During a fixed axis camera rotation every image point is moving on a conic section. If the point is a vanishing point the conic section is invariant to possible translations of the observer. Given the rotation axis and the inter-frame correspondence of a set of parallel lines we are able to compute the intrinsic parameters without knowledge of the rotation angles. We propagate the error covariances and we remove the bias in the computation of the conic. We experimentally study the sensitivity of calibration to the amount of rotation and we compare our performance to the performance of a recent active calibration technique.