How to use the angle of depression calculator
Four quick steps turn a sight line into its angle of depression and geometry — the line-of-sight distance, the matching angle of elevation, the slope grade and the distance-to-height ratio.
Pick what you know
Height & distance, height & angle, or distance & angle.
Enter the values
The observer height above the target, the horizontal distance, or the angle.
Choose a unit
Feet, meters or yards — the angle stays the same whichever you pick.
Read results & save a PDF
Get the angle, line of sight, grade and ratio — then download a report.
The formulas behind the angle
The angle, the line of sight and the grade all come from the right triangle of height and horizontal distance.
▶ Worked example
An observer 50 ft above a target that is 120 ft away horizontally.
Angle of depression = arctan(50 ÷ 120) = 22.62°, the same as the angle of elevation looking back up.
Line of sight = √(50² + 120²) = 130 ft; grade = 50 ÷ 120 × 100 = 41.67%.
Angle 22.62° · line of sight 130 ft · grade 41.67% · ratio 2.4 : 1
This is the classic 5–12–13 right triangle, scaled by ten.
Angle of depression quick reference
The sight-line formulas, the geometry by angle, and the geometry by distance — both for a 50 ft observer height.
| Quantity | Formula |
|---|---|
| Angle of depression | arctan(height ÷ distance) |
| Angle of elevation | = angle of depression |
| Line of sight (slant) | √(height² + distance²) |
| Distance from angle | height ÷ tan(angle) |
| Height from angle | distance × tan(angle) |
| Grade | height ÷ distance × 100 |
| Angle | Horizontal distance | Line of sight | Grade |
|---|---|---|---|
| 5° | 571.50 ft | 573.69 ft | 8.7% |
| 10° | 283.56 ft | 287.94 ft | 17.6% |
| 20° | 137.37 ft | 146.19 ft | 36.4% |
| 30° | 86.60 ft | 100.00 ft | 57.7% |
| 45° | 50.00 ft | 70.71 ft | 100.0% |
| 60° | 28.87 ft | 57.74 ft | 173.2% |
| 75° | 13.40 ft | 51.76 ft | 373.2% |
| Horizontal distance | Angle | Line of sight | Grade |
|---|---|---|---|
| 50 ft | 45.00° | 70.71 ft | 100.0% |
| 100 ft | 26.57° | 111.80 ft | 50.0% |
| 120 ft | 22.62° | 130.00 ft | 41.7% |
| 150 ft | 18.43° | 158.11 ft | 33.3% |
| 200 ft | 14.04° | 206.16 ft | 25.0% |
| 250 ft | 11.31° | 254.95 ft | 20.0% |
| 300 ft | 9.46° | 304.14 ft | 16.7% |
Both tables hold the observer height at 50 ft. The angle, grade and ratio depend only on the height-to-distance ratio, so they are the same in meters or yards — only the lengths change label.
Everything the calculator returns
One calculation gives the full sight-line picture — every part of the triangle, in your unit.
The sight line at a glance
The core relationships, and the default result.
Built for the way you work
Whether you are sighting from a high point, flying a drone, or working a trig problem, the geometry starts from the same inputs.
Working out a sight line or a grade from a raised instrument down to a point, and need the angle and line-of-sight distance.
- Use the real horizontal distance
- Read the grade alongside the angle
- Get the slant for the sight line
Setting a camera tilt to frame a subject below and want the ground distance for a given height and angle.
- Enter height and camera tilt
- Get the ground distance
- Check the line of sight
Solving or setting the classic cliff, tower and lighthouse problems and want to check the angle, distance or height.
- Solve for any missing side
- See depression equals elevation
- Verify the worked answer
Get the sight line right
Seven things that keep an angle-of-depression result correct.
Depression equals elevation
The angle down from the observer equals the angle up from the target — they are alternate angles across the same line of sight.
Measure to the horizontal
The angle is from a level line, and the distance is horizontal — not along the slope. Mixing in the slant throws the angle off.
Line of sight is the hypotenuse
The slant distance is always longer than either the height or the horizontal distance. Use it for the actual sight line or cable.
Angle isn’t grade
A 45° angle is a 100% grade, not 45%. Convert through the tangent, not by reading one as the other.
Keep units consistent
Height and distance must be in the same unit. The angle, grade and ratio are pure numbers — unaffected by the unit.
Use height above the target
It’s the vertical difference between the observer’s eye and the target, not the observer’s height above the ground at their feet.
Pick the mode you can measure
Solve from whatever two you actually have — a measured angle plus a height, or a known distance plus an angle — and read the third.
Frequently asked questions
Common questions about the angle of depression, line of sight, elevation and slope grade.
The angle of depression is the angle below the horizontal from an elevated observer down to a target. You find it from the vertical height of the observer above the target and the horizontal distance to it: the angle is the arctangent of the height divided by the distance.
The height and distance are the two legs of a right triangle, and the angle of depression is measured at the observer, down from the level line of sight. The line-of-sight distance is the hypotenuse, the square root of the height squared plus the distance squared.
For example, an observer 50 feet up looking at a target 120 feet away horizontally has an angle of depression of the arctangent of 50 over 120, about 22.62 degrees, with a 130 foot line of sight. This calculator works it out from any two of height, distance and angle.
They are the same angle, measured from the two ends of the same line of sight. The angle of depression is measured at the higher point, downward from the horizontal to the target below. The angle of elevation is measured at the lower point, upward from the horizontal to the observer above.
Because the two horizontal lines are parallel, the angle of depression and the angle of elevation are equal — they are alternate interior angles across the sloped line of sight. So a 22.62 degree angle of depression looking down is a 22.62 degree angle of elevation looking back up.
For example, from a 50 foot height to a target 120 feet away, you look down 22.62 degrees and the target looks up at you 22.62 degrees. This calculator reports both so the relationship is clear.
The line-of-sight distance, also called the slant distance, is the straight-line distance from the observer’s eye to the target — the hypotenuse of the right triangle formed by the height and the horizontal distance. It is longer than either leg.
You find it as the square root of the height squared plus the horizontal distance squared, or equivalently the height divided by the sine of the angle, or the distance divided by the cosine of the angle.
For example, a 50 foot height and a 120 foot horizontal distance give a line of sight of the square root of 50 squared plus 120 squared, which is 130 feet. This calculator reports the line-of-sight distance alongside the angle and grade.
Yes. If you know the angle of depression and the observer’s height above the target, the horizontal distance is the height divided by the tangent of the angle. The line-of-sight distance is the height divided by the sine of the angle.
This is useful when you can measure or set an angle — with an inclinometer, a sight level or a drone’s camera tilt — and know how high you are, and want the ground distance to the target.
For example, from 50 feet up at a 20 degree angle of depression, the horizontal distance is 50 divided by the tangent of 20 degrees, about 137.4 feet. This calculator takes a height and an angle and returns the distance and line of sight.
Yes. If you know the angle of depression and the horizontal distance to the target, the observer’s height above the target is the distance times the tangent of the angle. The line-of-sight distance is the distance divided by the cosine of the angle.
This is the setup when you know how far away something is on the ground and the angle you are sighting down at, and want to work out how high the observation point is.
For example, at a 25 degree angle of depression to a target 200 feet away, the height is 200 times the tangent of 25 degrees, about 93.3 feet. This calculator takes a distance and an angle and returns the height and line of sight.
They describe the same incline in different units. The slope grade is the height over the horizontal distance as a percentage, while the angle of depression is the same ratio expressed as an angle — the arctangent of height over distance.
Because grade is a tangent and the angle is an arctangent of the same ratio, they do not scale together: a 45 degree angle is a 100 percent grade, not 45 percent, and a gentle 5 degree angle is about an 8.7 percent grade.
For example, a 50 foot height over a 120 foot distance is a 22.62 degree angle of depression and a 41.67 percent grade. This calculator reports the grade and the distance-to-height ratio alongside the angle.
It comes up anywhere an elevated point sights down to something lower. Surveyors and builders use it for sight lines, grading and setting levels; it is the basis of classic trigonometry word problems about cliffs, towers and lighthouses.
It is also handy for drones and cameras — the camera tilt to frame a target below, and the ground distance that implies — and for aiming, line-of-sight and visibility checks from a raised vantage point.
In every case it links a height, a horizontal distance and an angle through a right triangle. This calculator solves that triangle from any two of the three and gives the line of sight and grade too.
No. The angle of depression, the grade and the distance-to-height ratio depend only on the ratio of height to distance, not on the unit you measure them in. As long as the height and the distance are in the same unit, the angle comes out the same whether you use feet, meters or yards.
Only the lengths — the height, the distance and the line of sight — carry a unit and change their numeric value between systems. The angle, grade and ratio are pure numbers.
This calculator lets you pick feet, meters or yards; it keeps the height, distance and line of sight in that unit and leaves the angle, grade and ratio unchanged. Just keep both lengths in the same unit.
Disclaimer: Right-triangle trigonometry, lengths in feet, meters or yards (both lengths in the same unit). Angle of depression = arctan(height ÷ distance), and equals the angle of elevation from the target; line of sight = √(height² + distance²) = height ÷ sin(angle) = distance ÷ cos(angle); grade = height ÷ distance × 100; ratio = distance ÷ height. It assumes a flat, level horizontal reference and a straight line of sight — it does not account for earth curvature, refraction, terrain between the points, or instrument height. A reference aid only — confirm critical measurements with a proper instrument or survey.