Tree Height Calculator
Calculate the height of a tree by measuring the angle of elevation to the top of the tree and your distance from its base.
Formula
Tree Height (H) = d × tan(θ) + heye
- d = horizontal distance from the observer to the base of the tree (meters)
- θ = angle of elevation from the observer's eye to the top of the tree (degrees)
- heye = height of the observer's eye above the ground (meters)
- tan(θ) = trigonometric tangent of the angle of elevation
The formula is derived from basic trigonometry: in a right triangle formed by the observer, the base of the tree, and the top of the tree, the opposite side (height above eye level) equals the adjacent side (distance) multiplied by the tangent of the angle. The observer's eye height is then added to get the total tree height from the ground.
Assumptions & References
- The ground between the observer and the tree is assumed to be flat and level.
- The distance is measured horizontally from the observer's position to the base of the tree trunk.
- The angle of elevation is measured from the observer's eye level to the very top of the tree.
- The default observer eye height of 1.6 m (≈ 5 ft 3 in) represents an average adult eye level.
- For sloped terrain, corrections must be applied to the horizontal distance and angle measurements.
- A clinometer, theodolite, or smartphone inclinometer app can be used to measure the angle of elevation accurately.
- Reference: Avery, T.E. & Burkhart, H.E. (2002). Forest Measurements (5th ed.). McGraw-Hill. — Standard forestry trigonometric height measurement method.
- Reference: Philip, M.S. (1994). Measuring Trees and Forests (2nd ed.). CAB International. — Describes tangent-based height estimation techniques.