Tree Height Estimator (Shadow/Angle Method)
Estimate the height of a tree using either the Shadow Method (similar triangles) or the Angle of Elevation Method (trigonometry). Choose your preferred method below.
m
Height of a person or stick whose shadow you can measure.
m
Length of the shadow cast by the known object at the same time.
Enter values above and click Calculate.
Formulas Used
Shadow Method (Similar Triangles):
Tree Height = (Known Object Height ÷ Known Object Shadow) × Tree Shadow Length
This relies on the fact that at the same moment, all vertical objects cast shadows proportional to their height.
Angle of Elevation Method (Trigonometry):
Tree Height = (Horizontal Distance × tan(Elevation Angle)) + Observer Eye Height
The tangent of the elevation angle gives the vertical rise over horizontal run. Eye height is added because the angle is measured from eye level, not ground level.
Assumptions & References
- Shadow Method: Both shadows must be measured at the same time and on flat, level ground so the sun angle is identical for both objects.
- Shadow Method: The known object (stick or person) must be perfectly vertical.
- Angle Method: The ground between you and the tree base must be approximately level. For sloped terrain, corrections are needed.
- Angle Method: The angle is measured from the observer's eye level to the very top of the tree.
- Both methods assume the tree grows vertically (not leaning).
- Accuracy improves with careful measurement; a clinometer or smartphone inclinometer app is recommended for the angle method.
- Reference: Avery, T.E. & Burkhart, H.E. (2002). Forest Measurements, 5th ed. McGraw-Hill.
- Reference: Similar triangles principle — Euclid's Elements, Book VI, Proposition 4.