We derive inequalities which restrict the precision of the Stokes parameters imposed by photon noise. The signal-to-noise ratio of the measured Stokes parameters is never better than the square root of the number of detected photons. In case of weakly polarized sources (i.e., most astronomical sources), such an inequality imposes no practical limit and it should be replaced by the intensity-to-noise ratio, which approximately follows the same square root law. Besides these general results, we also find relationships between the errors of the Stokes parameters which apply to particular (although fairly common) analyzers. The equations are presented in a device-independent fashion, so that they can be used to tell, in an absolute sense, whether photon noise allows the measurement of small polarimetric signals.