Height from an Angle of Elevation
In a right triangle with the distance as the base, the rise is distance × tan(angle). You measure from eye level, so add your eye height at the end. A phone inclinometer is enough to measure a tree without a ladder.
Your numbers
Object height
25.04m
Rise
23.44m
Hypotenuse
38.07m
Formula
Object height = Distance (km) × tan Angle (°) + Eye height
Near 90° the tangent explodes and a small angle error becomes a large height error. Stand far enough back to keep the angle between 30° and 45°.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Distance (km) (m)Distance measured in kilometres. | 30 | 0 and up |
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 38 | 0 ~ 89.9 |
| Eye height (m)Ground to eye; add it at the end for the true height. | 1.6 | 0 and up |
Step by step
Quick reference table
Results when only Distance (km) (m) changes and everything else stays put.
| Distance (km) (m) | Object height (m) | Rise (m) | Hypotenuse (m) |
|---|---|---|---|
| 15 | 13.32 | 11.72 | 19.04 |
| 22.5 | 19.18 | 17.58 | 28.55 |
| 30 | 25.04 | 23.44 | 38.07 |
| 45 | 36.76 | 35.16 | 57.11 |
| 60 | 48.48 | 46.88 | 76.14 |
What each result means
| Result | At default values |
|---|---|
| Object height (m)The full height of the object you are measuring. | 25.04 |
| Rise (m)How far it climbs, straight up. | 23.44 |
| Hypotenuse (m)The longest side of a right triangle, facing the right angle. | 38.07 |
Common mistakes
Near 90° the tangent explodes and a small angle error becomes a large height error. Stand far enough back to keep the angle between 30° and 45°.
Glossary
- Distance (km)
- Distance measured in kilometres.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- Eye height
- Ground to eye; add it at the end for the true height.
- Object height
- The full height of the object you are measuring.
- Rise
- How far it climbs, straight up.
- Hypotenuse
- The longest side of a right triangle, facing the right angle.
Frequently asked questions
Q. How is Height from an Angle of Elevation calculated?
Object height = Distance (km) × tan Angle (°) + Eye height — In a right triangle with the distance as the base, the rise is distance × tan(angle). You measure from eye level, so add your eye height at the end. A phone inclinometer is enough to measure a tree without a ladder.
Q. Can you walk through an example?
With Distance (km) 30m, Angle (°) 38°, Eye height 1.6m, the answer is Object height 25.04m.
Q. What do I need to enter?
Enter Distance (km), Angle (°), Eye height. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Distance (km) (m) moves the answer to Distance (km) (m) 15 → Object height (m) 13.32 and Distance (km) (m) 60 → Object height (m) 48.48. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Near 90° the tangent explodes and a small angle error becomes a large height error. Stand far enough back to keep the angle between 30° and 45°.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.