Tree Height Estimator

The shadow method uses similar triangles to estimate the height of a tall object. At the same time of day, all shadows maintain the same ratio to their object height.

Tree Height = (Tree Shadow Length / Stick Shadow Length) × Stick Height

Unit conversions:

• Imperial: Measurements in feet
• Metric: Measurements in meters

How to measure:

1. Place a stick (or any known-height object) upright in the ground near the tree
2. Measure the stick height (the part above ground)
3. Measure the stick shadow length on the ground
4. Measure the tree shadow length on the ground
5. All measurements must be taken at the same time (shadows change as the sun moves)

Tips for accuracy:

• Measure on a sunny day, when the shadows have crisp edges
• Take both measurements on flat ground. A slope stretches or shortens one shadow and not the other, which is the single biggest source of error
• Measure from the base of the object to the tip of its shadow
• A 4 foot (1.2 m) stick is about right: easy to hold plumb, and it casts a shadow long enough to measure without a magnifying glass
• Late afternoon or mid morning beats noon. When shadows are longer than the objects casting them, a small error in the tape reading matters less

Where the shadow method goes wrong

The whole thing rests on both shadows falling on the same plane. If the tree’s shadow runs up a bank, across a driveway that sits six inches proud, or partway into a hedge, the tape reads a distance that is not the shadow’s true length on level ground, and the answer comes out high. Walk the shadow before you measure it.

Trees also lean. The method measures the height of the tip above the ground, which for a leaning tree is less than the length of the trunk. That is usually the number you want anyway, since it is what decides whether the thing reaches your roof.

Alternative methods:

• Clinometer or phone app: measure the angle to the top from a known distance away, then add your eye height
• Known reference: compare against something nearby you can measure. One storey of a house is roughly 10 ft (3 m), a standard door is 6 ft 8 in (2 m)