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How to express the size of slope with mathematical formula?
Use the percentage method.

The most commonly used method to express the slope, that is, the percentage of the height difference between two points and its horizontal distance, is calculated as follows: slope = (height difference/horizontal distance) x 100%. When percentages are used, I = h/l x 100%.

For example, a slope of 3% means that the horizontal distance rises (falls) by 3 meters every 100 meters; 1% means every 100m in the horizontal direction and every 1m in the vertical direction. And so on.

Degree method: the slope is expressed in degrees and calculated by inverse trigonometric function, and its formula is as follows: tanα (slope) = height difference/horizontal distance.

So α (slope) =arc tan (height difference/horizontal distance)

Extended data:

The measurement method of automobile climbing ability is slope. This slope is not the angle of the slope we usually understand, but the ratio of the height of the slope to the horizontal distance. Generally expressed as a percentage, it can also be expressed as a decimal. that is

Slope = (horizontal distance of height/slope) * 100%

For example, if the slope of a road is 30%, the vertical height will actually increase by 30 meters every time the horizontal distance advances 100 meters, but the angle of this road is16 42 ",not 30. The slope is 100% and the slope angle is 45.

The gradient of urban roads is generally less than 5%, and it is steep when it exceeds 10%. The design speed is 120, and its slope generally cannot exceed 5%. The slope of "Devil's Highway" in Yunnan is over 8%, so accidents occur frequently. Our underground parking lot looks steep. In fact, the designed slope is only about 15%, which is about 8.6 when converted into an angle.