Randomised trials confirm that anticoagulants reduce the risk of emboli in atrial fibrillation. To apply this evidence to practice, we developed an expression relating all relevant factors. Trial-based estimates of the risks of emboli and haemorrhage, and of the effects of anticoagulants on these risks were used to derive the extent to which haemorrhage has to be seen to be more detrimental than emboli to justify not using anticoagulants. Information from other studies was used to assess the risks for the types of patients not included in the trials. Haemorrhage needs to be assessed as being at least six times more detrimental than emboli to warrant withholding anticoagulants from patients like those in the trials. Only in patients with lone atrial fibrillation and in those with features suggesting a bleeding risk six times higher than the trials' average would a perception of equal detriment risk justify not giving anticoagulation.