Shadow Length Calculator

A shadow forms when an object blocks sunlight. The length of the shadow depends on two things: the height of the object and the angle of the sun above the horizon.

The formula:

Shadow Length = Height / tan(Sun Elevation Angle)

Where tan is the trigonometric tangent function. The sun elevation angle is measured in degrees from the horizon — 0° means the sun is at the horizon (very long shadows), and 90° means the sun is directly overhead (no shadow at all).

Why does the angle matter so much?

At a low sun angle (like early morning or late afternoon), shadows are very long. At a high sun angle (like noon in summer), shadows are short. At exactly 45°, the shadow equals the object’s height.

Metric example:

A 10-meter tree with the sun at 30° elevation:

Shadow = 10 / tan(30°) = 10 / 0.577 = 17.3 meters

Imperial example:

A 30-foot flagpole with the sun at 45° elevation:

Shadow = 30 / tan(45°) = 30 / 1.0 = 30 feet

Reference table — shadow multiplier by sun angle:

Practical uses:

• Estimating the height of a tree or building from its shadow
• Planning where a fence or building will cast shade in your yard
• Photography — predicting where golden-hour shadows will fall
• Architecture — designing overhangs to shade windows at specific times of year
• Astronomy education — understanding how ancient Egyptians used shadows to measure the Earth

Finding the sun’s elevation angle: You can look up the current sun elevation for your location using a sun position app or website. It varies by location, season, and time of day. At solar noon in summer, mid-latitude locations typically see 60–70°. In winter noon, it may be 20–30°.