How to Calculate Shadow Length
Simple formula and free visual calculator for determining shadow length at any time.
The Shadow Length Formula
Shadow Length Formula
Shadow Length = Height ÷ tan(Sun Altitude)
This formula comes from basic trigonometry. When the sun shines on an object, the shadow forms a right triangle where:
- Object height is the vertical side (opposite)
- Shadow length is the horizontal side (adjacent)
- Sun altitude is the angle between the sun's rays and the ground
The tangent function relates these: tan(angle) = opposite / adjacent, which rearranges to: adjacent = opposite / tan(angle), or Shadow = Height / tan(Sun Altitude).
Shadow Multiplier by Sun Altitude
The "shadow multiplier" tells you how many times longer the shadow is compared to the object height. Multiply the object height by this number to get the shadow length.
| Sun Altitude | Shadow Multiplier | Example (6ft person) | Typical Condition |
|---|---|---|---|
| 5° | 11.4x | 68.5 ft shadow | Just after sunrise / before sunset |
| 10° | 5.7x | 34.1 ft shadow | Golden hour |
| 20° | 2.7x | 16.5 ft shadow | Morning/afternoon |
| 30° | 1.7x | 10.4 ft shadow | Winter noon (mid-latitudes) |
| 45° | 1.0x | 6 ft shadow | Shadow = height |
| 60° | 0.58x | 3.5 ft shadow | Summer noon (mid-latitudes) |
| 75° | 0.27x | 1.6 ft shadow | Summer noon (tropics) |
| 90° | 0x | No shadow | Sun directly overhead |
Worked Examples
Example 1: Building at noon in winter
A 50-foot building at noon in New York City during winter (sun altitude ≈ 26°).
Shadow = 50 ÷ tan(26°)
Shadow = 50 ÷ 0.488
Shadow ≈ 102.5 feet
Example 2: Tree at golden hour
A 30-foot tree during golden hour (sun altitude ≈ 5°).
Shadow = 30 ÷ tan(5°)
Shadow = 30 ÷ 0.087
Shadow ≈ 343 feet
Example 3: Person at summer noon
A 6-foot person at noon in summer (sun altitude ≈ 70°).
Shadow = 6 ÷ tan(70°)
Shadow = 6 ÷ 2.747
Shadow ≈ 2.2 feet
Use SunMap for Visual Shadow Calculation
Instead of manual calculations, use SunMap to visualize shadows in 3D:
- 1
Navigate to your location
Open SunMap and find the building or area you want to analyze.
- 2
Set the date and time
Use the sliders to set your desired date and time.
- 3
See the sun altitude and shadow multiplier
SunMap displays the current sun altitude and shadow multiplier. Multiply any height by this number.
- 4
View real building shadows
The 3D map shows actual shadows cast by real buildings based on their heights from OpenStreetMap.
See Shadows Visually in 3D
Skip the math—use SunMap to see exactly how shadows fall at any location and time.
Open Shadow Calculator