Shadow Length Calculator
Calculate shadow lengths from sun position, or determine object heights from their shadows. Useful for time-based and shadow-themed puzzles.
Angle of sun above horizon (0-90°)
Results
Shadow Length
1.80 m
Sun Altitude
45.0°
Shadow Ratio
1:1.00
Shadow Diagram
shadow = height / tan(sun altitude)
Common Shadow Ratios
15°
3.73× height
30°
1.73× height
45°
1× height
60°
0.58× height
75°
0.27× height
90°
0× (no shadow)
Shadow Length Calculation
Shadow length depends on the height of an object and the angle of the sun above the horizon (sun altitude). The relationship is:
Shadow Length = Object Height / tan(Sun Altitude)
Understanding Sun Altitude
Sun altitude is the angle of the sun above the horizon, measured in degrees:
- 0°: Sun at horizon (sunrise/sunset)
- 45°: Shadow equals object height
- 90°: Sun directly overhead (no shadow)
Shadow Puzzles in Geocaching
Shadows are used in various puzzle types:
- Timed puzzles: Visit at specific time when shadow points to coordinates
- Measurement clues: Shadow length gives numbers for coordinates
- Sundial caches: Use shadow direction at specific times
- Photo puzzles: Determine time from shadow length in images
Factors Affecting Shadows
- Latitude: Determines maximum sun altitude
- Season: Sun path changes throughout the year
- Time of day: Sun moves across the sky
- Terrain: Hills and buildings can block direct sunlight
The Math
The shadow, object, and sun ray form a right triangle:
- tan(θ) = opposite/adjacent = height/shadow
- shadow = height × cot(θ) = height / tan(θ)
- height = shadow × tan(θ)