  Scintillation detectors are essential tools for radiation measurement, but
calibrating them accurately can be challenging, especially when full-energy
peaks are not prominent. This is common in detectors like plastic
scintillators. Current methods for calibrating these detectors often require
manual adjustments. To address this, we propose a new method called the
convolution model. This model accurately calibrates the energy-channel
relationship of the Compton edge in various detectors. We tested it with
plastic scintillator BC408, NaI crystal, and LaBr$_3$ crystal. Using
${}^{137}$Cs radioactive sources, we calibrated NaI and LaBr$_3$ detectors
using full-energy peaks, then applied the convolution model to fit the Compton
edge. Our results show errors within 1\% when compared to full-energy peak
calibration.
