Calculate angle, depth, or horizontal distance from any 2 values using degrees or radians and meters, feet, centimeters, or inches.
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Angle Depth Formula
The angle depth relationship comes from right-triangle trigonometry. The angle is measured from the horizontal direction, depth is the vertical side, and horizontal distance is the adjacent side.
\theta = \arctan(D/H)
D = H \tan(\theta)
H = D / \tan(\theta)
- θ = angle from the horizontal
- D = depth, or vertical distance
- H = horizontal distance
- tan = tangent function
- arctan = inverse tangent function
If you enter depth and horizontal distance, the calculator solves for the angle using inverse tangent. If you enter angle and horizontal distance, it solves for depth using tangent. If you enter angle and depth, it solves for horizontal distance by dividing depth by the tangent of the angle.
For the trigonometric calculation, angle values are converted as needed. Length values are converted to meters internally, then converted back to your selected output unit.
Common Angle and Depth Relationships
The table below shows how much depth you get for each 10 units of horizontal distance at common angles.
| Angle | tan(angle) | Depth for 10 m Horizontal Distance | Depth for 10 ft Horizontal Distance |
|---|---|---|---|
| 5° | 0.0875 | 0.875 m | 0.875 ft |
| 10° | 0.1763 | 1.763 m | 1.763 ft |
| 15° | 0.2679 | 2.679 m | 2.679 ft |
| 30° | 0.5774 | 5.774 m | 5.774 ft |
| 45° | 1.0000 | 10.000 m | 10.000 ft |
Length Unit Conversions Used
| Unit | Meters | Use in the Calculator |
|---|---|---|
| Meter | 1 m | Base length unit |
| Foot | 0.3048 m | Converted to meters before solving |
| Centimeter | 0.01 m | Converted to meters before solving |
| Inch | 0.0254 m | Converted to meters before solving |
Example Calculations
Example 1: Find depth from angle and horizontal distance
Suppose the angle is 30° and the horizontal distance is 12 meters.
D = 12 \tan(30^\circ)
D = 12(0.5774) = 6.9288
The depth is about 6.9288 meters.
Example 2: Find angle from depth and horizontal distance
Suppose the depth is 5 feet and the horizontal distance is 20 feet.
\theta = \arctan(5/20)
\theta = \arctan(0.25) = 14.0362^\circ
The angle is about 14.0362 degrees.
FAQ
What does the angle represent?
The angle is measured from the horizontal line to the sloped line. In the triangle, horizontal distance is the adjacent side and depth is the opposite side. A larger angle gives more depth for the same horizontal distance.
Can you use degrees or radians?
Yes. You can enter the angle in degrees or radians. The calculator converts radians to degrees for display and uses the equivalent angle in the tangent or inverse tangent calculation.
Why can horizontal distance be undefined?
Horizontal distance is calculated as depth divided by tan(angle). If the angle is 0°, tan(angle) is 0, so division is not possible. Angles very close to 90° can also produce very large or unstable horizontal distance results because the tangent value changes sharply near 90°.
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