The equilibrated residual method provides a posteriori estimates without generic constants in the main term and can also be found with the name hypercircle method. The essential idea is a comparison of a primal and a dual variational problem and may be traced back to Prager and Synge [1949]. The method is extended here to the nonconforming element of M. Crouzeix and P.-A. Raviart [Rev. Franc. Automat. Inform. Rech. Operat. 7(1973), R-3, 33–76 (1974; Zbl 0302.65087)]. Roughly speaking the error is split into a conforming and a nonconforming part. To this end a Helmholtz decomposition is applied to the nonconforming gradient. When there are jumps in the coefficients, the nonmonotonicity of the jumps on paths around a node gives rise a multiplicative factor in the error bound.