HesapHanem

Angle of Elevation Calculator

Enter the height and horizontal distance to compute the angle of elevation.

How it is calculated

The angle comes from the right triangle formed by the vertical rise and the horizontal run: θ = atan2(height, distance) × 180 ÷ π, which for a positive distance equals arctan(height ÷ distance). Height is how far the target is above your eye level, and distance is the level distance to the point directly below it; both must be in the same unit, whichever one you use, because only their ratio matters. The tool also gives the angle in radians and the straight line-of-sight length √(height² + distance²), in the same length unit. The distance must be above zero. A negative height is accepted and returns a negative angle, meaning the target is below the horizontal (an angle of depression).

Worked example

You stand 40 m from the foot of a tower and the top is 18.5 m above your eye level. The ratio is 18.5 ÷ 40 = 0.4625. The arctangent of 0.4625 is 24.8205 °, which is 0.433200 radians. The line of sight to the top is √(18.5² + 40²) = √(342.25 + 1600) = √1942.25 = 44.0710 m. So you look up about 24.8 degrees.

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Common mistakes

  • Entering the full height of the object instead of its height above your eye level. If your eyes are 1.6 m above the ground and the tower is 20 m, the height to enter is 18.4.
  • Entering the sloping line-of-sight or ground-slope distance as the distance. The field needs the level, horizontal distance.
  • Mixing units, such as height in metres and distance in feet. The ratio is then wrong, and so is the angle.
  • Reading the answer as a percent slope. An angle of 24.82 ° is a gradient of about 46 %, not 24.82 %.
  • Entering a distance of 0 for a target straight overhead. The tool returns no result in that case.

About this calculator

The angle of elevation is the angle between a horizontal line of sight and the line to an object above it, found with basic trigonometry as θ = arctan(height ÷ horizontal distance) — the same right-triangle relationship used in reverse for angle of depression. Because tangent relates the opposite and adjacent sides of a right triangle, only the vertical rise and horizontal run are needed, with no direct-line-of-sight distance required.

This calculator takes a height and a horizontal distance and returns the elevation angle in degrees (and radians). Surveyors and construction estimators use it to check sightlines and roof or ramp angles, students use it for trigonometry word problems involving flagpoles, buildings, or kites, and photographers and drone pilots use it to plan shots at a known height and distance.

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Comments (1)

  • Editorial team

    A ramp is a handy real check. A rise of 1 over a run of 12 gives 4.7636 °, the angle behind the familiar 1:12 accessibility ramp rule. Use the horizontal run, not the length of the sloped surface, and keep both in the same unit. A negative height returns a negative angle, so the same tool covers a view looking down from a balcony. What are you measuring, a roof, a ramp or a sightline?

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