Free · Biology and garden models

Tree Height by Angles or Shadow Proportion

Calculate tree height by angles or shadow proportion with the retained input modes, unit choices and stated arithmetic assumptions.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 2 m reference height casting a 4 m shadow and a tree casting a 20 m shadow imply a 10 m tree height under the similar-triangle model.

Height = d tan(top angle)+eye offset; elevated-base height = d[tan(top angle)−tan(base angle)]; shadow height = reference height × tree shadow/reference shadow.

Worked example

Enter these known values and leave the other values blank.

Method
Shadow measurement
Your height
2 m
Length of your shadow
4 m
Length of the tree's shadow
20 m
Tree height
10 m

Assumptions and limitations

  • Measure horizontal distance for the angle methods. Top and base angle conventions must match the selected below/level/elevated-base diagram.
  • The shadow method assumes parallel sunlight, level reference geometry and measurements made at the same time. Leaning trees and uneven ground can change the result.
  • Tangent angles must stay inside their finite physical branches. A positive top-to-base height is required; these geometric measurements are estimates rather than surveyed clearance dimensions.

Common questions

What does this result represent?

Measure horizontal distance for the angle methods. Top and base angle conventions must match the selected below/level/elevated-base diagram.

Can I solve for another quantity?

Enter the known quantities and clear the unknown where an inverse relationship is available. Selection presets remain separate from measurements you supply; use locks to retain known inputs.

References

Bookify enforces finite physical or discrete inputs for this model and detects the stated selected-scenario relationships without changing the captured arithmetic graph. Replace the captured external diagrams with original accessible descriptions of every measurement/grid variant, retaining all variant conditions.

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