Height from Shadows Calculator
Estimate an object’s height from its shadow and a reference object measured at the same time. Mix length units and see the similar-triangle proportion.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Parallel sunlight produces similar right triangles when both objects are vertical and the ground is level. Their height-to-shadow ratios match. Multiply the target shadow by the reference height divided by its shadow.
Target height = reference height × target shadow / reference shadow
Worked example
A vertical 1.5 m reference casts a 2 m shadow while a tree casts a 12 m shadow. The tree height is 1.5×12/2=9 m. The implied solar elevation is about 36.87°.
Assumptions and input details
Measure both shadows at the same time on the same level plane and measure each from the object’s base to the shadow tip. Objects must be vertical; slopes, leaning objects and unclear shadow tips invalidate the simple proportion. All lengths must be positive and between 1e−12 and 1e12 meters after conversion. The drawing is schematic; measurement uncertainty is not estimated.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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