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This paper presents the analytical in-plane compliance calculation methods for single axis circular flexure hinges and compares the methods with Finite Element Analysis (FEA). These comparisons are also made for varying geometric parameters not only for “b” (the width of the flexure) but also “t” (the shortest distance of the flexure) parameter. The analyses give us the selectable calculation methods for certain “b” and “t” parameters besides they show which geometric parameter (b or t) have more influence on in which direction of compliances. Thus, while designing a flexure based mechanism this work gives us the advantage of selecting right in-plane compliance calculation methods which are less time consuming and easier than FEA and it also helps us to choose the right geometric parameters by showing the effects of them on the compliances.