Productive ToolboxShadow Length Calculator
Calculate shadow length from object height and sun elevation angle. Free online sun shadow calculator for architecture, solar planning, and photography.
Shadow Length Calculator
Calculate shadow length instantly using object height and sun elevation angle. Perfect for architecture, planning, and design.
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What Is a Shadow Length Calculator?
This shadow length calculator works out how long a shadow is from the height of an object and the sun's elevation angle. You can set the angle yourself, or choose a city (or type coordinates), a date and a local time and let it calculate where the sun is, how long the shadow is and which way it points, with an hour-by-hour table for the whole day.
The calculation relies on a single trigonometric relationship — Shadow Length = Object Height ÷ tan(Sun Angle) — but applying it manually requires knowing the tangent value for the angle, which most people don't have memorized. The relationship is also non-linear: going from 15° to 30° cuts the shadow in half, but going from 60° to 75° only reduces it by about 3 meters for a 10-meter object. This tool handles the math instantly and visualizes the geometry so the result is immediately understandable.
Built for architects checking building shadow impact on neighboring properties, urban planners conducting shadow studies for permit applications, photographers planning golden-hour shoots, teachers demonstrating trigonometry, and solar panel installers calculating shading distances. We do not collect or store what you enter.
How Shadow Length Is Calculated
The calculation is based on right-triangle trigonometry. The object is the vertical leg, the shadow is the horizontal leg, and the sun's ray is the hypotenuse. The angle between the sun's ray and the ground is the elevation angle.
Shadow Length Formula
Shadow Length = Object Height ÷ tan(Sun Elevation Angle°)
Example: 10m building at 30° → 10 ÷ tan(30°) = 10 ÷ 0.577 = 17.32 m
Example: 10m building at 60° → 10 ÷ tan(60°) = 10 ÷ 1.732 = 5.77 m
Key relationships to understand:
- At 45° — shadow length exactly equals object height (tan 45° = 1)
- Below 45° — shadow is longer than the object (sun is lower)
- Above 45° — shadow is shorter than the object (sun is higher)
- Below 10° — shadows become very long (tan approaches 0); sunrise/sunset conditions
- Above 80° — shadows are very short; only possible in tropical locations near midday
How to Use the Shadow Length Calculator
Step-by-Step Guide
- 1Enter the object height: Type the height of the building, tree, pole or person and choose meters or feet.
- 2Set the sun angle — or let the tool find it: Drag the sun elevation slider, or choose Use date, time & place and pick a city or enter coordinates, a date and a local time; the sun's elevation and direction are worked out for you.
- 3Read the shadow length and direction: The shadow length appears in your unit and the other one. In date-and-place mode you also see which compass direction the shadow points.
- 4Check the whole day: Open Shadow through the day to see the shadow length and direction on every hour while the sun is up.
- 5Copy, save or export: Copy the result, save it to the history, or download the diagram as an image or the result as text.
What This Calculator Provides
- ✓Shadow length from any object height and sun angle
- ✓Sun elevation and direction from a date, local time and place
- ✓13 US, European and Australian cities, or your own coordinates
- ✓Shadow direction as a compass bearing
- ✓Hour-by-hour shadow table for the chosen day
- ✓Meters and feet, with a live diagram
- ✓Copy, history, and export as image or text
- ✓Your inputs are not collected or stored
Real-World Use Cases
Building Shadow Impact Assessment
An architect is designing a 24-meter residential tower in a dense urban neighborhood. Local planning rules require a shadow study showing impact at 9am, 12pm, and 3pm on the winter solstice. At 51° N latitude, winter solstice noon sun angle is approximately 15°. At that angle, the tower casts a 24 ÷ tan(15°) = 89.6-meter shadow — nearly 90 meters extending north. The architect uses this result to adjust the tower's footprint and orientation before submitting the planning application.
Solar Panel Shading Distance
A homeowner in Edinburgh (56° N) is planning rooftop solar panels but has a 3-meter parapet wall at the south end of the roof. At winter solstice noon, the sun elevation is approximately 10.5°. The parapet casts a shadow of 3 ÷ tan(10.5°) = 16.2 meters — meaning panels must be placed at least 17 meters from the parapet to avoid shading during the worst case of the year. The roof is only 12 meters deep, so the parapet height needs to be reduced or the panels placed differently.
Photography Golden Hour Planning
A portrait photographer is scouting a location for a sunset shoot. At 6pm in July at 52° N, the sun elevation is approximately 8°. A 1.75-meter subject at 8° sun casts a 1.75 ÷ tan(8°) = 12.5-meter shadow — long enough to create dramatic leading lines across the ground. The photographer confirms the shadow direction (toward the camera) and books the location for the shoot with confidence the shadow will fall as planned.
Tree Placement for Garden Shade
A landscape designer is recommending tree placement for a new garden. The client wants a tree that shades the patio (8 meters from the planned planting spot) at 2pm in summer. At 2pm on a summer afternoon at 48° N, sun elevation is approximately 50°. A tree at that distance would need to be at least 8 × tan(50°) = 9.5 meters tall to cast a shadow reaching the patio. The designer specifies a mature height species of 10–12 meters to guarantee shade within the patio area.
Construction Site Temporary Shading
A site manager needs to verify that a 12-meter construction crane won't cast shadows onto a neighboring building's solar installation during morning operating hours. At 9am in autumn, sun elevation is approximately 22°. The crane casts a shadow of 12 ÷ tan(22°) = 29.7 meters to the west. The neighboring solar array is 18 meters west of the crane — inside the shadow zone. The manager schedules crane operation to avoid the critical 8–10am window when the solar array is most active.
Urban Street Canyon Analysis
A city planner is reviewing proposals for a 30-meter mixed-use building on a north–south street. They need to determine how many hours the opposite sidewalk will be in shadow on the spring equinox. At equinox at 45° N, noon sun elevation is 45° and shadow equals building height (30m). The street is 20 meters wide. Working backwards: the building casts a 20-meter shadow when the sun elevation reaches arctan(30/20) = 56°. The planner calculates that the sidewalk is in shadow from sunrise until approximately 10:30am — acceptable under local sunlight access guidelines.
Shadow Length Reference Tables
Shadow Length by Sun Angle (10m Object)
| Sun Angle | Shadow (10m) | Typical Time |
|---|---|---|
| 5° | 114.3 m | Sunrise / sunset |
| 10° | 56.7 m | Early morning / late evening |
| 15° | 37.3 m | Winter midday at 52° N |
| 20° | 27.5 m | Morning / afternoon |
| 30° | 17.3 m | Mid-morning / mid-afternoon |
| 45° | 10.0 m | Shadow = object height |
| 50° | 8.4 m | Late morning / early afternoon |
| 60° | 5.8 m | Summer midday at 45° N |
| 70° | 3.6 m | Summer midday at 35° N |
| 80° | 1.8 m | Near-vertical sun (tropics) |
Winter Solstice Noon Sun Angle by Latitude
| Latitude | Example City | Winter Noon Angle |
|---|---|---|
| 25° N | Miami / Karachi | 41.5° |
| 35° N | Los Angeles / Tokyo | 31.5° |
| 45° N | Portland / Milan | 21.5° |
| 51° N | London / Warsaw | 15.5° |
| 53° N | Dublin / Berlin | 13.5° |
| 60° N | Oslo / Helsinki | 6.5° |
| 25° S | São Paulo / Brisbane | 41.5° |
| 34° S | Sydney / Cape Town | 32.5° |
* Winter solstice noon angle = 90° − latitude − 23.5°. Southern hemisphere winter is June solstice.
Frequently Asked Questions
What is a shadow length calculator?
A shadow length calculator is a free online tool that computes the length of a shadow cast by any object based on the object's height and the sun's elevation angle. It uses the trigonometric formula Shadow Length = Object Height divided by tan(Sun Angle) to produce an accurate result instantly. It is used by architects, photographers, solar panel installers, teachers, and anyone who needs to estimate shadow length at a specific time of day.
How do you calculate shadow length from sun angle?
Shadow length is calculated by dividing the object height by the tangent of the sun's elevation angle: Shadow Length = Height / tan(Angle). For a 10-meter building at 30°, the shadow is 10 / tan(30°) = 17.3 meters. At 45°, the shadow equals the object height exactly. At 60°, the shadow is 5.77 meters — shorter because the sun is higher.
How do I find the sun's elevation angle?
Choose Use date, time & place in the calculator: pick a city or type latitude and longitude, set the date and local time, and the sun's elevation and compass bearing are calculated with the NOAA solar position method. As a rule of thumb, the noon elevation is about 90° − latitude, plus up to 23.4° in summer and minus up to 23.4° in winter.
What is the shadow length when the sun is at 45 degrees?
When the sun is at exactly 45° elevation, the shadow length equals the object height. This is because tan(45°) = 1, making the formula Shadow = Height / 1 = Height. A 5-meter fence post casts a 5-meter shadow. A 20-meter building casts a 20-meter shadow.
Why are shadows longer in the morning and evening?
Shadow length is determined by the tangent of the sun's angle. At sunrise and sunset, the sun is near 0° elevation and the tangent approaches zero, making shadows extremely long. As the sun rises, the elevation angle increases, the tangent grows, and shadows shorten. The shortest shadows occur at solar noon when elevation is at its peak.
How do architects use shadow length calculations?
Architects use shadow calculations to determine whether a proposed building will cast shadows onto neighboring properties, public spaces, or streets. Many planning authorities require shadow impact studies as part of building permit applications, especially for tall urban projects. Calculations are run for multiple times of day and dates to show the full range of shadow conditions.
Can this calculator be used for objects other than buildings?
Yes. The formula applies to any vertical object: trees, flagpoles, fences, utility poles, solar panel arrays, antennas, or people. The only inputs are the object height and the sun's elevation angle. A 15-meter tree at 60° sun casts an 8.66-meter shadow. A 1.8-meter person at 20° sun casts a 4.95-meter shadow.
Does terrain slope affect shadow length?
Yes. This calculator assumes flat, level ground. On an upward slope toward the sun, the shadow appears shorter because the ground rises to meet it sooner. On a downward slope away from the sun, the shadow appears longer. For most architectural site analysis purposes, the flat-ground result is used as a baseline with slope adjustments noted separately.
What sun angle should I use for solar panel shading analysis?
Start with the lowest sun of the year: the noon elevation on the winter solstice, roughly 90° − latitude − 23.5°. At 51° N that is about 15.5°, so a 2 m fence casts a shadow about 7 m long. Shadows are longer still in the early morning and late afternoon, so a full shading check also looks at the hours either side of noon.
Is my data private when using this calculator?
Yes. We do not collect or store what you enter.
Which direction does a shadow point?
Directly away from the sun. In the Northern Hemisphere the noon sun is to the south, so noon shadows point north; in the morning the sun is in the east and shadows point west, and in the evening the reverse. Date-and-place mode shows the exact bearing for the time you choose.
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