This paper analyses the dual-ramp A to D converter error due to dielectric absorption of the integrator capacitor with a rigorous mathematical method. It is proved that if the dual-ramp A to D converter runs continuously and if same voltage have been measured for a sufficiently long time the dielectric absorption of the integrator capacitor will not cause any error. When measured voltage changes abruptly the dielectric absorption of capacitor will cause error for first a few measurements. The formula for calculating error and its time constant is obtained.