Hematocrit (Hct) values after the initiation of cardiopulmonary bypass (CPB) must be maintained appropriately to avoid perioperative complications. Therefore, an accurate prediction is required. However, the standard prediction equation often results in actual values that are lower than the predicted values. This study aimed to clarify the limits of agreement (LOA) and bias of the prediction equations and investigate better the prediction equations. A retrospective study was performed on adult patients between April 2015 and December 2020. Study 1 included 158 patients, and Study 2 included 55 patients. The primary outcomes were the LOA and bias between the predicted and measured Hct values after the initiation of CPB, and two studies were conducted. In Study 1, total blood volume (TBV) was estimated, and the new blood volume index (BVI) was calculated. BVI was also evaluated for the overall value and gender differences. Therefore, the patient’s background was compared by gender differences. In, Study 2 the conventional predicted equation (Eq. 1), the predicted equation using the new BVI (Eq. 2), and the predicted equation using the new BVI including physiological factors in the TBV equation (Eq. 3) were compared. In Study 1, BVI was 53 (44–67) mL/kg. In Study 2, bias ± LOA was − 2.5 ± 6.8% for Eq. 1, 0.1 ± 6.6% for Eq. 2, and 0.4 ± 6.2% for Eq. 3. The new equation is expected to predict the Hct value after the initiation of CPB with better LOA and bias than the conventional equation.