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Sun Angle & Shadow Length Calculator

Estimate solar elevation angle and shadow length by latitude, date, and time of day.

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Everyday utility math — the kind you'd otherwise pull up four browser tabs for. I keep it to one clean answer.

Try a scenario

Click to load — tweak from there.

Inputs

Result

Shadow length (-1 = sun below horizon)

5.2

Sun elevation angle

48.8

Solar declination

23.4

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How to use this

  1. 1Enter latitude (°N).
  2. 2Enter day of year (1-365).
  3. 3Enter hours from solar noon.
  4. 4Enter object height (ft).
  5. 5Read your shadow length (-1 = sun below horizon) on the right — it updates as you type.
  6. 6Hit Share to keep the scenario or send it to someone.

About this calculator

Shadow length depends on the sun's elevation angle above the horizon, which changes with your latitude, the date (via solar declination), and time of day relative to solar noon. This calculator uses standard solar position astronomy — computing solar declination from day-of-year, then hour angle from time offset from solar noon, then combining both with your latitude to get elevation angle — the same math behind sundials, solar panel tilt optimization, and architectural shading design. It's a simplified single-point calculation that ignores atmospheric refraction and the equation of time correction, so treat it as accurate to within about 15-20 minutes of true solar timing, good enough for shadow planning, garden layout, and window overhang design.

FormulaDeclination δ = 23.45°×sin(360×(284+n)/365); hour angle H = 15°×(hours from solar noon); elevation = asin(sin(lat)sin(δ)+cos(lat)cos(δ)cos(H)); shadow length = object height ÷ tan(elevation).

Worked example

Using the values the calculator loads with:

Inputs

  • Latitude: 40 °N
  • Day of year (1-365): 172
  • Hours from solar noon: 3
  • Object height: 6 ft

Results

  • Shadow length (-1 = sun below horizon): 5.2
  • Sun elevation angle: 48.8
  • Solar declination: 23.4

What each field means

Inputs

Latitude (°N)
The latitude used in the calculation, measured in °N. Starts at 40 °N so you have a working example on load. Accepted range: -66–66 °N.
Day of year (1-365)
The day of year (1-365) used in the calculation. Starts at 172 so you have a working example on load. Accepted range: 1–365.
Hours from solar noon
The hours from solar noon used in the calculation. Starts at 3 so you have a working example on load. Accepted range: -8–8.
Object height (ft)
The object height used in the calculation, measured in ft. Starts at 6 ft so you have a working example on load.

Results

Shadow length (-1 = sun below horizon)
Returned as a decimal number and shown as the headline result. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
Sun elevation angle
Returned as a whole number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.
Solar declination
Returned as a whole number. It recalculates instantly whenever you change an input, so you can compare scenarios without reloading.

FAQ

Why does shadow length depend on the date, not just time of day?

Earth's axial tilt changes the sun's maximum elevation angle throughout the year (solar declination), so the same object at solar noon casts a much longer shadow in December than in June at the same latitude — this is also the underlying reason for seasons.

How accurate is this compared to a solar position app?

Reasonably close for planning purposes, but it omits the equation of time (a ±15 minute wobble in when true solar noon occurs relative to clock noon) and atmospheric refraction near the horizon, so treat results as approximate rather than survey-grade.

Why do I need day-of-year instead of just picking a month?

Solar declination changes continuously and non-linearly through the year, changing fastest near the equinoxes (around day 80 and 266) and slowest near the solstices (day 172 and 355), so a specific day gives meaningfully more accurate results than a monthly average.

What is this useful for besides curiosity?

Architects and gardeners use exactly this math to plan roof overhangs that block high summer sun but admit low winter sun, to space rows of plants to avoid shading each other, and to orient solar panels for maximum year-round exposure.

Accuracy and limitations

  • Estimates assume standard, average conditions — local rules, pricing, and materials vary.
  • Results are rounded for readability; add a buffer before ordering, booking, or committing.
  • Double-check anything with a real cost attached against a local quote.

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Cite this calculator

Writing about this topic? Grab a citation — every link helps keep these tools free.

APA
RevenueLab. (2026). Solar Shadow Length Calculator. Retrieved from https://www.revenuelab.fyi/toolbox/solar-noon-shadow-length
HTML
<p>Source: <a href="https://www.revenuelab.fyi/toolbox/solar-noon-shadow-length" target="_blank" rel="noopener">Solar Shadow Length Calculator — RevenueLab</a> (2026).</p>
Markdown
Source: [Solar Shadow Length Calculator — RevenueLab](https://www.revenuelab.fyi/toolbox/solar-noon-shadow-length) (2026).
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