Angle of Depression Calculator

An angle of depression measures how far a line of sight slopes downward from a horizontal line at the observer. Surveyors, builders, engineers, pilots, and students use this right-triangle relationship whenever an elevated observation point looks toward a lower target. The observer height and target height establish the vertical drop, while the measured ground distance establishes the horizontal leg. Because both legs must describe the same scale, you may use feet, meters, yards, or another length unit as long as every entry uses that one unit. The calculator first subtracts the target height from the observer height. It then divides that vertical drop by the horizontal distance and applies the inverse tangent function. The result is converted from radians to degrees. It also applies the Pythagorean theorem to the two legs to report the direct line-of-sight distance. For example, a 50-foot observation point looking toward ground level 100 feet away creates a drop-to-run ratio of 0.5, an angle of about 26.57 degrees, and a sight line of about 111.8 feet. Accurate field measurements matter more than extra decimal places. Measure horizontal distance on a level projection rather than along the slope, and use elevations referenced to the same datum. If the target itself stands above ground, enter its height so the calculator uses only the true elevation difference. Obstacles, earth curvature, atmospheric refraction, and instrument height can matter on long professional surveys; this simple calculator models a straight, level horizontal reference and a right triangle. In construction, the result can support preliminary drainage checks, sight-line planning, roof observations, excavation layouts, and height estimates. It is also useful for classroom trigonometry because it displays the vertical difference and hypotenuse alongside the angle. Treat the output as a planning aid rather than a stamped survey. Confirm critical boundaries, structural decisions, and safety-sensitive layouts with calibrated equipment and a qualified professional.