Three very simple algorithms are presented that facilitate calculation of the analysis of variance for data from any block design. The first provides the sums of squares for treatments and error. The second calculates the treatment means with adjustment for any non-orthogonality and also gives the degrees of freedom. The third gives the constant needed to derive the variance of an unconfounded contrast from the error mean square. All depend upon sweeping and are therefore iterative. They are intended for use with experiments that have suffered damage and therefore no longer conform to any recognised design. They could also be useful when an experiment is conducted under such physical constraints that it has been necessary to adopt some unconventional design. Another use could arise when assessing students (treatments) who opt for different papers (blocks) in an examination, the papers being possibly of varying difficulty.