Tornadoes form in unusually violent thunderstorms when there is sufficient (1) instability, and (2) wind shear present in the lower atmosphere. Instability refers to warmer and more humid than usual conditions in the lower atmosphere, and possibly cooler than usual conditions in the upper atmosphere. Wind shear in this case refers to the wind direction changing, and the wind speed increasing, with height. An example would be a southerly wind of 15 mph at the surface, changing to a southwesterly or westerly wind of 50 mph at 5,000 feet altitude.

This kind of wind shear and instability is usually exists only ahead of a cold front and low pressure system. The intense spinning of a tornado is partly the result of the updrafts and downdrafts in the thunderstorm (caused by the unstable air) interacting with the wind shear, causing a tilting of the wind shear to form and upright tornado vortex. Helping the process along, cyclonically flowing air around the cyclone, already slowly spinning in a counter-clockwise direction (in the Northern Hemisphere), converges inward toward the thunderstorm, causing it to spin faster. This is the same process that causes an ice skater to spin faster when she pulls her arms in toward her body.

Other processes can enhance the chances for tornado formation. For instance, dry air in the middle atmosphere can be rapidly cooled by rain in the thunderstorm, strengthening the downdrafts that are needed for tornado formation. Notice that, in virtually every picture you see of a tornado, the tornado has formed on the boundary between dark clouds (the storm updraft region) and bright clouds (the downdraft region), evidence for the importance of updrafts and downdrafts to tornado formation. Also, an isolated strong thunderstorm just ahead of a squall line that then merges with the squall line often becomes tornadic; isolated storms or more likely to form tornadoes than squall lines, since an isolated storm can form a more symmetric flow pattern around it and also have less competition for unstable air "fuel" than if it were part of a solid line of storms.

Because both instability and wind shear are necessary for tornado information, sometimes weak tornadoes can occur when the wind shear conditions are strong, but the atmosphere is not very unstable. This sometimes happens in southern California in the winter, for instance, when a strong low pressure system comes ashore. Similarly, weak tornadoes can occur when the airmass is very unstable, but has little wind shear. For instance, Florida has many weaker tornadoes of this variety. Of course, the most violent tornadoes occur when both strong instability and strong wind shear are present.