Sun position (azimuth and elevation)

Model: NREL Solar Position Algorithm (topocentric, with refraction from pressure and temperature); ΔT from Espenak and Meeus unless given; NOAA equations as a cross-check

Accuracy: ±0.0003° (SPA, −2000 to 6000) with UT1; taking UT1 as UTC adds up to about 0.004° of azimuth

When to use this: Use this when you need where the sun is at a moment: the azimuth and elevation for shadow studies, solar panel aiming, camera and survey planning, glare and hotspot checks, or the incidence angle on a sloping surface. It also gives the shadow an object of a given height casts, with its direction.

Limitations: Refraction near the horizon depends on the pressure and temperature you give it, and a low sun is where that matters most. Taking UT1 as UTC costs up to about four thousandths of a degree of azimuth, which is only a concern for survey work, where DUT1 from IERS belongs in the input. It is the sun's geometry, not the weather: cloud, haze, and terrain are yours to account for.

Worked example: Denver at 12:00 MDT on the June solstice. Source: NREL SPA.

Review: Not yet independently reviewed by a geodesist.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-19, result change: Sun position is now stable, so its results no longer carry the EXPERIMENTAL_TOOL warning. The UT1 warning moved to the first position; no numbers changed. Changelog
• 2026-09-18, changed: The first six tools passed the stable verification bar: a derivation, an independent worked example, invariant and differential tests, and at least 20 golden vectors each. Changelog
• 2026-09-18, result change: Sun position uses the NREL Solar Position Algorithm (±0.0003°) instead of the NOAA equations (about ±0.01°). Elevation and azimuth changed by up to a few hundredths of a degree. Changelog

Checked against: 28 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• Solar Position Algorithm for Solar Radiation Applications (NREL/TP-560-34302), Reda, I., and Andreas, A., National Renewable Energy Laboratory, Revised January 2008. Sections 3.1 to 3.15 and Tables A4.2, A4.3; worked example in Table A5.1. Read free.
• Polynomial Expressions for Delta T, Espenak, F., and Meeus, J., NASA Goddard Space Flight Center, Five Millennium Canon of Solar Eclipses. ΔT polynomials, −1999 to +3000. Read free.
• NOAA Solar Calculator: General Solar Position Calculations, NOAA Global Monitoring Laboratory, Spreadsheet and equations after Meeus (1998). Declination, equation of time, hour angle, refraction, and sunrise at −0.833°. Read free.

Terms

DUT1: UT1 minus UTC

The difference between Earth-rotation time and UTC, always under 0.9 s, broadcast so users can recover UT1. Source: IERS Bulletin C (leap seconds)

IERS: International Earth Rotation and Reference Systems Service

The service that maintains the ITRF and Earth orientation data, and announces leap seconds in Bulletin C. Source: IERS Bulletin C (leap seconds)

NOAA: National Oceanic and Atmospheric Administration

The US agency that includes the National Geodetic Survey and the National Weather Service. Source: NOAA Solar Calculator

TT: Terrestrial Time

The uniform time scale of astronomical ephemerides: TAI plus 32.184 seconds. Source: Espenak and Meeus Delta T polynomials

UT1: Universal Time 1

Time kept by Earth's actual rotation. It drifts against atomic time, and UTC is kept within 0.9 s of it. Source: IERS Bulletin C (leap seconds)

UTC: Coordinated Universal Time

The world's civil time standard, kept within 0.9 s of Earth's rotation by leap seconds. Aviation calls it Zulu time, written with a Z. Source: IERS Bulletin C (leap seconds)