Measurements of the absorbed dose and quality assurance programs play an important role in radiotherapy. Ionization chambers (CIs) are considered the most important dosimeters for their high accuracy, practicality and reliability, allowing absolute dose measurements. However, they have a relative large physical size, which limits their spatial resolution, and require a high bias voltage to achieve an acceptable collection of charges, excluding their use for in vivo dosimetry. In this paper, we propose new real time radiation detectors with electrodes based on graphene or vertically aligned multiwall carbon nanotubes (MWCNTs). We have investigated their charge collection efficiency and compared their performance with electrodes made of a conventional material. Moreover, in order to highlight the effect of nanocarbons, reference radiation detectors were also tested. The proposed dosimeters display an excellent linear response to dose and collect more charge than reference ones at a standard bias voltage, permitting the construction of miniaturized CIs. Moreover, an MWCNT based CI gives the best charge collection efficiency and it enables working also to lower bias voltages and zero volts, allowing in vivo applications. Graphene based CIs show better performance with respect to reference dosimeters at a standard bias voltage. However, at decreasing bias voltage the charge collection efficiency becomes worse if compared to a reference detector, likely due to graphene's semiconducting behavior.