A calculable sensor has been developed for electrical impedance tomography. An analytical model of the sensor is established, in order to show the calculable property of the sensor. The sensor obtains the information of both conductivity distribution and permittivity distribution of the cross-section of the pipe and provides a new strategy of dual mode tomography. Experimental results on the prototype are presented to validate the calculable property of the sensor, and to illustrate the effectiveness of the model with a fast and robust image restoration algorithm based on the energy method.