Extracorporeal blood treatment apparatus, comprising: a blood treatment device; an extracorporeal blood circuit (6, 7) coupled to the blood treatment device, the extracorporeal blood circuit (6, 7) comprising a blood withdrawal line connected to a blood inlet port of the blood treatment device and blood return line connected to a blood outlet port of the blood treatment device; a blood pump, a pump section of the extracorporeal blood circuit (6, 7) being configured to be coupled to the blood pump; optionally, a treatment fluid circuit operatively connected to the extracorporeal blood circuit (6, 7) and/or to the blood treatment device; at least a pressure sensor (24, 25) located in a respective measurement site on the extracorporeal blood circuit (6, 7), said at least a pressure sensor (24, 25) comprising a first pressure sensor located on the blood withdrawal line upstream the blood treatment device and a second pressure sensor located on the blood return line downstream the blood treatment device; an electronic control unit operatively connected at least to the pressure sensor (24, 25); wherein the electronic control unit is configured to perform at least the following procedure: - receiving from the second pressure sensor a signal correlated to a second measured blood pressure (P2measured) in the measurement site; characterized in that the procedure further comprises: - correcting the second measured blood pressure (P2measured) through a second mathematical correction model to obtain a second blood actual pressure (Poutlet) in a reference site other than the measurement site; the reference site being at the blood outlet port of the blood treatment device, wherein, between the reference site and the measurement site, a circuit section is positioned; wherein the second mathematical correction model is a model of a pressure drop in the circuit section, the second mathematical correction model being a function of blood flow rate in the circuit section. a blood treatment device; an extracorporeal blood circuit (6, 7) coupled to the blood treatment device, the extracorporeal blood circuit (6, 7) comprising a blood withdrawal line connected to a blood inlet port of the blood treatment device and blood return line connected to a blood outlet port of the blood treatment device; a blood pump, a pump section of the extracorporeal blood circuit (6, 7) being configured to be coupled to the blood pump; optionally, a treatment fluid circuit operatively connected to the extracorporeal blood circuit (6, 7) and/or to the blood treatment device; at least a pressure sensor (24, 25) located in a respective measurement site on the extracorporeal blood circuit (6, 7), said at least a pressure sensor (24, 25) comprising a first pressure sensor located on the blood withdrawal line upstream the blood treatment device and a second pressure sensor located on the blood return line downstream the blood treatment device; an electronic control unit operatively connected at least to the pressure sensor (24, 25); wherein the electronic control unit is configured to perform at least the following procedure: - receiving from the second pressure sensor a signal correlated to a second measured blood pressure (P2measured) in the measurement site; - receiving from the second pressure sensor a signal correlated to a second measured blood pressure (P2measured) in the measurement site; characterized in that the procedure further comprises: - correcting the second measured blood pressure (P2measured) through a second mathematical correction model to obtain a second blood actual pressure (Poutlet) in a reference site other than the measurement site; the reference site being at the blood outlet port of the blood treatment device, wherein, between the reference site and the measurement site, a circuit section is positioned; wherein the second mathematical correction model is a model of a pressure drop in the circuit section, the second mathematical correction model being a function of blood flow rate in the circuit section. - correcting the second measured blood pressure (P2measured) through a second mathematical correction model to obtain a second blood actual pressure (Poutlet) in a reference site other than the measurement site; the reference site being at the blood outlet port of the blood treatment device, wherein, between the reference site and the measurement site, a circuit section is positioned; wherein the second mathematical correction model is a model of a pressure drop in the circuit section, the second mathematical correction model being a function of blood flow rate in the circuit section.