Depression Angle — Surveying & Construction Trigonometry
Compute the angle of depression from observer height, target height, and horizontal distance. Supports three modes: from heights and distance, from known angle and distance, or from slope percentage. Used in surveying, construction layout, and engineering.
Why This Construction Metric Matters
Why: Depression angles are essential for surveying elevation differences, building height verification, drainage design, and ADA ramp compliance. Accurate angles ensure proper sight lines, drainage slopes, and accessibility.
How: θ = arctan((observer height − target height) / horizontal distance). From slope: θ = arctan(slope%/100). Line of sight = √(D² + (H₁−H₂)²). All calculations use consistent units (feet or meters).
- ●Ensure horizontal reference is level; instrument calibration matters.
- ●1% slope ≈ 0.57°; 8.33% (1:12) ≈ 4.76° for ADA ramps.
- ●Height errors amplify at long distances; verify measurements.
- ●Atmospheric refraction affects very long sight lines.
Compact Examples
From Heights & Distance
Calculate angle from observer height, target height, and horizontal distance
📐 Input Values
Planning estimates only. Verify with a licensed engineer or contractor before construction.
📐 Construction Industry Facts
Depression = angle from horizontal downward to line of sight
— Trigonometry
ADA ramp max slope: 8.33% (1:12) = 4.76°
— ADA 405.2
Aircraft approach angles typically 2.5°–6°
— FAA
Drainage pipe fall: 0.5°–5° typical
— IPC
📋 Key Takeaways
- • θ = arctan((H₁ − H₂) / D) | Depression = angle from horizontal downward
- • Elevation = 90° − θ | Line of sight = √(D² + (H₁−H₂)²)
- • Slope % → angle: θ = arctan(slope/100) | 1% ≈ 0.57°, 10% ≈ 5.71°
- • Modes: from heights, from angle, from slope %
Did You Know?
Depression = angle from horizontal down. Elevation = complement.
Source: Trigonometry
Surveying: measure elevation differences between points.
Source: Surveying
Aircraft approach: typically 2.5°–6° glide path.
Source: Aviation
ADA ramp max slope: 4.76° (1:12).
Source: ADA
Drainage: 0.5°–5° for pipe fall.
Source: Plumbing
Ski slopes: 15°–35° typical. Black diamond ~30°+.
Source: Skiing
How It Works
θ = arctan(rise/run). From heights: rise = H₁−H₂, run = D. From slope: θ = arctan(slope%/100).
From Heights
θ = arctan((H₁ − H₂) / D)
From Slope
θ = arctan(slope% / 100)
Expert Tips
Level Check
Ensure horizontal reference is level.
Units
Use consistent ft or m.
Accuracy
Height errors amplify at long distances.
Refraction
Atmospheric refraction affects long sight lines.
Slope to Angle Comparison
| Slope % | Angle | Use |
|---|---|---|
| 1% | ~0.57° | Drainage |
| 5% | ~2.86° | Gentle ramp |
| 8.33% | ~4.76° | ADA max |
| 10% | ~5.71° | Moderate |
| 25% | ~14.04° | Steep |
Frequently Asked Questions
What is angle of depression?
Angle from horizontal downward to line of sight. Complement of elevation angle (90° − θ).
What is the formula from heights?
θ = arctan((observer height − target height) / horizontal distance). All units must be consistent.
What is 1% slope in degrees?
arctan(0.01) ≈ 0.57°. Slope % = (rise/run) × 100.
What is ADA ramp max slope?
1:12 = 8.33% = 4.76° max slope. Ensures wheelchair accessibility compliance.
What is the line of sight formula?
L = √(D² + (H₁−H₂)²). Direct distance from observer to target.
What are typical aircraft approach angles?
Typically 2.5°–6° for landing glide path. Varies by aircraft type.
Key Numbers
📚 Sources
⚠️ Disclaimer: Calculations are for planning. Verify with professional survey for critical applications. Atmospheric and instrument errors apply.
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