Self-compassion, which refers to compassion directed toward oneself, is associated with mental health and well-being. Traditionally, self-compassion has been measured and quantified using questionnaire scales such as the Self-Compassion Scale (SCS). In recent years, interest in quantifying psychology using text described by people and state-of-the-art natural language processing methods has increased. In this study, short open-ended free texts were collected from participants asking about their thoughts (general thoughts and those about themselves and others) and behaviors (how they act after experiencing challenging situations) in three challenging situations. Then, a regression model was developed to predict the self-compassion score with BERT, one of the language models. The results showed that the BERT model estimated people's self-compassion scores from free descriptions with high accuracy. Furthermore, the results suggest that thoughts, behaviors, and levels of self-compassion may differ across situations and that the SCS score is related to both cognition (thoughts) and behaviors. The method of psychological quantification using free text may be less prone to priming or bias than measurement using questionnaires, and thus, future studies are encouraged.