Okay, let me see if I understand this.

Gradient, which is a PERCENTAGE is the vertical distance divided by the horizontal distance?

But this formula gives the ANGLE: arctan(verticla/horizontal) = a result in DEGREES?

If I have that right, I have two questions. First, which figure, percentage or degrees is most often used in hill descriptions (I think it is percentage)?

Second, since I'm trying to set up formulas for calculating the hills, I ran into a problem. Using Excel spreedsheet, it seems that "arctan" is not a term it recognizes. I found Atan, AtanH, and Atan2, but none of them seems to give a result like you show for the 1 mile vertical on a 5 mile ride. Any ideas on what the formula should be in excel?