This paper applies linear elastic theory and Castigliano's first theorem to design nonlinear (stiffening) flexures used as load cells with both large force range and large resolution. Low stiffness at small forces causes high sensitivity, while high stiffness at large forces prevents over-straining. With a standard 0.1 lm deflection sensor, the nonlinear load cell may detect 1% changes in force over five orders of force magnitude. In comparison, a traditional linear load cell functions over only three orders of magnitude. We physically implement the nonlinear flexure as a ring that increasingly contacts rigid surfaces with carefully chosen curvatures as more force is applied. We analytically describe the load cell performance as a function of its geometry. We describe methods for manufacturing the flexure from a monolithic part or multiple parts. We experimentally verify the theory for two load cells with different parameters.