It turns out that the incline (incline, or grade) – the steepness of a road or slope – has quite an obvious definition, but I never really thought about it. It means the ratio of the projection of a line on the terrain to the vertical plane to the projection of the same line on the horizontal. In other words, the magnitude of the incline equals the tangent of the angle between the rise of the slope and the horizontal (the tangent of the angle of inclination).
Thus, a “steep climb” sign of 10% indicates just about 5.71 degrees of inclination. This is arctan(0.1).
It also turned out that formally among specialists when reading the notation, the “%” sign is pronounced as “hundredths.”









