About the Shadow Length Calculator

The Shadow Length Calculator is a fast, accurate tool designed to calculate the length of shadows cast by objects based on their height and the sun's elevation angle. Using basic trigonometry, this calculator provides instant results for architects, engineers, construction planners, photographers, and students working with light, shadows, and spatial design.

How to Use the Calculator

Step 1: Enter Object Height

Input the height of the object that will cast a shadow. You can use either meters or feet as your unit of measurement.

Step 2: Set Sun Elevation Angle

Use the slider to adjust the sun's elevation angle from 1° (low sun, near horizon) to 89° (sun nearly overhead). The angle dramatically affects shadow length.

Step 3: View Results

The calculator instantly displays the shadow length in your chosen unit, plus a visual diagram showing the relationship between object height, sun angle, and shadow projection.

Step 4: Export or Save

Copy results to clipboard, export the visual diagram as an image, or save calculations to history for future reference.

Understanding the Formula

Shadow length is calculated using basic trigonometry:

Shadow Length = Object Height ÷ tan(Sun Angle)

Where the sun angle is measured in degrees from the horizon

The tangent function relates the angle of elevation to the ratio of opposite side (object height) to adjacent side (shadow length). As the sun rises higher (larger angle), the tangent increases, resulting in shorter shadows. When the sun is low (small angle), shadows are much longer.

Shadow Length by Sun Angle

Sun Angle	Shadow Length (10m object)	Description
15°	37.3 m	Very long shadow, early morning/late evening
30°	17.3 m	Long shadow, mid-morning/mid-afternoon
45°	10.0 m	Shadow equals object height
60°	5.8 m	Short shadow, late morning/early afternoon
75°	2.7 m	Very short shadow, near midday

Applications

Architecture & Building Design

Calculate shadow impact on neighboring properties, design building setbacks, plan outdoor spaces, and optimize natural lighting by understanding shadow patterns throughout the day.

Urban Planning

Analyze shadow effects on streets, parks, and public spaces. Ensure adequate sunlight access for pedestrian areas and comply with shadow regulations in dense urban environments.

Photography & Cinematography

Plan outdoor shoots by predicting shadow lengths at different times of day. Optimize lighting conditions and create desired shadow effects for artistic compositions.

Education & Learning

Teach trigonometry concepts, demonstrate practical applications of mathematics, and help students understand the relationship between angles and ratios.

Key Concepts

Sun Elevation Angle

The angle between the sun and the horizon, measured in degrees. 0° means sun at horizon (sunrise/sunset), 90° means sun directly overhead (only possible in tropics). Higher angles produce shorter shadows.

Tangent Function

A trigonometric function that relates an angle to the ratio of opposite to adjacent sides in a right triangle. In shadow calculations, tan(angle) = height ÷ shadow length.

Shadow Direction

Shadows always point away from the sun. In the Northern Hemisphere, shadows point north at midday. Shadow direction changes throughout the day as the sun moves across the sky.

Special Case: 45° Angle

When the sun is at 45° elevation, the shadow length exactly equals the object height. This is because tan(45°) = 1, making the calculation simple: shadow = height ÷ 1 = height.

Practical Examples

Building Shadow Analysis

A 20-meter tall building at 30° sun angle casts a 34.6-meter shadow. This helps determine if the shadow will affect neighboring properties or public spaces.

Tree Planting

A 15-meter tree at 60° sun angle casts an 8.7-meter shadow. Use this to plan tree placement that provides shade without blocking windows or solar panels.

Photography Planning

A 2-meter person at 20° sun angle casts a 5.5-meter shadow. Photographers can use this to plan portrait sessions with desired shadow lengths for dramatic effect.

Frequently Asked Questions

Why can't I use 0° or 90° angles?

At 0°, the sun is at the horizon and shadows are infinitely long. At 90°, the sun is directly overhead and there is no shadow (or a very tiny one directly beneath the object). The tangent function is undefined or approaches infinity at these extremes.

How do I find the sun's elevation angle?

Sun elevation varies by location, date, and time of day. You can use sun position calculators, smartphone apps, or astronomical tables. At solar noon (when sun is highest), elevation equals 90° minus your latitude (adjusted for season).

Does this account for terrain slope?

This calculator assumes flat, level ground. On sloped terrain, shadow length will vary depending on whether the slope faces toward or away from the sun. For sloped surfaces, more complex calculations are needed.

Why do shadows change length throughout the day?

As the sun moves across the sky, its elevation angle changes. Shadows are longest at sunrise and sunset (low angles) and shortest at solar noon (highest angle). The rate of change is fastest near sunrise/sunset.

Can I use this for indoor lighting design?

Yes! The same trigonometric principles apply to artificial light sources. Replace "sun angle" with the angle of your light source relative to the ground, and calculate shadow lengths for interior design and stage lighting.

How accurate is this calculator?

The calculator uses standard trigonometric formulas and is mathematically accurate. Real-world shadows may vary slightly due to atmospheric refraction, terrain irregularities, or object shape complexity, but results are suitable for most practical applications.

Design Guidelines

✓Calculate shadows at multiple times of day for comprehensive analysis
✓Consider seasonal variations in sun angle for year-round planning
✓Account for shadow impact on solar panels, gardens, and outdoor spaces
✓Use shadow analysis to optimize building orientation and window placement
✓Verify calculations with local building codes and shadow regulations
✓Consider cumulative shadow effects from multiple buildings or objects
✓Document shadow studies for planning approvals and design presentations

Why Use This Calculator?

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Instant Results

Real-time calculations with immediate visual feedback and diagram

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Accurate Formula

Based on standard trigonometric principles used in professional applications

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Easy to Use

Simple interface with visual diagram and export options

Professional Shadow Calculation Tool

This calculator is designed for architects, engineers, planners, photographers, and students who need quick and accurate shadow length calculations. It combines mathematical precision with an intuitive interface and visual diagram, making trigonometry accessible while maintaining professional-grade accuracy. All calculations run entirely in your browser with no data sent to servers, ensuring privacy and instant performance. Use this tool for preliminary analysis, educational purposes, and design planning.

Shadow Length Calculator

Settings

Input Parameters

Quick Examples