We applied a data-driven method to derive the invisible energy for air showers using the publicly available data of the KASCADE experiment. The universal relation between the invisible energy and the number of muons measured by the shielded KASCADE detectors was adopted. In this way, we determine the invisible energy for the first time from measured data between PeV and EeV energies. We also present new energy calibration of the signals induced in KASCADE detectors exploiting the lateral shape parameter and reducing the bias on the estimated shower energy.