Shadow Length Calculator
Relate sun height in the sky to how long a shadow an object casts — useful for photography and site planning.
By Aryan Khan, Founder & Editor · Updated October 2026
For example, a 10-metre building in New York casts a noon shadow of just 3.11 metres at the June solstice — and 20.62 metres in December, which is why winter sun feels rationed.
How to use Shadow Length Calculator
One right triangle runs the whole page:
The Shadow Length Calculator works out how long a shadow an object casts, from its height and the Sun's altitude — length equals height divided by the tangent of the sun angle. Enter the height and read the shadow — the arithmetic behind sundials, gardens and solar siting.
- 1Set location and check solar position (altitude).
- 2Use height ÷ tan(altitude) for approximate shadow length when the sun is above the horizon.
What people use Shadow Length Calculator for
1. Garden and greenhouse planning
Will the fence shade the beds in December? At London's winter noon a 2 m fence throws 7.4 m of shadow (computed) — plant with the winter number, not June's optimism. The angle comes from the Sun Altitude Calculator.
2. Solar panel siting
Row spacing and rooftop obstructions are shadow problems: keep December's long shadow off the next row.
3. Photography and film
Long-shadow golden looks are a sun-altitude choice; compute when your location's shadows reach the ratio you want.
4. Playground and building shade studies
Shade audits for schools and planning applications begin with this triangle, run month by month.
Worked examples
10 m object, solar noon: June 21 sun altitude 72.7° → shadow 3.11 m. December 21 altitude 25.9° → shadow 20.62 m. Same building, a 6.6× longer winter shadow.
A 1.8 m person at London's December noon (altitude 15.1°) casts 6.68 m — nearly four body lengths, the longest selfie backdrop of the year.
Shadow ratios by sun altitude
Shadow length as a multiple of object height (height ÷ tan altitude).
| Sun altitude | Shadow |
|---|---|
| 10° | 5.67 × height |
| 20° | 2.75 × height |
| 30° | 1.73 × height |
| 45° | 1.00 × height — shadow equals height |
| 60° | 0.58 × height |
| 72.7° (NYC June noon) | 0.31 × height |
Assumes flat ground and a vertical object; slopes stretch or shrink the real shadow — the calculator's flat-ground assumption is stated, not hidden.
Shadows follow the sun’s elevation
When the sun is high, shadows shrink; near sunrise and sunset they stretch. For a vertical object on flat ground, length is roughly height divided by the tangent of solar elevation.
Photographers use this to anticipate whether a building or tree will throw shade across a subject. Site planners use it for rough massing studies. Terrain slope and nearby walls still win over pure trigonometry outdoors.
Pair solar position with sunrise and golden-hour tools when the time of day matters as much as the angle.
How to interpret the result
The most common errors come from using a correct result to answer the wrong geographic question. Keep these points in mind for Shadow Length Calculator:
- When comparing day length across a year, remember the curve is your latitude's signature: near-equatorial sites hover at twelve hours while high latitudes swing wildly. Choose expectations by latitude, not by calendar folklore.
- Convert solar times to local clock times deliberately: the sun keeps astronomical time, while governments keep political time, and the gap between them is large in many countries. State both when sharing results.
Limits & appropriate use
Solar arithmetic's limits are small but real: the official zenith encodes average refraction, not today's atmosphere; coordinates are rounded to your input's precision; and terrain is absent unless you add height yourself — a mountain rises the sun late and the formulas won't know. Time adds the political layer: zones and DST are human law, and western edges of big zones (Spain, western China) make solar noon wander hours from clock noon. Every output here therefore carries its convention and both clocks, because an unanchored sunrise time is an argument, not a fact.
Lunar and seasonal outputs carry their own gentle limits: phase from the synodic approximation is hours-precise, which outruns every planning need but not ephemeris science; day length is geometric daylight, not sunshine, and clouds belong to climate's department. Escalation is rare and well-defined — astronomical almanacs and ephemerides for science, terrain-aware apps for mountain photography, and the tz database maintainers whenever a government invents a new DST rule at 48 hours' notice, as they delight in doing.
- Science-grade ephemerides → astronomical almanacs/JPL horizons.
- Mountain sunrise/sunset → terrain-aware horizon adjustments.
- Legal daylight definitions → jurisdictional statutes (they vary!).
Data & methodology
Solar elevation from position algorithms; shadow length from basic trigonometry on flat ground.
For source details, licences and model limitations, see Data Sources and Methodology.
Key terms worth knowing
- Civil twilight
- Sun between 0° and −6°: usable outdoor light without lamps.
- Synodic month
- The 29.53-day new-moon-to-new-moon cycle behind phases.
Editorial guidance: MapBench explains the method and limitations so the tool can be used as a transparent reference, not as a black-box answer. For legal boundaries, safety-critical routing, surveying, engineering, regulated decisions or official statistics, verify the result with the responsible authority or a qualified professional.
Category: Sun & Moon. Results are intended for everyday analysis and planning unless a page explicitly states otherwise.
Method, assumptions & limits
- This tool’s method
- Solar elevation from position algorithms; shadow length from basic trigonometry on flat ground.
- Before relying on the answer
- Check the date, location and time zone together. A solar or lunar event is tied to all three, and some events do not occur at high latitudes on a given date.
- What the result cannot establish
- A calculated event assumes the model's horizon and atmospheric conventions. Buildings, terrain and local weather can alter what you observe.
Coverage: Worldwide. Search, basemap and external data requests may use third-party services; browser-based does not mean every operation is offline. Read the source and licence notes, calculation methodology and privacy policy. If a result looks inconsistent, report a correction with the inputs and mode used.
Frequently asked questions
Clear answers about the calculation, accuracy and appropriate use.
Exact physics?
Shadow length ≈ height / tan(solar elevation). Use solar position for elevation angle at your place and time.
Flat ground?
Assumes level ground; slopes change real shadow length.
Are sunrise and solar times exact to what I will see?
Calculated events use astronomical geometry. Terrain, buildings, weather and atmospheric conditions can shift what an observer actually sees.
Does daylight saving change the Sun's position?
No. Daylight saving changes the civil clock label, not solar geometry. Timezone rules affect displayed local time.
Why can polar locations show unusual results?
High latitudes can have days when the Sun does not rise or set, so some solar events legitimately do not occur on a selected date.
What is the formula?
Shadow = height ÷ tan(sun altitude). At 45° the shadow equals the height; below that it grows fast, which the ratio table makes visceral.
Where does the sun angle come from?
From place, date and time via the solar-position math — or type an altitude directly if you measured one. The Sun Altitude Calculator is the dedicated source.
Morning and evening shadows point where?
Opposite the Sun's azimuth: morning shadows point west-ish, evening east-ish, swinging with the season — direction is the Sun Azimuth Calculator's department.
Can it work backwards (shadow to height)?
Yes — measure a shadow and the Sun's altitude and the same triangle returns the object's height: the surveyor's oldest trick.
What about sloped ground?
Slopes change everything: downhill shadows stretch, uphill shrink. The calculator assumes flat ground and says so; treat sloped results as first approximations.
Trees and soft shadows?
The triangle gives the shadow's core (umbra) length; leafy canopies feather the edge. For siting decisions the core length is the conservative number.
Shadow at sunrise or sunset?
Infinite in the limit — as altitude approaches zero the shadow leaves the map. Practically, buildings and terrain end it first.
Related tools and resources
The angle: the Sun Altitude Calculator; the direction: the Sun Azimuth Calculator; both at once: the Solar Position Calculator.
More free tools
Sources, methodology & editorial trust
- ✓ Browser-first processing where supported
- ✓ External sources are documented
- ✓ No account required for public tools
- ✓ Review data sources
Calculations are documented with their assumptions, limitations and source context rather than presented as unexplained answers.
Reviewed and maintained by Aryan Khan, Founder & Editor of MapBench.
Part of our sun & moon hub
Shadow Length Calculator sits in the sun & moon cluster, alongside 27 other tools that answer neighbouring questions with different methods or datasets.
You may also need
When this answer is only part of the job, these clusters cover the next step.
Read the guide behind this tool
Chasing Golden Hour: A Photographer's Solar Toolkit — Golden hour is an altitude band, not a fixed clock time. How to plan light with solar tools — windows, horizons and moon phase — instead of guessing.