Slope and Grade Angle Calculator

On a construction site, slope is calculated from measurements: the difference in level between two points (rise) and the horizontal distance between them (run). From these you get the gradient as a percentage and ratio, the angle and the sloping length along the surface. This calculator does all of that from your survey or drawing measurements.

How to use it

1. Enter the rise, the vertical difference in level, for example from a level survey.
2. Enter the run, the horizontal distance.
3. Read the grade percentage, ratio, angle and sloping (inclined) length.

Formulas

• Grade % = rise / run × 100
• Ratio = 1 : (run / rise)
• Angle = arctan(rise / run)
• Sloping length = √(rise² + run²)

Worked example: driveway

A driveway rises 1.2 m over a horizontal distance of 15 m. Grade = 1.2 / 15 = 8%, ratio 1:12.5, angle 4.57°, sloping length = √(1.44 + 225) = 15.05 m. Many guidelines limit residential driveways to about 12 to 20%, so this is comfortable.

Worked example: drainage pipe

A 100 mm drain must fall at least 1:60. Over a 24 m run, the minimum fall is 24 / 60 = 0.40 m.

Why sloping length matters

Quantities measured along the surface, such as paving area, geotextile, turf or embankment protection, use the sloping length, not the horizontal run. On gentle slopes the difference is small, but on a 1:2 embankment the sloping length is 12% longer than the plan length.

Site tips

• Measure rise with a dumpy level or laser level, not by eye.
• Check local codes for maximum slopes of ramps, stairs, driveways and embankments.