Simple, approximate formulas are developed to calculate the mean gain and excess noise factor for avalanche photodiodes using the dead-space multiplication theory in the regime of small multiplication width and high applied electric field. The accuracy of the approximation is investigated by comparing it to the exact numerical method using recursive coupled integral equations and it is found that it works for dead spaces up to 15% of the multiplication width, which is substantial. The approximation is also tested for real materials such as GaAs, InP and Si for various multiplication widths, and the results found are accurate within ∼ 15% of the actual noise, which is a significant improvement over the local-theory noise formula. The results obtained for the mean gain also confirm the recently reported relationship between experimentally determined local ionization coefficients and the enabled non-local ionization coefficients.