This study investigates the principles of frequency-size of geological disaster in loess hilly region. Baota district in Yan’an city in Shaanxi province is chosen as the typical geological disaster region in loess plateau. The database of geological disaster in Baota district is built through 3S technology

field survey and remote sensing interpretation. In the view of the holism and in the base of scale distribution analysis and maximum entropy principle

the theory that the parameters of frequency-size such as the length

width and thickness of collapse

landslide and unstable slope accorded with negative exponential distribution is come up for the first time using mathematical statistic method. As a result

a simple and effective formula about frequency- size distribution is put forward. At the end

the formula is verified by the example of Baota district. (1) The results mainly show that the geological disaster of Baota district is mainly middle-scale landslide and collapse; however

large-scale disaster plays important role in the control of total area and volume of collapse. (2) Then this study defines the grade index of volume size for researching size distribution of geological disaster. The results show that the size grade index of landslide

collapse and unstable slope is mainly in (5.5

6]

(4

4.5] and (5

5.5]

respectively. (3) The frequency-size distribution of collapse

landslide

and the length

width and thickness of unstable slope accord with the exponential relation; furthermore

the curve would not have rollover effect. (4) One of simple methods to solve the frequency-size distribution is to get the square root of area and cube root of volume. The results show that they present negative exponential distribution with a good fitting effect (R2>0.9

P<0.05). Thus the formula plays important role in the prediction of the occurrence frequency of landslide in any size.