Many factors contribute to the width of a tornado. Things like actual tornado size, cloud base height, moisture content of the air all play a role. Overall though, a storm that produces a mile wide tornado has a violent, broad area of rotation as opposed to a smaller, tighter area of rotation.
9/10 times, the wider the tornado, the stronger the tornado. Reason being, you need more energy involved to rotate this large area of a thunderstorm; that energy is translated into high wind speeds and stronger storms.
The average width of a tornado is about 200 yards, or 1/10 mi. Mile-wide tornadoes are quite rare, and the all time record for width is a mammoth 2.5 miles (Nebraska, 2004). This should serve as a sort of "ceiling" for conceivable width, although there's nothing to say that something larger COULDN'T happen.
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