Height Of Object From Shadow Calculator

Work out height of object from shadow instantly with clear inputs, formula shown and shareable results.

About Height Of Object From Shadow Calculator

The object, its shadow and the sun's ray form a right triangle in which the elevation angle sits at the shadow tip. So height = shadow × tan(elevation), the method Thales reportedly used on the Great Pyramid.

Formula

Height from shadow

h = shadow length × tan(sun elevation)

Worked example

With the default values below, Height Of Object From Shadow Calculator returns Object height of 8.4025. Change any input above and every figure here is recalculated in your browser.

Inputs used

Shadow lengthminimum 0: 12
Sun elevation angleaccepts 0–90 °: 35 °

Results

Object height: 8.4025
Distance from shadow tip to the top: 14.6493
Height ÷ shadow: 0.7002
tan of the elevation angle: 0.70020754

Step by step

1Values used
2Height from shadow
3Object height= 8.4025
4Distance from shadow tip to the top= 14.6493
5Height ÷ shadow= 0.7002
6tan of the elevation angle= 0.70020754

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Shadow 12 m, sun at 35°?

12 × tan 35° ≈ 8.402 m tall.

Why does the shadow lengthen near sunset?

As the elevation angle drops toward zero, tan of it approaches zero, so the shadow needed to reach the same height grows without bound.