One slope, five ways to write it
A slope is rise over run. Plans write it in whichever form suits the trade: road and site grades as a percent, embankments as a horizontal to vertical ratio, ramps as rise to run, pipes as a percent or inches per foot, and survey and structural work in degrees. They are all the same number underneath, and converting between them is simple arithmetic that is easy to get backwards in a hurry.
How to convert a slope to a percent grade
Type the slope in any box and the others follow. Percent grade is rise divided by run, times 100. H:V is run divided by rise, to 1. Rise:run is 1 to run divided by rise. Degrees is the arctangent of rise over run. Inches per foot is rise over run, times 12. The formulas are listed under the boxes so you can show your working.
H:V or V:H: read the order
The most common slope mistake is reading a ratio backwards. Civil and geotechnical drawings write side slopes horizontal first, so a 3:1 slope is 3 across for every 1 up, about 33%. Accessibility rules write rise first, so a 1:12 ramp is 1 up for every 12 across, 8.33%. A 3:1 embankment read as 1:3 would be three times steeper than intended. When a note is unclear, write it with letters, such as 3H:1V, and the ambiguity goes away.
Grades between points
Grading plans are full of spot elevations. The grade between two of them is the difference in elevation divided by the horizontal distance between them. Enter both elevations and the distance to get the grade, its H:V ratio, the rise, and the length measured along the slope. To go the other way, enter a start elevation, a grade (negative when it falls), and a distance to get the elevation at the end, the way you'd set a flow line or a finished grade.
Slopes worth knowing
- 1:48 (2.08%): the steepest cross slope on an accessible walking surface (2010 ADA Standards, 403.3).
- 1:20 (5%): the steepest running slope for an accessible walking surface that isn't a ramp (403.3).
- 1:12 (8.33%): the steepest running slope for an accessible ramp (405.2).
- 4:1, 3:1, and 2:1 (25%, 33.3%, 50%): side slopes you will see on grading plans; the allowed steepness depends on the soil, the use, and local rules.
Slopes on the drawing
Slopes come off plans as spot elevations, contour spacing, and labelled grades. The free grading tool draws contours from feature lines you sketch on a site plan, and the measure tool gives the horizontal distance between two spots at the drawing's scale, which is the run this calculator needs.