This paper presents an efficient and accurate numerical analysis technique to simulate single event upsets (SEUs) in logic circuits. Experimental results that show the method is accurate to within 10% of the results obtained using SPICE are provided. The proposed method is used to study the ability of a CMOS gate to tolerate SEUs as a function of injected charge and transistor sizing (aspect ratio W/L). A novel radiation hardening technique to calculate the minimum transistor size required to make a CMOS gate immune to SEUs is also presented. The results agree well with SPICE simulations, while allowing for very fast analysis. The technique can be easily integrated into design automation tools to harden sensitive portions of logic circuits.