Evidence suggests that several elements (i.e., subsystems) of the Earth’s climate system could tip into a qualitatively different state due to on-going and future anthropogenically induced climate change. Risks associated with tipping could form a component of critical climate risks, and their consideration should be indispensable in decision-making. However, there is lack of scientific knowledge about the risks associated with tipping elements, inhibiting their incorporation into comprehensive risk assessments of climate change (i.e., assessments of impact, adaptation, and mitigation with uncertainty). Using two major tipping elements (Arctic summer sea-ice loss and Greenland ice-sheet melting) as examples, this study attempted to address this lack of knowledge by conducting several calculations under various policy choices based on target temperature, including (i) the probability of passing a threshold temperature in this century and (ii) the potential impact of passing a threshold temperature on a millennial timescale beyond this century. The first theme of this study [Item (i) above] suggested that probability of exceeding the threshold within this century is 24.8% for the Greenland ice sheet and 2.7% for Arctic summer sea ice under a 1.5 °C temperature goal. However, it should be noted that the estimated probabilities of exceeding the threshold are largely dependent on the specification of the probability density function and key assumptions. With regard to the second theme of this study [Item (ii) above], estimation of the potential global coastal exposure using the estimated sea level exhibited a significant gap between scenarios not exceeding the threshold (1.5 °C target) and those exceeding the threshold.