We demonstrate an optomechanical accelerometer that uses an optical frequency comb readout method and internal calibration to perform acceleration measurements with low uncertainty. The resulting intrinsic accuracy was evaluated in comparison to a primary vibration calibration system and gravity. The average agreement was found to be 2.1 % of the calibration system from 0.1 kHz to 15 kHz and better than 0.2 % for the static acceleration due to gravity. This performance shows that low-uncertainty acceleration measurements can be performed using an in-situ characterization of the sensor parameters, obviating the need for external calibrations using traditional methods. This capability could greatly enhance the performance of inertial and remotely deployed accelerometers. Due to the fundamental nature of the internal calibration, it could be extended to other optomechanical transducers, including force and pressure sensors.