Shadow Length & Sun Angle Calculator
Use this calculator to find shadow length, sun elevation angle, or object height. Great for quick field checks in architecture, photography, landscaping, and classroom math.
Use values between 0 and 90 degrees (not inclusive).
Rearranged forms:
Shadow length = height / tan(θ), Height = shadow length × tan(θ), θ = arctan(height / shadow length)
What Is a Shadow Calculator?
A shadow calculator is a simple geometry tool that helps you estimate how long a shadow will be, how high the sun is in the sky, or how tall an object is. It relies on right-triangle trigonometry, where the object height is one side, the shadow is another side, and the sun’s elevation angle sets the triangle shape.
If you have ever wondered why shadows are very long in the morning and evening but short at noon, this calculator gives a numerical answer. Lower sun angle means longer shadows. Higher sun angle means shorter shadows.
How the Math Works
The Core Relationship
For level ground and straight sunlight, the relationship is:
- tan(θ) = height / shadow length
- θ is the sun elevation angle above the horizon.
- Height and shadow length must use the same unit.
This is why shadow math appears in school geometry, surveying, and practical field work. It is quick, reliable, and easy to check with a calculator.
Three Useful Modes
- Find shadow length: Enter object height and sun angle.
- Find sun angle: Enter object height and measured shadow.
- Find object height: Enter shadow length and sun angle.
How to Use This Shadow Calculator
- Select a mode based on what you already know.
- Pick your preferred unit (meters or feet).
- Enter positive values only.
- For angles, keep values between 0° and 90°.
- Click Calculate to see the result instantly.
Tip: for best real-world results, measure shadows on flat ground and avoid times when light is being blocked by trees, buildings, or nearby structures.
Practical Uses
1) Solar Planning
Before installing solar panels, people often check seasonal shading from nearby trees and rooftops. Estimating shadow length at different sun angles helps identify whether a location gets enough direct sunlight.
2) Photography & Filmmaking
Photographers can predict light direction and contrast by understanding sun angle. If a location will cast long shadows at the intended shooting time, that can dramatically affect composition.
3) Construction & Design
Architects and landscape designers use shadow calculations to improve outdoor comfort, daylight exposure, and placement of structures. This is especially useful for patios, courtyards, and walkways.
4) Outdoor Education
Teachers and students use shadows to demonstrate real-world trigonometry. Measuring a flagpole’s shadow can estimate its height without climbing it.
Example Scenarios
- Example A: A 3 m pole with a 30° sun angle casts a shadow of about 5.20 m.
- Example B: A 6 ft person casting an 8 ft shadow implies a sun angle of about 36.87°.
- Example C: A 12 ft shadow at 40° corresponds to an object height of about 10.07 ft.
Accuracy Tips and Common Mistakes
- Use the same unit for all length values.
- Do not use 0° or 90° as direct inputs; both produce unstable geometry for this model.
- Measure the shadow from object base to the tip, in a straight line.
- Avoid uneven surfaces if you want precise estimates.
- Remember this is a geometric estimate; atmospheric refraction and terrain can cause slight deviations.
Shadow Calculator FAQ
Can I use this as a shadow length calculator for trees?
Yes. Enter approximate tree height and a sun elevation angle to estimate shadow length. For irregular canopies, treat the tree as a simplified vertical object.
What is a typical sun angle at noon?
It depends on latitude and season. Summer noon sun angles are usually much higher than winter noon angles, which is why winter shadows are often longer.
Does this work indoors with artificial light?
The same geometry works for any directional light source, but the “sun angle” would then be the elevation angle of your lamp or spotlight.
Can this calculator help estimate building height?
Absolutely. If you can measure the shadow length on level ground and estimate the sun angle, you can calculate height quickly and non-invasively.
Whether you are planning a garden, solving a trigonometry problem, or checking site conditions for a project, this shadow calculator gives a fast and practical way to convert between height, angle, and shadow length.