Bourke and Smith developed 2 equations to estimate the allowable blood loss for a patient who is bleeding and who is to be replaced only with colloid solutions. This can help identify patients who might not need blood transfusion, as well as to decide when to start using blood products. This allows for better use of blood inventory.

allowable blood loss in mL =

= (blood volume in mL) * LN ((initial hematocrit) / (final hematocrit)) =

= (blood volume in mL) * ((LN(initial hematrocrit)) -  (LN(final hematrocrit)))



• Hematocrits may be either as percents (from 0 to 100) or as decimal fractions (0 to 1)

• The final hematocrit is the lowest allowable hematocrit for the patient.


Since they felt that natural logarithm tables might not be available to clinicians, they developed a second equation that they thought would be easier to calculate.


allowable blood loss in mL =

= (blood volume in mL) * ((initial hematocrit) - (final hematocrit)) * (3 – (average of the 2 hematocrits))


average of the 2 hematocrits =

= ((initial hematocrit) – (final hematocrit)) / 2



• Hematocrits are in decimal fractions


NOTE: This method seems to slightly overestimate the blood volume as compared to other equations.

To read more or access our algorithms and calculators, please log in or register.