Solar Noon Calculator — Sun At Zenith & Shadow Length
Find the exact moment the sun reaches its highest point for any latitude, longitude, and date — plus the maximum altitude and the shadow-length multiplier. Uses the NOAA Solar Position Algorithm with the equation-of-time correction. Today is May 28, 2026.
Quick Conversion
Formula: shadow = height × cot(altitude)
Sun At Solar Noon — Shadow Indicator
Solar Noon Reference Points
Sun Altitude → Shadow Length (1 m gnomon)
| Altitude (°) | Shadow (m) | When |
|---|---|---|
| 90° | 0.000 | Zenith (equator equinox) |
| 75° | 0.268 | Summer mid-lat noon |
| 60° | 0.577 | Summer mid-lat noon |
| 45° | 1.000 | Spring/autumn noon |
| 30° | 1.732 | Spring/autumn noon |
| 20° | 2.747 | Winter low sun |
| 15° | 3.732 | Winter low sun |
| 10° | 5.671 | Winter low sun |
| 5° | 11.430 | Winter low sun |
| 2° | 28.636 | Winter low sun |
| 1° | 57.290 | Winter low sun |
Need other solar data? Golden hour · Blue hour
Solar Noon & Altitude Formula
altitude_max = 90° − |φ − δ|Where φ = latitude, δ = solar declination. At London (φ = 51.5°) on May 28, 2026 (δ ≈ +21.5°): altitude = 90 − 30 = 60°.
EoT(d) ≈ 9.87 sin(2B) − 7.53 cos(B) − 1.5 sin(B) where B = 2π(d−81)/365Equation of time in minutes. d = day of year. Peak +16 min around Nov 3; min −14 min around Feb 11.
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How To Use Solar Noon Data
- 1. Set your latitude and longitude (or pick a preset location).
- 2. Pick the date — the SVG repaints with the sun at that day's noon altitude.
- 3. Read the shadow factor — multiply by your object height for noon shadow length.
- 4. Use the EoT correction to align your sundial with clock time.
- 5. Save the lookup — for solar-array design, mark winter solstice values.
From Eratosthenes To NOAA — Two Millennia Of Solar Noon
In 2026, a solar photovoltaic designer in Bavaria is computing inter-row spacing for a 5 MW ground-mount installation. The critical constraint is winter-solstice shadow length at solar noon — if rows are spaced too tightly the back row loses 30% of its annual yield. That calculation hinges on the maximum sun altitude on December 21 at her exact latitude, the very same number Eratosthenes used in 240 BCE.
Eratosthenes of Cyrene (276-194 BCE), librarian of Alexandria, is credited with the first scientifically rigorous measurement of Earth's circumference. He knew that at Syene (modern Aswan, near the Tropic of Cancer) on the summer solstice, a vertical gnomon cast no shadow at noon — the sun was at the zenith. At Alexandria, ~800 km north, the same gnomon cast a 7.2° shadow at the same moment. Dividing 360° by 7.2° gave 50 "shadow segments" × 800 km = 40,000 km — within 1% of the modern 40,075 km equatorial value.
Tycho Brahe (1546-1601) brought solar-noon measurements to arc-minute precision at his Uraniborg observatory in Denmark. His apprentice Johannes Kepler (1571-1630) used those data to derive his three laws of planetary motion (Astronomia Nova, 1609 and Harmonices Mundi, 1619). Kepler's elliptical-orbit law is what produces the equation of time — Earth moves faster near perihelion (early January) than aphelion (early July), causing the sun-clock disagreement of up to ±16 minutes.
Sir Isaac Newton (Principia, 1687) provided the gravitational physics that explained Kepler's laws. The full modern calculation uses the IAU 2006 precession model, the Hipparcos solar coordinate system, and the NOAA Solar Position Algorithm (Reda & Andreas, NREL TP-560-34302, 2008) — accurate to ±0.0003° in solar position. The same algorithm powers PV tracking systems, sundial designs, and aviation navigation backups.
The analemma — the figure-8 path the sun traces if photographed daily at the same clock time — was first described by 17th-century Italian astronomers (notably Giovanni Cassini) and remains the most elegant visualization of solar-noon variability. Its vertical extent shows the ±23.44° declination cycle; its horizontal extent shows the equation of time. NASA's terrestrial analemma reference photographs document the loop year by year.
For practical applications: surveying (using the sun as an azimuth reference, per the US Bureau of Land Management Manual of Instructions §7.45), agronomy (sun-hours per day determines crop yield, per FAO-56), and solar-energy design (NREL System Advisor Model uses solar noon for daily-yield integration). The Eratosthenes-Kepler-NOAA chain is unbroken.
Continue with golden hour, blue hour, and planet visibility.
Engineers & Educators On The Solar-Noon Calculator
“The shadow-multiplier output saves me an Excel sheet per project. I size winter-solstice inter-row gaps in seconds now and the equation-of-time minutes match my Helioscope simulator exactly.”
“I restore 18th-century horizontal sundials and need the equation-of-time correction to set the engraved gnomon. This is the cleanest implementation I have used in years of conservation work.”
“I teach the Eratosthenes shadow-length experiment to undergraduates and use this tool as the live data source for the demonstration. Bonus: it works on every student phone.”
“We use solar noon as a backup compass calibration on rural site surveys when GPS magnetometer drifts. The azimuth + altitude fields cross-check our total station within arc-minutes.”
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