Teaching is one of the most stressful occupations. This study explores how teachers' psychological capital -- a combination of hope, resilience, optimism and self-efficacy -- is related to stress, wellbeing, appraisal and coping. Teachers (n = 1502) across New Zealand and from a range of teaching levels completed surveys. Participants with more psychological capital reported less stress and more wellbeing, saw work demands more as challenges than threats, and reported using more task-focused and less emotion-focused coping strategies. Psychological capital appeared to be directly related to increased wellbeing and reduced stress. Given the importance of teacher wellbeing for the profession and for students, we need ways to build teachers' personal resources and, importantly, to ensure that teaching environments support wellbeing.