Tree Height Calculator
Work out how tall a tree is from the distance and the angle to its top, and find where to stand for the smallest error.
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Disclaimer: this calculation is for informational purposes only. For important decisions, consult a qualified professional.
Measuring a tree's height from the ground
To find out how tall a tree is, you do not need to climb it: you just need the distance from the trunk and the angle at which you see the top. With a clinometer, a phone app that measures tilt or a simple protractor with a plumb line, trigonometry does the rest. This calculator returns the height, the likely error of the measurement and the ideal distance to repeat it from.
The same method works for poles, buildings, towers or any vertical object whose base you can see.
How the calculation works
- Distance: measure horizontally from where you stand to the base of the trunk, with a tape or by counting paces.
- Angle: point the instrument at the top and read the angle from the horizontal.
- Height above eye level: distance × tangent of the angle.
- Total height: add your eye height above the ground, because the angle starts there.
The verdict is based on the angle, because it determines how much a small reading error shifts the result.
Heights and precision at 20 m
With eyes 1.6 m above the ground and 20 m from the trunk:
| Angle | Tangent | Height | Error for ±1° | Relative error |
|---|---|---|---|---|
| 15° | 0.268 | 7.0 m | 0.37 m | 5.4% |
| 20° | 0.364 | 8.9 m | 0.40 m | 4.5% |
| 30° | 0.577 | 13.1 m | 0.47 m | 3.5% |
| 40° | 0.839 | 18.4 m | 0.60 m | 3.2% |
| 45° | 1.000 | 21.6 m | 0.70 m | 3.2% |
| 50° | 1.192 | 25.4 m | 0.85 m | 3.3% |
| 60° | 1.732 | 36.2 m | 1.40 m | 3.9% |
| 70° | 2.747 | 56.5 m | 2.99 m | 5.3% |
| 75° | 3.732 | 76.2 m | 5.23 m | 6.9% |
Why 45° is the best angle
The relative error on the part of the tree above eye level depends only on the angle: it is smallest at 45° and grows towards both shallow and steep angles. For a 1° reading error:
| Angle | Relative error on the part above eye level |
|---|---|
| 10° or 80° | 10.2% |
| 20° or 70° | 5.4% |
| 30° or 60° | 4.0% |
| 45° | 3.5% |
Between 30° and 60° the error stays close to the minimum. If the angle is shallower, move closer; if it is steeper, step back: the calculator tells you the distance from which you would see the top at 45°.
The 45° stick trick
Without instruments you can use a stick as long as your outstretched arm. Hold it upright at arm's length in front of your eyes and walk away from the tree until the bottom of the stick lines up with the base of the trunk and the tip with the top: at that point the angle is about 45°, and the height above your eyes equals your distance from the trunk. Just pace the distance and add your eye height.
The shadow method
On a sunny day, the tree's height is to its shadow as your height is to your shadow. If you are 1.70 m tall and your shadow is 2.50 m long, a tree with a 30 m shadow is about 30 × 1.70 / 2.50 = 20.4 m tall. The method only works on flat ground with well-defined shadows.
The bands of the verdict
- Below 20°: a less precise measurement; move closer.
- 20° to 30°: a fair measurement that improves as you move closer.
- 30° to 60°: good measuring conditions.
- Above 60°: a less precise measurement; step back.
Limits of the calculator
The calculation assumes level ground and an upright tree, with the top directly above the base. On a slope the base may be higher or lower than your eyes: in that case, also measure the angle to the base and add or subtract the two parts. In wide-crowned trees the true top may be hidden, and people tend to overestimate the height by aiming at a nearer branch.
Frequently asked questions
How do you calculate a tree's height?
Measure the horizontal distance from the trunk and the angle at which you see the top, multiply the distance by the tangent of the angle and add your eye height. At 20 m with a 45° angle and eyes at 1.6 m, the tree is 21.6 m tall.
What do I use to measure the angle?
A clinometer, a phone app that measures tilt or a protractor with a plumb line. Aim at the top and read the angle from the horizontal.
How far away should I stand?
At a distance where the top appears between 30° and 60°, ideally close to 45°: there a reading error has the least effect on the result.
How accurate is the measurement?
With a 1° angle error, around 45° the height changes by about 3-4%. With very shallow or very steep angles the error can exceed 5-10%.
Why add my eye height?
Because the angle is measured from your eyes, not the ground: trigonometry only gives the part of the tree above your eyes.
What is the stick trick?
With a stick as long as your outstretched arm, held upright, you walk back until it exactly covers the tree: there the angle is about 45° and the height above your eyes equals the distance.
How does the shadow method work?
The tree's height is to its shadow as your height is to your shadow: measure both shadows and work out the proportion.
What if the ground slopes?
Also measure the angle to the base of the trunk and calculate the two parts separately: add them if the base is below your eyes and subtract if it is above.
Does it work for buildings too?
Yes, for any vertical object whose distance from the base you know: poles, towers, buildings.
Why does the height sometimes come out too high?
In wide-crowned trees people tend to aim at a branch nearer to them that looks like the top, so the distance to the trunk no longer matches the point observed.
Can I measure the distance in paces?
Yes, if you know your pace length: measure it first over a known distance. An error in distance carries over proportionally to the height.
Does the calculator use feet?
No, it uses metres and degrees. Convert first: one foot is about 0.305 m.
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