given tipping point has on accelerating the crossing of other tipping points, and addresses uncertainties in the temperature thresholds that trigger the tipping points. To demonstrate the added value of the new metric, we apply it to emissions stemming from end-of-life of plastic polymers and compare them with commonly used metrics. This highlights the need to consider climate tipping in sustainability assessment of products and services.