The tree height calculator takes angle between the viewpoint and the tree base (α), angle between the viewpoint and the tree base (α), angle between the viewpoint and the treetop (β), angle between the viewpoint and the treetop (β), distance from the tree, distance from the tree, your height, length of your shadow, length of the tree’s shadow and tan and returns tree height and eye level. It is built for quick answers, for checking somebody else’s arithmetic, and for the moments when a formula book is not within reach.
What Is the Tree Height Calculator?
The tree height calculator works out tree height and eye level from angle between the viewpoint and the tree base (α), angle between the viewpoint and the tree base (α), angle between the viewpoint and the treetop (β), angle between the viewpoint and the treetop (β), distance from the tree, distance from the tree, your height, length of your shadow, length of the tree's shadow and tan.
Biological relationships are usually approximations rather than exact laws, so the output is best treated as an estimate with a sensible range around it.
How the Tree Height Calculation Works
The calculation applies the relationship as published, step by step, so each intermediate value can be checked against the underlying theory.
Keep the units consistent throughout. Mixing a percentage with a proportion is the single most common source of an answer that is out by a factor of a hundred.
Assumptions Worth Knowing
Any relationship used here assumes a constant rate, a representative sample, or a stable population. Real populations rarely meet those conditions for long, so treat the answer as a guide.
Where the inputs are field measurements, a single misread value can shift the result noticeably. Measure carefully and record what you used.
A Worked Example
Working through an example, with angle between the viewpoint and the tree base (α) set to 10, angle between the viewpoint and the tree base (α) set to 5, angle between the viewpoint and the treetop (β) set to 2, the calculator returns eye level of -16.9, and tree height of -28.33, and tree height (tree height shadow method) of 0.2. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out tree height?
Enter angle between the viewpoint and the tree base (α), angle between the viewpoint and the tree base (α), angle between the viewpoint and the treetop (β), angle between the viewpoint and the treetop (β), distance from the tree, distance from the tree, your height, length of your shadow, length of the tree's shadow and tan. The calculator then works through the relationship and reports tree height and eye level.
What does the tree height actually calculate?
It takes angle between the viewpoint and the tree base (α), angle between the viewpoint and the tree base (α), angle between the viewpoint and the treetop (β), angle between the viewpoint and the treetop (β), distance from the tree, distance from the tree, your height, length of your shadow, length of the tree's shadow and tan and converts them into tree height and eye level using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter angle between the viewpoint and the tree base (α)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.