Angle of Elevation Calculator

This angle of elevation calculator works out the angle you look up through to see a point above you, using only the horizontal distance to that point and the vertical height difference between your eye level and the point. It matters whenever you need a sight line angle rather than a raw measurement: surveyors setting out levels, builders checking roof pitches or ladder angles, navigators judging bearings, and students working through right angle triangle trigonometry. Enter the horizontal distance and the vertical height into the two fields above, and the calculator instantly returns the angle of elevation in degrees, the same angle in radians, and the line of sight distance, the straight hypotenuse length between you and the point. It treats your two measurements as the shorter sides of a right angled triangle, with the height as the side opposite the angle and the distance as the side adjacent to it, so the tangent of the angle equals height divided by distance, and the angle itself is the arctangent of that ratio. The worked example below shows a distance and height of 10 each giving a clean 45 degree angle, so you can check the calculator against your own numbers. Because the maths assumes level ground and a true right angle, the accuracy of your result depends entirely on how precisely you measure the distance and height you enter.

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Horizontal distance

Vertical height

Angle (radians)

Line of sight

The formula

The angle of elevation theta satisfies tan(theta) = height / horizontal distance, so theta = arctan(height / distance). The line of sight is the hypotenuse, sqrt(distance^2 + height^2).

Worked example

With a horizontal distance of 10 and a height of 10, tan(theta) = 10 / 10 = 1, so theta = 45 degrees. Enter 10 and 10 above to confirm.

Frequently asked questions

What is the formula for the angle of elevation?

theta = arctan(vertical height / horizontal distance). The tangent of the angle is the height divided by the horizontal distance.

What is the difference between elevation and depression?

Elevation is the angle looking up from the horizontal, depression is the angle looking down. The arithmetic is identical; only the direction differs.

What is the line of sight value?

The straight distance to the point, the hypotenuse, equal to sqrt(distance squared plus height squared).

Who this calculator is for

This calculator is for students, surveyors, builders and navigators measuring sight line angles.

What this calculator assumes

You enter the horizontal distance and the vertical height.
The ground is treated as level and the triangle as right angled.
Results are rounded for display.

Formula and sources

Related calculators

Trig Calculator: all six trig functions at once.
Degrees to Radians Calculator: convert angle units.
Right Angle Triangle Calculator: solve a right triangle.

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