Several data sets for the electrical breakdown in air of single-wall carbon nanotubes (SWNTs) on insulating substrates are collected and analyzed. A universal scaling of the Joule breakdown power with nanotube length is found, which appears to be independent of the substrate thermal properties of their thickness. This suggests that the thermal resistances at SWNT-insulator and at SWNT-electrode interfaces govern heat sinking from the nanotube. Analytical models for the breakdown power scaling are presented, providing an intuitive, physical understanding of the breakdown process. The electrical and thermal resistances at the electrode contacts limit the breakdown behavior for sub-micron SWNTs; the breakdown power scales linearly with length for tubes that are microns long, and a minimum breakdown power (∼0.05 mW) is observed for the intermediate (∼0.5 µm) length range.