Calculate angle of arrival, distance, or height from any two values using trigonometry with meters, feet, miles, centimeters, or inches.
Related Calculators
- Antenna Axial Ratio Calculator
- Electrical Length Calculator
- Rf Gain Calculator
- Link Margin Calculator
- All Physics Calculators
Angle Of Arrival Formula
The angle of arrival is found from a right triangle using the horizontal distance and the height difference. The calculator can solve for angle, height, or distance when you enter the other two values.
\theta = \tan^{-1}(h/d) * 180/\pih = d * \tan(\theta * \pi/180)
d = h / \tan(\theta * \pi/180)
- θ = angle of arrival, in degrees
- h = height difference between the two points
- d = horizontal distance between the two points
- π = pi, approximately 3.14159
- tan = tangent function
- tan-1 = inverse tangent, also called arctangent
If you enter distance and height, the calculator uses inverse tangent to find the angle. If you enter distance and angle, it uses tangent to find the height. If you enter height and angle, it rearranges the tangent formula to find the distance.
Distance and height can be entered in different units. The calculation converts them to meters internally, then converts the missing length back to the unit you selected.
Common Angle Ratios
These tangent values show how the angle changes as height becomes larger compared with distance.
| Angle | tan(θ) | Meaning |
|---|---|---|
| 5° | 0.0875 | Height is about 8.75% of the distance |
| 10° | 0.1763 | Height is about 17.63% of the distance |
| 30° | 0.5774 | Height is about 57.74% of the distance |
| 45° | 1.0000 | Height equals distance |
| 60° | 1.7321 | Height is about 1.73 times the distance |
Length Unit Conversions Used
| Unit | Meters per unit |
|---|---|
| Centimeter (cm) | 0.01 m |
| Inch (in) | 0.0254 m |
| Foot (ft) | 0.3048 m |
| Meter (m) | 1 m |
| Kilometer (km) | 1000 m |
| Mile (mi) | 1609.34 m |
Example Problems
Example 1: Find the angle of arrival
You have a height difference of 20 m and a horizontal distance of 100 m.
\theta = \tan^{-1}(20/100) * 180/\pi\theta = 11.3099^\circ
The angle of arrival is about 11.31°.
Example 2: Find the height
You have a distance of 250 ft and an angle of arrival of 8°.
h = 250 * \tan(8 * \pi/180)
h = 35.1367 ft
The height difference is about 35.14 ft.
FAQ
What does angle of arrival mean?
Angle of arrival is the angle at which a line, signal, ray, or path reaches a point compared with a horizontal reference line. In this calculator, it is treated as the angle of a right triangle formed by horizontal distance and height difference.
Do distance and height need to use the same unit?
No. You can enter distance and height in different units. The calculator converts both lengths to meters for the calculation. For a missing distance or height, it converts the answer back to the selected output unit.
Why can’t the distance be zero when finding the angle?
The angle formula divides height by distance. If distance is zero, the division is undefined, so the calculator cannot use the arctangent formula. For a vertical line, the angle approaches 90°, but that case is outside this right-triangle calculation.