Originally Posted by AndrewP

Grade is vertical rise divided by distance traveled, so a 45 degree hill is 71%, not 100%. The error in using the rise divided by horizontal distance (as read from a map) is only 0.1% for a 14% grade, and 0.01% for a 7% grade. When grades were being measured during the construction of railways they measured the distance tranveled by the engine and the altitude gained, and 5% was the most they could take without wheel spin.