What is the Angle of Depression?
The angle of depression is the angle formed between a horizontal line from the observer and the line of sight looking downward to an object below. In construction, this concept is essential for calculating drainage slopes, ramp grades, roof pitches viewed from above, and setting up surveying instruments for elevation shots.
The angle of depression from point A to point B equals the angle of elevation from point B to point A, by the alternate interior angles theorem. This reciprocal relationship is frequently used in surveying calculations.
Formula
Construction Applications
- Drainage Design: Storm water drainage pipes require a minimum slope (typically 1-2%) for gravity flow.
- ADA Ramp Design: Accessible ramps must not exceed a 1:12 slope ratio (4.76 degrees, 8.33% grade).
- Grading & Excavation: Site grading plans specify slopes as angles of depression from reference elevations.
- Surveying: Surveyors measure angles of depression with theodolites to calculate elevation differences.
- Roof Drainage: Flat roofs need minimum slopes for water runoff, typically 1/4" per foot (1.19 degrees).
Slope Reference Table
| Angle (degrees) | Slope (%) | Ratio | Typical Use |
|---|---|---|---|
| 0.5° | 0.87% | 1:115 | Flat roof minimum |
| 1.2° | 2.1% | 1:48 | Parking lot drainage |
| 2.9° | 5.0% | 1:20 | Sidewalk maximum |
| 4.8° | 8.3% | 1:12 | ADA ramp maximum |
| 14.0° | 25% | 1:4 | Steep driveway |
| 26.6° | 50% | 1:2 | 6/12 roof pitch |
| 45.0° | 100% | 1:1 | 12/12 roof pitch |
Frequently Asked Questions
What is the difference between angle of depression and angle of elevation?
The angle of depression is measured downward from a horizontal line, while the angle of elevation is measured upward. If you stand on a roof looking down at the ground, you use the angle of depression. If you stand on the ground looking up at the roof, you use the angle of elevation. They are equal in magnitude by geometry.
How do I convert between slope percentage and angle?
Slope percentage is (rise/run) x 100. To convert to angle: angle = arctan(slope% / 100). For example, a 5% slope = arctan(0.05) = 2.86 degrees. Conversely, angle to slope%: slope% = tan(angle) x 100.
What slope is required for drainage?
Most building codes require a minimum 2% slope (about 1/4 inch per foot) for surface drainage. Sewer pipes typically require 1-2% minimum slope depending on pipe diameter. Flat roofs need at least 1/4 inch per foot (1.19 degrees) per the International Building Code.