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We investigate the origin of the coplanar helicoidal magnetic structure andthe ferroelectric polarization in Cu3Nb2O8 by combining first-principlescalculations and our spin-induced ferroelectric polarization model. Thecoplanar helicoidal spin state comes from the competition between the isotropicexchange interactions, and the ferroelectric polarization from the symmetricexchange striction with slight spin canting. However, the direction of thepolarization is not determined by the orientation of the spin rotation plane.

Helicoidal magnetic structure and ferroelectric polarization in Cu3Nb2O8