What factor represents the difference in light intensity for one whole-number magnitude step?

Approximately 2.512

The modern, precise astronomical magnitude scale is built upon a specific logarithmic relationship reflecting how the human eye perceives light intensity, rather than perceiving it linearly. Astronomers standardized the difference between any two consecutive whole-number magnitudes to correspond to a fixed multiplicative factor in terms of light received. This standardization dictates that a star one magnitude brighter must be brighter by a factor of approximately 2.512 times than the dimmer star. For instance, a magnitude 1 star is about 2.512 times brighter than a magnitude 2 star. This factor is the fundamental unit used to calculate larger brightness differences across multiple magnitude steps, as it quantifies the fixed ratio by which light intensity changes for every single step along the scale.