An elevator comprising: an elevator shaft defined by surrounding walls and top and bottom end terminals; an elevator car vertically movable in the elevator shaft; an elevator hoisting machinery adapted to drive the elevator car; an electromechanical braking apparatus (12A, 12B) configured to brake movement of the elevator car; a first measuring device (14A, 14B, 14C) adapted to provide first position data and first speed data of the elevator car; a second measuring device (15A, 15B) adapted to provide at least a second position data of the elevator car; a safety monitoring unit communicatively connected to the first measuring (14A, 14B, 14C) device and the second measuring device (15A, 15B) and configured to determine a synchronized position of the elevator car from the first and the second position data, and to determine an elevator car slowdown failure in the proximity of the top or the bottom end terminal from the first speed data and from the synchronized position of the elevator car, wherein the safety monitoring unit is adapted to cause braking of the elevator car with the electromechanical braking apparatus (12A, 12B) upon determination of the slowdown failure, characterised by: the safety monitoring unit is configured to calculate from the current speed data onwards, with the maximum acceleration, speed prediction for the elevator car speed after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate from the current synchronized position onwards, with the maximum acceleration, the closest possible position of an approaching elevator car to the top or bottom end terminal after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate a maximum initial speed for the elevator car to decelerate from said closest possible position to the terminal speed of said top or bottom end terminal, to determine an elevator car slowdown failure if said speed prediction meets or exceeds said maximum initial speed. an elevator shaft defined by surrounding walls and top and bottom end terminals; an elevator car vertically movable in the elevator shaft; an elevator hoisting machinery adapted to drive the elevator car; an electromechanical braking apparatus (12A, 12B) configured to brake movement of the elevator car; a first measuring device (14A, 14B, 14C) adapted to provide first position data and first speed data of the elevator car; a second measuring device (15A, 15B) adapted to provide at least a second position data of the elevator car; a safety monitoring unit communicatively connected to the first measuring (14A, 14B, 14C) device and the second measuring device (15A, 15B) and configured to determine a synchronized position of the elevator car from the first and the second position data, and to determine an elevator car slowdown failure in the proximity of the top or the bottom end terminal from the first speed data and from the synchronized position of the elevator car, wherein the safety monitoring unit is adapted to cause braking of the elevator car with the electromechanical braking apparatus (12A, 12B) upon determination of the slowdown failure, characterised by: the safety monitoring unit is configured to calculate from the current speed data onwards, with the maximum acceleration, speed prediction for the elevator car speed after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate from the current synchronized position onwards, with the maximum acceleration, the closest possible position of an approaching elevator car to the top or bottom end terminal after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate a maximum initial speed for the elevator car to decelerate from said closest possible position to the terminal speed of said top or bottom end terminal, to determine an elevator car slowdown failure if said speed prediction meets or exceeds said maximum initial speed. the safety monitoring unit is configured to calculate from the current speed data onwards, with the maximum acceleration, speed prediction for the elevator car speed after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate from the current synchronized position onwards, with the maximum acceleration, the closest possible position of an approaching elevator car to the top or bottom end terminal after reaction time of the electromechanical braking apparatus (12A, 12B), to calculate a maximum initial speed for the elevator car to decelerate from said closest possible position to the terminal speed of said top or bottom end terminal, to determine an elevator car slowdown failure if said speed prediction meets or exceeds said maximum initial speed.