Sun Position Calculator (Solar Azimuth & Altitude)

Where is the sun right now? Altitude and azimuth explained

Determining the precise position of the Sun from any vantage point on Earth requires two independent spherical coordinate angles measured relative to the observer's local horizon:

• Solar Altitude (Elevation Angle, α): The vertical angle between the center of the solar disk and the observer's local horizontal plane. An altitude of 0° marks geometric sunrise or sunset; 90° represents the absolute celestial zenith directly overhead; and negative values indicate the Sun is positioned beneath the horizon during night.
• Solar Zenith Angle (θ_z): The complement of solar altitude (θ_z = 90° - α), representing the angular distance between the Sun and the vertical zenith vector.
• Solar Azimuth Angle (A): The horizontal compass bearing of the Sun along the horizon, measured in degrees clockwise from True North (000°). Due East is 090°, due South is 180°, and due West is 270°.

Accurate knowledge of these two angles is essential across multiple technical fields: civil engineering (building orientation and passive solar heating), agriculture (crop canopy radiation), photovoltaic energy (optimizing solar panel tilt and dual-axis tracking), and cinema/photography (golden hour planning).

Why solar noon isn’t at 12:00 (equation of time)

A common assumption is that the Sun is always due south at 12:00 PM on clock time. In reality, mechanical clocks measure mean solar time, whereas actual sundials measure apparent solar time. The discrepancy between the two is known as the Equation of Time (EoT):

The Equation of Time oscillates between -14.2 minutes (in mid-February) and +16.4 minutes (in early November) due to two combined astronomical mechanics:

If you photograph the Sun from the exact same location at the exact same clock minute every few days for a full year, the Sun traces a graceful figure-8 curve across the sky known as the analemma.

How the sun position calculator works

Search for a place or click anywhere on the map, and the calculator returns the sun's current altitude and azimuth for that coordinate. Under the hood it uses the Jean Meeus / NOAA solar position equations, the first of the two standard approaches below, which are accurate to about a hundredth of a degree for everyday use:

• Jean Meeus “Astronomical Algorithms” (1991): The classic computational framework used by astronomers. It models Earth's mean anomaly, the center equation, ecliptic coordinates, and nutation using Fourier series expansions, achieving an angular accuracy of roughly 0.01 degrees.
• NREL Solar Position Algorithm (SPA, not used here): Developed by Ibrahim Reda and Afshin Andreas at the National Renewable Energy Laboratory (NREL) in 2004. Based on the VSOP87 planetary theory, SPA computes solar coordinates with an unprecedented uncertainty of ±0.0003 degrees across the years -2000 to +6000, factoring in topocentric parallax, nutation, aberration, and Earth-Moon barycenter motion.

Sun altitude formula, step by step

Given observer latitude φ, solar declination δ, and the local solar hour angle H, solar altitude α and azimuth A are calculated via spherical trigonometry:

Midday sun angle in major cities

Reference this benchmark table documenting peak solar elevations across representative global latitudes at the solstices and equinoxes:

How accurate is the sun position near the horizon?

When applying solar calculations to real-world sensors, telescopes, and solar energy installations, two physical corrections must be accounted for:

• Atmospheric Refraction: When the Sun is near the horizon (α ≤ 10°), terrestrial refraction bends incoming rays downward, making the Sun appear higher than its geometric position. Exactly on the horizon, refraction lifts the solar disk by approximately 34 arcminutes (0.57°)—more than the entire diameter of the Sun itself. At temperatures below -20°C, arctic refraction can exceed 1 degree.
• Topocentric Parallax: The Sun is located approximately 149.6 million kilometers away. Because the observer sits on Earth's surface rather than at the geocentric center of the planet, topocentric parallax introduces a minor angular shift of up to 8.79 arcseconds. High-precision algorithms (NREL SPA) correct for parallax, whereas simple educational formulas omit it.