Maths⏱ 4 min read
How to Calculate the Height of a Tree (Without Climbing It)
You can measure a tree accurately using nothing more than a stick, your shadow, or basic trigonometry. Here is three different methods ranked by accuracy and equipment needed.
Measuring tree height is a classic applied maths problem -- useful for planning felling, assessing subsidence risk, or simply satisfying curiosity. The methods range from ancient Greek to modern clinometer.
Method 1: Shadow Method (Simplest)
Works when both you and the tree cast measurable shadows.
Tree height / Tree shadow = Your height / Your shadow
If you are 1.75m tall:
Your shadow: 2.1m
Tree shadow: 14.7m
Tree height = (14.7 / 2.1) x 1.75 = 7 x 1.75 = 12.25m
Works best: sunny day, around midday, flat ground.
Limitation: need clear view of the tree's shadow tip (may be hidden).
Method 2: Stick Method (Classic)
Hold a stick vertically at arm's length (approximately 60cm).
Walk back until the top of the stick aligns with the top of the tree
and the bottom aligns with the base.
At this position: distance to tree = tree height
Example:
Arm length: 60cm
Stick length used: 60cm (same = makes a 45-degree angle)
Distance to tree base: 15.3m
Tree height: approximately 15.3m
For accuracy: measure arm length and stick length separately:
Tree height = (Stick length / Arm length) x Distance to tree
Stick 45cm, arm 60cm, distance 20m:
Tree height = (45/60) x 20 = 0.75 x 20 = 15m
Method 3: Trigonometry (Most Accurate)
Measure the angle to the tree top from a known distance.
Equipment: clinometer, phone inclinometer app, or protractor.
Stand 20m from the base of the tree.
Measure angle of elevation to the top: 38 degrees.
Tree height above eye level = distance x tan(angle)
= 20 x tan(38) = 20 x 0.7813 = 15.6m
Add your eye height: 15.6 + 1.65 = 17.25m total tree height
If the ground slopes:
Measure angle going up (a) and angle going down (b)
Height = distance x (tan a + tan b) / (1 + tan a x tan b)
[Or measure from both sides and average the two estimates]
What Tree Heights Mean in Practice
Subsidence risk assessment (insurance/mortgage purposes):
Trees within a distance equal to their height can affect foundations
Particularly: oak, poplar, willow, elm near clay soils
Tree preservation order (TPO):
Trees above approximately 75mm trunk diameter at 1.5m height
may require council consent to fell or heavily prune.
Safe felling zone:
Tree should fall into a clear area of at least 1.5x the tree height.
17m tree: need at least 25.5m clear fall zone.
Felling a tree in a smaller space requires sectional felling
(removing limb by limb from the top) by a qualified arborist.