A gage for detecting the diameter of a bolt hole back socket, consisting of a go side cylinder, a holder I, a digital depth gage I, a screw I, a handle, a no-go side cylinder, a holder II, a digital depth gage II and a screw II; wherein the go side cylinder is fixed at one end of the handle via the screw I; the diameter of the go side cylinder is equal to a lower deviation of the plane diameter of a bolt hole back socket; a cylinder through hole is formed on the left side of the go side cylinder; the digital depth gage I is fixed on the go side cylinder via the holder I so that the gage is adapted to determine whether the lower deviation of the plane diameter of the bolt hole back socket is qualified, wherein the no-go side cylinder is fixed at the other end of the handle via the screw II, the diameter of the no-go side cylinder is equal to the upper deviation of the plane diameter of the bolt hole back socket, and a cylinder through hole is formed on the right side of the no-go side cylinder; the digital depth gage II is fixed on the no-go side cylinder via the holder II so that the gage is adapted to determine whether the upper deviation of the plane diameter of the bolt hole back socket is qualified; wherein the gage is adapted to determine whether the lower deviation of the plane diameter of the bolt hole back socket is qualified as follows: in a first initial state, a lower side of the go side cylinder is placed on the plane of the bolt hole back socket, wherein a top of a probe of the digital depth gage I and the upper surface of the go side cylinder are on one horizontal plane; during a first measurement, the probe of the digital depth gage I is pressed through the cylinder through hole to contact the plane of the bolt hole back socket via the cylinder through hole; and after the first measurement, the probe automatically rebounds and returns to the first initial state. wherein the go side cylinder is fixed at one end of the handle via the screw I; the diameter of the go side cylinder is equal to a lower deviation of the plane diameter of a bolt hole back socket; a cylinder through hole is formed on the left side of the go side cylinder; the digital depth gage I is fixed on the go side cylinder via the holder I so that the gage is adapted to determine whether the lower deviation of the plane diameter of the bolt hole back socket is qualified, wherein the no-go side cylinder is fixed at the other end of the handle via the screw II, the diameter of the no-go side cylinder is equal to the upper deviation of the plane diameter of the bolt hole back socket, and a cylinder through hole is formed on the right side of the no-go side cylinder; the digital depth gage II is fixed on the no-go side cylinder via the holder II so that the gage is adapted to determine whether the upper deviation of the plane diameter of the bolt hole back socket is qualified; wherein the gage is adapted to determine whether the lower deviation of the plane diameter of the bolt hole back socket is qualified as follows: in a first initial state, a lower side of the go side cylinder is placed on the plane of the bolt hole back socket, wherein a top of a probe of the digital depth gage I and the upper surface of the go side cylinder are on one horizontal plane; during a first measurement, the probe of the digital depth gage I is pressed through the cylinder through hole to contact the plane of the bolt hole back socket via the cylinder through hole; and after the first measurement, the probe automatically rebounds and returns to the first initial state.