How is a 45-degree slope expressed in percentage?

To express a slope in percentage, the formula used is:

[

\text{Percentage} = \left( \frac{\text{Rise}}{\text{Run}} \right) \times 100

]

In the case of a 45-degree slope, the rise and run are equal, meaning for every unit of vertical rise, there is an equal unit of horizontal run. This gives a rise/run ratio of 1, or:

[

\text{Percentage} = \left( \frac{1}{1} \right) \times 100 = 100%

]

Thus, a 45-degree slope corresponds to a 100% slope when expressed in percentage terms. Understanding this relationship is crucial for various applications, such as construction or landscaping, where slope assessment is important for safety and performance.