A 45-degree slope is equal to what percentage slope?

To determine the percentage slope corresponding to a 45-degree angle, it's important to understand how to calculate slope percentage from an angle. The formula to convert degrees into a percentage is derived from the tangent of the angle.

The tangent of a 45-degree angle is 1, which means that for every 1 unit of vertical rise, there is an equal horizontal run of 1 unit. To express this as a percentage, you multiply the tangent value by 100. Therefore:

1 (tangent of 45 degrees) x 100 = 100%

However, because a percentage slope is typically expressed as the ratio of the rise to the run, the calculation can also be approached through a shift in perspective: for a 45-degree slope, if we consider the sides of a right triangle where both the rise and the run are equal, the slope can be considered as a 1:1 ratio (which translates back to the tangent).

When you express this ratio as a percentage, you again arrive at the conclusion that a 45-degree slope translates into a 100% slope. Therefore, a 45-degree slope directly corresponds to a percentage slope of 100%.