Tree height calculator

How do I measure a tree’s height?

Stand on level ground, measure your distance to the trunk, and use a clinometer (or a phone app) to read the angle up to the treetop. Height = distance × tan(angle) + your eye height.

Example

NASA’s GLOBE program: 60 m from the tree at an angle of 34°, plus 1.5 m eye height — about 42 m. (GLOBE rounds tan 34° to 0.67 and gets 41.7 m.)

Where should I stand?

GLOBE suggests standing at least as far from the tree as the tree is tall, and, for the most accurate result, at a distance where the clinometer reads as close to 30° as possible. Do not choose a spot where you must look nearly straight up. The section on the angle below shows why shallow angles are the ones to avoid.

Why add my eye height?

The angle is measured from your eye, so the calculation gives the height above eye level. Add the height of your eyes above the ground at the base.

What if the ground slopes?

The formula assumes you stand level with the base. On a slope, read two angles: up to the top and down (or up) to the base. Uphill of the tree, the height is the distance × (tan of the angle up + tan of the angle down); downhill, subtract the tangent of the angle up to the base. From 40 m with the top 30° above eye level and the base 10° below it: 23.1 m + 7.1 m = 30.1 m, with no eye height added because the lower angle already includes it. GLOBE describes three other methods in its Biometry Protocol.

What if the tree leans?

GLOBE says to measure to the top of the tree as usual. The result is then the vertical height of the top above the ground, which is less than the length of a leaning trunk.

How the height is found

The tree, the ground and your line of sight form a right triangle. Its horizontal side is your distance from the trunk, the angle at your eye is what the clinometer reads, and the vertical side is the part of the tree above your eye level: height above eye = distance × tan(angle). Your eye height is added to that. The method needs level ground, a horizontal distance and an angle from the horizontal. GLOBE suggests practicing on an object of known height, such as a flagpole.

Worked example

GLOBE's example is 60 m from the tree at an angle of 34°. tan 34° = 0.6745, so the part above eye level is 60 × 0.6745 = 40.5 m, and with a 1.5 m eye height the tree is 42.0 m tall. GLOBE rounds the tangent to 0.67 and gets 41.7 m. Reading the angle one degree low or high would give 40.5 m or 43.5 m, so a single degree of error moves the answer by about 1.5 m.

Where the angle is easiest to trust

GLOBE asks you to stand at least as far from the tree as the tree is tall, so the angle is about 45° or less, and says the most accurate result comes when the angle is as close to 30° as possible. It does not say why. A one-degree misreading changes the height above eye level by about 4.1% at 30° and 3.6% at 45°, but 5.5% at 20° and 10.2% at 10°, so very shallow angles are the ones to avoid.

Common mistakes

Measuring the distance along a slope, forgetting the eye height and reading the angle from the vertical instead of the horizontal are three easy errors. Standing so close that you look nearly straight up is another; GLOBE advises against it. With a phone app, try it on a known height first.

Sources: NASA GLOBE Program, “Investigation Instruments: Clinometer,” GLOBE 2014 (formula, example, standing distance, level-ground note, leaning trees); the slope variant and the error figures follow from the same trigonometry. Related: right triangle calculator, slope calculator, sun angle calculator, mulch calculator. How we check our calculators.