How to Define the Sun's Position in the Sky
Welcome to the Sun Angle Calculator, which tells you the Sun's location for any given place on Earth and any moment in time. Read on to learn how we define the Sun's position in the sky and how to calculate the Sun's elevation and azimuth angles.
We can express the Sun's location in the sky using two values, imagining it travels on the surface of a sphere. Instead of flat x- and y-coordinates, it is far more convenient to use angles. The most common way to describe the Sun's position is to give its elevation and azimuth angles, which closely relate to spherical coordinates.
- Elevation (α) — the Sun's height relative to the horizon line. It ranges from −90° to 90°. Positive values mean the Sun is above the horizon, while negative values mean it is below. The Sun reaches its maximum elevation at the zenith — directly above your head.
- Azimuth (β) — how much you must turn clockwise to look directly at the Sun. The reference direction is north, and the azimuth spans 0° to 360°. The most common bearings are North (0°), East (90°), South (180°) and West (270°).
Where Is the Sun Right Now? Using the Solar Angle Calculator
Let's say you are in Saint Louis (38.6° N, 90.2° W) on the 20th of February 2023. The sky is completely overcast, the clock has just hit 3 p.m., and you are wondering: "Where is the Sun right now?" The quickest way to solve the problem is to use the Sun Angle Calculator:
- Type the location's coordinates: 38.6° for latitude and −90.2° for longitude (west longitudes are negative).
- Set the date to the 20th of February 2023 and the time to 3:00 p.m. (15:00).
- Select the time zone for your location — in this case it should be CST (UTC−6).
As a result, you will see that the solar elevation angle equals about 27.4° and the solar azimuth angle is about 227°. This means the Sun is roughly a third of the way between the horizon and the zenith, close to the southwest direction.
💡 The exact values you get may fluctuate slightly from year to year, and the elevation shown includes a correction for atmospheric refraction.
The Formulas for Solar Elevation and Azimuth — Computing the Sun's Location
The calculator follows the well-known NOAA solar position algorithm. In simplified form, the steps are:
- Convert the calendar date and local time (with the UTC offset) into a Julian date.
- Compute the Sun's mean longitude, mean anomaly and the orbital eccentricity of the Earth.
- Apply the equation of center to obtain the Sun's true and apparent ecliptic longitude.
- Use the obliquity of the ecliptic to find the solar declination (δ).
- Compute the equation of time and the hour angle (H) from the true solar time.
- Finally, combine latitude (φ), declination and hour angle:
- Elevation: sin(α) = sin(φ)·sin(δ) + cos(φ)·cos(δ)·cos(H)
- Azimuth: derived from the zenith angle, latitude and declination, measured clockwise from north.
The result is then adjusted for atmospheric refraction so that the elevation matches what an observer would actually see near the horizon.
A Note on Units
Sun angles are expressed in degrees, a unit that is identical in both the American (imperial) and the metric measurement systems, so no unit conversion is required. Geographic coordinates are entered in decimal degrees: positive latitude is north, negative is south; positive longitude is east, negative is west.
FAQ
What is the difference between elevation and altitude?
They mean the same thing in this context: the angular height of the Sun above the horizon. "Altitude" is the traditional astronomical term, while "elevation" is widely used in everyday language.
Why is the elevation negative?
A negative elevation means the Sun is below the horizon — it is night, twilight, or the Sun has not yet risen at that location and time.
What does an azimuth of 180° mean?
An azimuth of 180° means the Sun is due south. In the Northern Hemisphere the Sun is roughly due south at solar noon. 0° is north, 90° is east and 270° is west.
When is the Sun at its highest point?
The Sun reaches its maximum elevation at solar noon, which usually differs from clock noon because of your longitude within the time zone and the equation of time.
🔎 If you want to know when the Sun rises and sets, head to our sunrise–sunset calculator.