The absolute response of a real-time proton detector, composed of a microchannel plate (MCP) assembly, an imaging lens, and a charge-coupled device (CCD) camera, is calibrated for the spectral characterization of laser-accelerated protons, using a Thomson parabola spectrometer (TPS). A slotted CR-39 plate was used as an absolute particle-counting detector in the TPS, simultaneously with the MCP-CCD detector to obtain a calibration factor (count/proton). In order to obtain the calibration factor as a function of proton energy for a wide range of proton numbers, the absolute response was investigated for different operation parameters of the MCP-CCD detector, such as MCP voltage, phosphor voltage, and CCD gain. A theoretical calculation for the net response of the MCP was in good agreement with the calibrated response of the MCP-CCD detector, and allows us to extend the response to higher proton energies. The response varies in two orders of magnitude, showing an exponential increase with the MCP voltage and almost linear increase with the phosphor voltage and the CCD gain. The calibrated detector enabled characterization of a proton energy spectrum in a wide dynamic range of proton numbers. Moreover, two MCP assemblies having different structures of MCP, phosphor screen, and optical output window have been calibrated, and the difference in the absolute response was highlighted. The highly-sensitive detector operated with maximum values of the parameters enables measuring a single proton particle and evaluating an absolute spectrum at high proton energies in a single laser shot. The absolute calibrations can be applied for the spectral measurement of protons using different operating voltages and gains for optimized response in a large range of proton energy and number.