The calorimetric energy of a cosmic-ray shower is measured by optical telescopes from the emission of isotropic fluorescence light or from the collimated Cherenkov light through the number of charged secondary particles. To reconstruct the energy of the primary cosmic ray the calorimetric energy needs to be further corrected for the energy that is not deposited in the atmosphere. This invisible energy is a substantial source of systematic uncertainties in the energy spectrum of cosmic rays measured by optical telescopes below 1 EeV. Usually, estimations of the invisible energy below 1 EeV relied on Monte Carlo simulations despite the fact that models of hadronic interactions have problems in describing the measured air-shower data. We apply a data-driven method to derive the invisible energy for air showers using the publicly available data of the KASCADE and IceTop experiments. The universal relation between the invisible energy and the number of muons measured by the detectors was utilized. In this way, we determine the invisible energy from measured data between PeV and EeV energies and compare with invisible-energy models adopted at the Pierre Auger and Telescope Array observatories.