Angle of Elevation Calculator in Degrees

Calculator Inputs

Example Data Table

Formula Used

Right-triangle relationships

• tan(A) = Opposite / Adjacent
• sin(A) = Opposite / Hypotenuse
• cos(A) = Adjacent / Hypotenuse
• Hypotenuse = √(Opposite² + Adjacent²)

Common rearrangements

• A = arctan(O/D) (angle from height and distance)
• O = D · tan(A) (height from angle and distance)
• D = O / tan(A) (distance from angle and height)
• H = D / cos(A) or H = O / sin(A) (line of sight)

How to Use This Calculator

1. Select what you want to solve for from the dropdown.
2. Enter the required known values (use any consistent length unit).
3. Choose your preferred decimal places for rounding.
4. Click Calculate to show the result above the form.
5. Use the download buttons to save CSV or PDF.

Angle of Elevation in Field Measurements

Angle of elevation is the upward viewing angle from a horizontal reference line to a target point. In a right triangle model, the observer is at the vertex, the horizontal ground is the adjacent side, and the vertical rise is the opposite side. This calculator focuses on degrees because most handheld inclinometers and phone sensors report angles in degrees, typically to 0.1° or 0.5°.

Typical input ranges

For everyday surveying and construction checks, common angles fall between 5° and 45°. Very small angles produce large distances, so rounding matters. For example, with a 2 m height change, 5° implies about 22.86 m distance, while 6° implies about 19.05 m, a difference of nearly 3.8 m.

Using height and distance

When you know rise and run, the calculator uses A = arctan(O/D). If you measure a building top 12 m above eye level and stand 20 m away, the angle is arctan(12/20) ≈ 30.96°. This method is stable when both values are measured well.

Using line of sight

If you measure the line of sight (hypotenuse) with a laser rangefinder, angle can be computed from A = arcsin(O/H) or A = arccos(D/H). Keep the right-triangle assumption: the horizontal distance should be level, and the vertical rise should be perpendicular to it.

Height estimation from an angle

To estimate height, the calculator applies O = D · tan(A). With a 35 m horizontal distance and a 28° angle, the height rise is 35·tan(28°) ≈ 18.60 m. Add your instrument height (eye level) if you need total height above ground.

Distance estimation from an angle

To estimate distance, it uses D = O / tan(A). This becomes sensitive near 0°, because tan(A) approaches zero. If O = 10 m and A = 3°, D ≈ 190.99 m; a small angle error can change distance a lot.

Accuracy tips

Use consistent units for all length inputs. Prefer larger distances for tall targets to reduce angle-reading error. If your device reports to 0.5°, consider setting decimals to 2–3 and recording multiple readings. Avoid angles near 90° because cos(A) becomes tiny and line-of-sight results can spike.

Where it is commonly used

Angle of elevation appears in surveying, roof pitch checks, crane planning, forestry height estimates, and classroom trigonometry. The calculator also provides the missing triangle sides, so you can cross-check measurements and export results as CSV or PDF for documentation.

FAQs

1) What is the angle of elevation?

It is the upward angle from a horizontal line to your line of sight. In a right-triangle model, it is measured at the observer between the ground (adjacent) and the sight line (hypotenuse).

2) Why must the angle be between 0° and 90°?

This calculator assumes a right triangle with an upward view. At 0° the target is level, and at 90° the target is directly overhead. Values outside that range do not match the intended geometry.

3) Do the unit options convert my inputs?

No. The unit menu is for display only. Enter all lengths in one consistent unit, such as meters or feet, and the results will be shown in that same unit label.

4) How do I include my eye or instrument height?

Compute the rise (opposite) using your measurements, then add your eye/instrument height to get total height above ground. Example: rise 18.6 m plus 1.6 m eye height gives 20.2 m total.

5) Which method is best: tan, sin, or cos?

Use tan when you have height and horizontal distance. Use sin or cos when you have the line of sight plus one side. Choose the pair that matches what you can measure most accurately.

6) Why do small angles cause large distance changes?

Because tan(A) is very small near 0°. When you divide by tan(A) to get distance, tiny angle changes create big differences. Taking multiple readings and averaging helps.

7) Can I use this for roof pitch?

Yes. If you know rise and run, calculate the angle using arctan(rise/run). You can also convert pitch to percent grade by 100·tan(A) if you need a slope percentage.