📐 Angle of Depression Calculator
Calculate angle of depression
How to Use This Calculator
Select Calculation Type
Choose to calculate from horizontal and vertical distance or from height and horizontal distance. Both methods give the same result.
Enter Distances
Input horizontal distance (run) and vertical distance (rise or drop) in feet. For height method, enter height instead of vertical distance.
Calculate and Review
Click "Calculate Angle of Depression" to see angle of depression, slope distance, slope ratio, and slope percentage. Use this for surveying and construction.
Apply Results
Use angle of depression for line of sight calculations, slope analysis, and construction planning. Verify measurements in the field.
Formula
Angle of Depression = arctan(Vertical / Horizontal)
Slope Distance = √(Horizontal² + Vertical²)
Slope Percent = (Vertical / Horizontal) × 100
Example 1: Horizontal = 100 ft, Vertical = 10 ft
Step 1: Angle of Depression = arctan(10 / 100) = arctan(0.1) = 5.71°
Step 2: Slope Distance = √(100² + 10²) = √10,100 = 100.5 feet
Step 3: Slope Percent = (10 / 100) × 100 = 10%
Example 2: Horizontal = 50 ft, Height = 5 ft
Step 1: Angle of Depression = arctan(5 / 50) = arctan(0.1) = 5.71°
Step 2: Slope Ratio = 50:5 = 10:1
About Angle of Depression Calculator
The Angle of Depression Calculator is an essential tool for surveyors, engineers, and construction professionals who need to calculate the angle of depression from a horizontal line to a point below. This calculator implements trigonometric formulas to determine angle of depression, slope distance, slope ratio, and slope percentage for surveying and construction applications.
When to Use This Calculator
- Surveying: Calculate angle of depression for topographic surveys
- Construction Planning: Determine slopes and grades for construction projects
- Road Design: Calculate road grades and slopes
- Drainage Design: Determine drainage slopes and grades
- Educational Use: Learn and understand angle of depression calculations
Why Use Our Calculator?
- ✅ Dual Calculation Modes: Supports horizontal-vertical and height-based calculations
- ✅ Accurate Formulas: Uses trigonometric equations for precise calculations
- ✅ Complete Analysis: Shows angle, slope distance, ratio, and percentage
- ✅ Easy to Use: Simple inputs for distance and height
- ✅ Time Savings: Instant calculations eliminate manual math
Understanding Angle of Depression
Basic Principle: Angle of depression is the angle between a horizontal line and a line of sight to a point below the horizontal. It's calculated as Angle = arctan(Vertical / Horizontal), where vertical is the drop or height difference and horizontal is the distance. Angle of depression is used in surveying, construction, and line of sight calculations.
Slope Calculations: Slope distance is the straight-line distance along the slope, calculated as √(Horizontal² + Vertical²). Slope ratio is Horizontal:Vertical (e.g., 10:1 means 10 feet horizontal per 1 foot vertical). Slope percent is (Vertical / Horizontal) × 100%.
Applications: Angle of depression is used for surveying slopes, calculating road grades, determining drainage slopes, and analyzing terrain. It's the opposite of angle of elevation (looking up).
Tips for Best Results
- Accurate Measurements: Measure horizontal and vertical distances accurately
- Consistent Units: Use consistent units (feet, meters) for all measurements
- Verify in Field: Verify calculated angles with actual field measurements
- Consider Terrain: Account for terrain variations in measurements
- Check Calculations: Verify results with manual calculations for critical projects
Frequently Asked Questions
How do I calculate angle of depression?
Angle of Depression = arctan(Vertical / Horizontal). For example, Horizontal = 100 ft, Vertical = 10 ft: Angle = arctan(10/100) = arctan(0.1) = 5.71°. The calculator does this automatically from horizontal and vertical distances or from height and horizontal distance.
What is the difference between angle of depression and angle of elevation?
Angle of depression is the angle from horizontal looking down to a point below (negative vertical). Angle of elevation is the angle from horizontal looking up to a point above (positive vertical). Both use the same formula: arctan(Vertical / Horizontal), but depression uses negative vertical or downward measurement.
How do I convert slope ratio to angle?
Slope ratio (H:V) converts to angle as Angle = arctan(V / H). For example, 10:1 slope means 10 feet horizontal per 1 foot vertical: Angle = arctan(1/10) = arctan(0.1) = 5.71°. The calculator shows slope ratio and angle automatically.
What is a typical angle of depression for roads?
Typical road grades: 2-6% slope (1.15-3.43° angle) for highways, 6-10% slope (3.43-5.71° angle) for local roads, up to 15% slope (8.53° angle) for steep roads. Maximum grades vary by road type and terrain. The calculator shows angle and slope percent automatically.
Does angle of depression depend on units?
No, angle of depression is independent of units as long as horizontal and vertical use the same units. For example, 100 meters horizontal and 10 meters vertical gives the same angle (5.71°) as 100 feet horizontal and 10 feet vertical. The formula uses ratios, so units cancel out.