Angle of Elevation & Depression Calculator
Solve angle of elevation and depression trigonometry problems: find the angle from height & horizontal distance, or reverse it - find height from angle & distance, or find distance from angle & height. Results in degrees, radians, and degrees-minutes-seconds, with an auto-updating right triangle diagram.
The math is identical to the angle of elevation: for the same triangle, the angle of depression equals the angle of elevation. Labels here use depression terms to stay true to your problem's context.
Triangle diagram
Yellow line = line of sight, blue line = object height, dashed line = horizontal distance.
Formulas used
- Angle of elevation / depression: θ = arctan(height / horizontal distance)
- Find height: height = horizontal distance × tan(θ)
- Find distance: horizontal distance = height / tan(θ)
Not what you are looking for? This calculator finds a right triangle\u2019s angle. If you need a triangle side (hypotenuse or leg), use the hypotenuse calculator. For ground, road, or roof slope angles (rise over run), use the slope angle calculator.
Frequently asked questions
What is the angle of elevation?
The angle of elevation is the angle formed between the observer's horizontal line of sight and the line of sight to an object HIGHER than the observer's eye level. For example, when you stand 100 meters from a tower and look up at its top, the angle between your straight-ahead gaze and your gaze at the tower top is the angle of elevation.
What is the difference between the angle of elevation and the angle of depression?
The angle of elevation is measured from below to above (the observer looks at a higher object), while the angle of depression is measured from above to below (the observer looks at a lower object). For the same right triangle, the two angles are IDENTICAL - both are the acute angles opposite each other on two parallel horizontal lines, so tan θ = height / horizontal distance holds for both.
What is the formula for the angle of elevation?
θ = arctan(object height / horizontal distance). Example: an 80-meter-tall object at a horizontal distance of 60 meters gives θ = arctan(80/60) = 53.13°. Note that the distance used is the horizontal distance (the triangle's base), not the slant distance from observer to object.
How do you find an object's height from the angle of elevation? (example: 50 m distance, 30° angle)
Reverse the formula: height = horizontal distance × tan(θ). Example: you stand 50 meters from a building and the angle of elevation to its roof is 30°, so the building height = 50 × tan(30°) = 50 × 0.5774 = 28.87 meters.
How do you find the horizontal distance from the angle and object height?
Use distance = height / tan(θ). Example: a 25-meter tower is seen at a 10° angle of elevation, so the observer's horizontal distance to the tower = 25 / tan(10°) = 25 / 0.1763 = 141.78 meters.
Why are the angle of elevation and angle of depression equal?
Because the horizontal line at the lower observer position and the horizontal line at the upper observer position are parallel, the angle of elevation and angle of depression are alternate interior angles, equal by geometry. So computing one automatically gives the other - this calculator's depression mode uses the same formula with honest labels.
What are radians and degrees-minutes-seconds (DMS)?
A radian is the SI angle unit: one full circle equals 2π radians (about 6.2832). DMS splits one degree into 60 minutes (1° = 60') and one minute into 60 seconds (1' = 60"). Example: an angle of 26.5651° equals 0.4636 radians and also 26° 33' 54.36". This calculator shows all three formats at once.
What input limits apply to this calculator?
Height and horizontal distance must be greater than 0, while the angle must be between 0° and 90° (excluding both). At 0° no triangle forms because the line of sight is parallel to the ground, while at 90° the object is directly above the observer so the horizontal distance is zero and tan(90°) is undefined.
When is the angle of elevation calculator used in the real world?
Land surveying (finding building or tree heights without climbing), flight navigation (a pilot's viewing angle to the runway), amateur astronomy (a celestial body's height above the horizon), construction (roof and stair slopes), drone photography (shooting angles), and school trigonometry problems.
How does it differ from the slope angle calculator?
Both do use the same arctan function, but the context differs. The slope angle calculator (rise over run) is for ground, road, or roof slopes - see our slope angle calculator at rise-run-degrees-calculator. This calculator is specifically for angle of elevation and depression trigonometry problems: object height, observer horizontal distance, and line of sight.