About the Sun Position Calculator
This sun position calculator gives the sun’s elevation (altitude angle above the horizon) and azimuth (compass direction) for any latitude and longitude at any date and local clock time. It also reports the solar declination, the equation of time, the hour angle, the time of solar noon and how long a shadow will be relative to the object casting it.
Photographers use it to plan the angle of light on a building or landscape, architects and gardeners to study shading, solar installers to understand the sun’s path across a roof, and students to explore why seasons happen. The chart traces the sun’s elevation across the whole day, so you can see when it climbs above or sinks below a given angle.
It uses the NOAA Solar Calculator equations (from Jean Meeus’s Astronomical Algorithms), which NOAA says work best for years between 1800 and 2100, and adds NOAA’s standard atmospheric refraction correction to the elevation. Enter the UTC offset that applies on that date, including daylight saving time. Azimuth is measured clockwise from true north (90° = east, 180° = south).
With the default inputs, the sun elevation (with refraction) is 68.89 °. Change any value above to recalculate instantly.
How to use the sun position calculator
- 1Enter the latitude and longitude of the place (decimal degrees, west and south negative).
- 2Pick the date and the local clock time.
- 3Enter the UTC offset in force on that date, including daylight saving time.
- 4Read the sun’s elevation and azimuth, plus declination and solar noon.
- 5Use the chart to see how high the sun gets at each hour of the day.
Formula and method
The calculator follows the NOAA Solar Calculator method, based on Jean Meeus’s Astronomical Algorithms. From the date and time it computes the Julian century, the sun’s mean longitude and anomaly, the equation of centre and the obliquity of the ecliptic, giving the solar declination δ and the equation of time. True solar time is clock time corrected for longitude, time zone and the equation of time; the hour angle H is how far the sun is from the local meridian (15° per hour).
Elevation α follows from spherical trigonometry using latitude φ, declination and hour angle; the zenith angle Z is 90° − α. Atmospheric refraction, which lifts the sun by about 0.5° at the horizon, is then added using NOAA’s piecewise formula. Azimuth is measured clockwise from true north. Shadow length per unit height is 1 ÷ tan(α).
- α
- Solar elevation angle
- φ
- Observer latitude
- δ
- Solar declination
- H
- Hour angle (0° at solar noon)
- Z
- Solar zenith angle (90° − α)
- Az
- Azimuth, clockwise from true north
Worked examples
New York at noon EDT on the June solstice
At 12:00 EDT the sun is still about an hour before solar noon (12:58), almost entirely because daylight saving time moves the clock an hour ahead; New York (74.0° W) sits close to its zone’s 75° W meridian, and the equation of time (−1.9 min) adds the last couple of minutes. It stands about 68.9° high in the southeast (azimuth 140.5°), with the declination at its yearly maximum of +23.44°; an hour later at solar noon it peaks near 72.7°.
London at 9:00 GMT on the March equinox
On 20 March (still GMT, offset 0) at 09:00 the sun is about 25.1° above the horizon in the southeast (azimuth 126°). Solar noon is at 12:08 because the equation of time is −7.5 minutes in March. Near the equinox the declination is close to 0°, so the sun rises almost due east everywhere.
Sydney at 15:00 AEDT on 21 December
In the southern-hemisphere summer the midday sun is in the north. By mid-afternoon it has swung round to the west-northwest at an azimuth of about 282°, still 60.4° high.
Frequently asked questions
What is solar elevation and azimuth?+
Elevation (or altitude) is the sun’s angle above the horizon, from 0° at sunrise to 90° directly overhead. Azimuth is its compass bearing measured clockwise from true north: 90° is east, 180° south and 270° west.
Why is solar noon not at 12:00?+
Clock time is shared across a whole time zone, while solar noon depends on your exact longitude. Daylight saving time adds an hour, and the equation of time shifts solar noon by up to about 16 minutes through the year because of Earth’s tilt and elliptical orbit.
How high does the sun get at noon?+
At solar noon, elevation ≈ 90° − |latitude − declination|. Declination ranges from +23.44° in June to −23.44° in December, so at 40° N the noon sun reaches about 73.4° at the June solstice and 26.6° at the December solstice.
How accurate is this sun position calculator?+
For years between 1800 and 2100 the NOAA/Meeus equations agree with other standard solar algorithms to within a few hundredths of a degree, far finer than you can measure with a protractor or phone. Refraction near the horizon varies with temperature and pressure, so elevations below about 2° can be off by a fraction of a degree in real conditions.
How do I find shadow length from the sun angle?+
Shadow length = object height ÷ tan(elevation). At 45° a shadow equals the object’s height; at 30° it is 1.73 times as long, and at 10° about 5.7 times. The shadow points in the opposite direction to the sun’s azimuth.