The present article provides a detailed mathematical treatise on the geometry of skateboard transition ramps. These usually form a circular segment shape and are used in skateboarding for transitioning from a horizontal plane to another angle of incline. Transitions play a crucial role in the flow of skateparks and are required, for example, for quarter pipes, mini ramps, vert ramps, or jump ramps. Skateboarding has been an Olympic sport since 2023, yet many publicly funded skateparks still do not meet the demands of the sport. On one hand, there is often a lack of willingness from authorities to engage with the athletes beforehand; on the other hand, the people involved in the planning process often lack the necessary experience and mathematical expertise to perfectly fulfill the users' needs. Thoughtful planning is particularly crucial for ramps with curved surfaces to ensure the flow of the skatepark. In addition to the mathematical analysis, source codes for programs are provided to make the calculations as convenient as possible for all users.