Shadow Length Calculator

Work out shadow length instantly with clear inputs, formula shown and shareable results.

About Shadow Length Calculator

Shadow length is height divided by the tangent of solar elevation. At 30 degrees a 10 m object casts a 17.3 m shadow; at 45 degrees the shadow equals the height exactly. The relationship is how Eratosthenes measured Earth's circumference and how solar access and overshadowing are assessed in planning.

Formulas

Shadow length

length = height / tan(solar elevation)

Inverse

height = shadow length x tan(solar elevation)

Worked example

With the default values below, Shadow Length Calculator returns Shadow Length of 17.321. Change any input above and every figure here is recalculated in your browser.

Inputs used

Object heightminimum 0 m: 10 m
Solar elevation angleaccepts 0.1–90 deg: 30 deg

Results

Shadow Length: 17.321 m
Shadow Length Per Unit Of Height: 1.732
Height Recovered From The Shadow: 10.000 m
Solar Elevation Used: 30.0 deg

Step by step

1Values used
2Shadow length
3Inverse
4Shadow Length= 17.321 m
5Shadow Length Per Unit Of Height= 1.732
6Height Recovered From The Shadow= 10.000 m
7Solar Elevation Used= 30.0 deg

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 3 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

At what sun angle does the shadow equal the height?

45 degrees, where the tangent is one. Below that shadows exceed the height and grow rapidly.

How is this used in planning?

To check overshadowing at the winter solstice, when the sun is lowest and shadows longest - the worst case for solar access.