This paper addresses the problem of children's online safety in the context of the growing digital landscape. With a surge in the use of digital technology among children, there has been an increase in online safety harms, risks and criminal incidents despite existing data protection and online privacy protection regulations. Most general security and privacy assessment approaches/standards focus mainly on protecting businesses from financial loss, but there remains a notable gap in methodologies specifically designed to cater to the unique challenges faced by children in the online space. To fill this gap, we propose a safety risk assessment approach that focuses specifically on children's online safety. The key novelty of our approach is providing an explainable and systematic evaluation of potential safety weaknesses of online services and applications based on precise automated mathematical reasoning. This framework has the potential to assist online service and app designers during the system design phase enabling them to proactively ensure Safety-by-Design, as well as auditors and users to understand the risks posed by existing services/apps, promoting further research on designing age-appropriate warnings and education materials for children and parents.