# How to calculate the height of a tree

## Height measurements | BC BigTree

#### Equipment needed

You only need three pieces of equipment to properly measure a tree: a measuring tape, a calculator (with cosine and tangent functions), and an inclinometer to measure angles.  If purchasing an inclinometer (Abney level, clinometer, etc.) is beyond your budget, or you can’t borrow one, there are mobile phone apps that allow you to use a smartphone as an inclinometer. Here are two possible options: Smart Measure and iHandy Carpenter.  See Gabriel Hemery’s helpful instructions on using iHandy Carpenter to measure tree height.

Today Foresters use a Hypsometer – an all in one tool that measures distance, angles and even calculates tree height for you.  This equipment hastens the measurement process, but it is not necessary.

#### For fun!

The stick method- how they built the pyramids!
This old but simple method only works on level ground.  It just requires a stick and a distance measuring tape.   The stick must be the same length as your arm or grasped at a point where the length of the stick above your hand equals that of your arm.  The stick is held pointing straight up, at 90 degrees to your outstretched, straight arm.  Carefully walk backwards until the top of the tree lines up with the top of your stick.  Mark where your feet are.   The distance between your feet and the tree is roughly equivalent to the height of the tree.  You might find it interesting to compare your results using this simple method with the standard methods described below.

#### How to measure height

Height is the hardest measurement to take accurately, especially for larger trees. Measurements become more reliable the greater the distance you are from the tree (the distance you are away from the tree must be greater than the total tree height).  In dense forests it can be challenging to get a clear view of the tree top.  The slope of the ground can also make measurement difficult.  Trees that are leaning significantly should be measured with the lean to the right or left, not with the lean toward or away from you.    In challenging forest situations we recommend making more than one attempt to measure height.  If possible try and remeasure from a different view point, and always double check your measurements.

#### The math used in height calculations

Working on level ground
Calculating tree height requires the use of basic trigonometry: h = Tan A x d, where h is the tree height, d is the distance from tree, and A is the angle to the top of the tree.  Since your measurements will be made at eye level, you need to know your eye height (height of your eye above the ground). The equation then becomes h = Tan A x d + eye height.

Working on moderately sloped terrain
If the only option available to you is to stand either up or down slope of the tree, and the gradient is such that the base of the tree is above or below eye level, additional angles need to be measured.   In addition to tree top angle, you need to measure the angle to the tree base.   These angles are either subtracted or added depending on whether you are above (added) or below (subtracted) the tree.

Tree base is obscured or hidden from view
Often obstacles such as shrubs, rocks, or fallen trees can obscure the tree base from view. In this case, you will need to measure the angle to a mark on the trunk that is a known height from the ground. One method, shown in the illustration below, is to have someone stand at the base of the tree and measure the angle to the top of their head (height x). If you can’t see them through the tall bushes, try having them hold a flag or bright coloured stick above their head at a known height.

Working on steep terrain
On very steep terrain it is almost impossible to accurately determine your horizontal distance from the tree. In situations where the ground is sloped (up or down) more than 6 degrees (10% slope) you will need to measure slope distance. Once you measure slope angle and slope distance, horizontal distance can be calculated.

## How to estimate the height of a tree?

There are a number of easy ways to get a rough estimate of the height of a tree.

You can obtain a rough guess of a tree's height by:

• comparing with a measurable object nearby the trunk, eg. a pole or a house of which you know or can measure the height and by looking from a distance how many times that objects fits the tree. You could also do this on a photograph that was preferably taken from a distance as large as possible (to have the smallest perspective distortion of the tree possible) with the largest zoomfactor your camera has (to have the least lens distortion possible).
• a more correct method is based on goniometry: you start to walk away from the base of the trunk until you see the tree's top from an angle of 45 (which you can check using your arm).

The height of the tree is then the distance from the tree to where you're standing (eg. 80 ft) + your eye height (the distance from the ground to your eyes, eg. 5 ft).

The idea is that if there's an angle of 45 (the angle between your line of sight and the ground) in a right-angled triangle (a triangle with an angle of 90, the corner tree-ground), then both small sides have an equal length. This means that the height of the tree then equals the distance tree-observer. But since your eyes are not on the ground, you need to add your own eye height as an extra (see image).

Provided you train yourself a couple of times in making steps of eg. 3 ft, you can relatively quickly determine the height of something. If you make your steps correctly (or use a tape to measure your distance from the tree) and if you're sufficiently able to determine an angle of 45 (or make you use of an inclinometer or tilt meter), then such a height guess can be quite good theoretically. But keep in mind that height measurements should be looked at very critically.

If you are not sure your guess of the 45 angle is any good, you can do it like this too: take a stick of about 1 to 2 ft and keep it vertically with a straight, horizontal arm. Walk away from the tree until the top of the tree corresponds with the tip of the stick, from your point of view. Then turn the stick horizontally and remember with which spot (as far away from you as the tree is) the tip of stick corresponds. The height of the tree equals the distance from the tree to that spot.

These methods assume the tree is not growing on a slope and the top of the tree can be determined (by surrounding trees or by the round shape of the crown the actual top of the tree can remain hidden for the observer). Also, 'distance to the tree' is not entirely correct: it should be 'distance to the orthogonal projection of the tree's top on the ground'. The difference between the 'distance to the tree' and that projection is half the diameter of the tree near the ground.

• another estimation useful for standalone trees standing on flat ground on sunny days is to measure the tree's shadow length on the ground. If you measure the shadow's length of an object with known length (e.g. yourself), this would allow a rough estimation of the tree's size as well. See this calculator.
• a third and the most accurate way consists of climbing to the top of the tree and doing a direct tape drop. Of course this is something that should only be doing taking extreme precautions. This method is rarely used. On the photo on the right you can see Ronny Schreurs climbing a giant sequoia in military area Massy in Houthalen-Helchteren (Belgium) to determine its height.

Video material of the tape drop of Hyperion, the tallest tree in the world.

Professional arborists measure trees' height by using a inclinometer like the Suunto clinometer or the Forester Vertex, by which a number of distances and angles are measured. In more recent years handy laser equipment is used and is rapidly replacing the traditional inclinometers. Using analoguous formulas from goniometry (like mentioned above) the height can be calculated.
A tape is used much more infrequently, except for specific trees like record trees or felled trees.

Above (left) you see the Nikon Forestry 550, a professional laser based range finder that can be used to measure the height of trees accurately and quickly. On the right see a climber working his way to the top of the tallest known beech tree in the Sonian forest to measure its height using a tape.

More on tree measuring:

• How to exactly measure tree height
• How to measure tree girth
• How to measure tree volume

## Determination of tree height and river width without special instruments

Determination of tree height and river width without special instruments - WoodWool

Landscaping, tree care
and green spaces

+7 (495) 961-05-69

+7 (903) 961-05-69