Sun Position Calculator

Enter your latitude, day of year, and local solar time to calculate the sun's elevation, azimuth, daylight hours, shadow length, and estimated UV index.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Your Latitude
Input your location's latitude in decimal degrees. Positive values are for the Northern Hemisphere, negative for the Southern.
2
Input Your Longitude
Provide your location's longitude in decimal degrees. This is used for general reference; solar time is derived from the hour input.
3
Specify the Day of Year
Enter the day number from 1 (January 1st) to 365 (December 31st). For example, June 21st is approximately day 172.
4
Set the Local Solar Time (Hour)
Enter the hour of the day in 24-hour format, based on local solar time, where 12 represents solar noon.
5
Review Your Results
The calculator will display the sun's elevation, azimuth, daylight hours, and other solar metrics.

Example Calculation

An astronomer in the Northern Hemisphere (37° latitude, 0° longitude) wants to know the sun's position on day 172 (around June 21st) at 2 PM local solar time.

Latitude (°)

Longitude (°)

Day of Year

172

Local Solar Time (Hour)

Results

60.9°

Tips

Account for Time Zones and Daylight Saving

The 'Local Solar Time' input is crucial. Convert your local clock time to solar time by accounting for your time zone offset from UTC and any daylight saving adjustments, as well as your longitude's offset from the center of your time zone.

Understand Solar Noon

Solar noon is when the sun reaches its highest point in the sky for that day, not necessarily 12:00 PM clock time. It varies based on your longitude within your time zone and the Equation of Time, which accounts for Earth's orbital eccentricity.

Latitude's Seasonal Impact

Your latitude profoundly affects seasonal variations. Locations closer to the equator experience less change in daylight hours and sun elevation throughout the year, while polar regions can experience periods of continuous daylight or darkness.

Pinpointing the Sun's Exact Location in the Sky

The Sun Position Calculator provides precise data on the sun's elevation and azimuth for any given location and time of year. This tool is invaluable for a wide range of applications, from architects designing energy-efficient buildings to photographers planning for the "golden hour," or astronomers calibrating their instruments. By understanding the sun's exact path, which can see its elevation range from 0° at the horizon to over 70° at solar noon in summer, users can optimize solar energy systems, plan outdoor activities, and gain deeper insights into celestial mechanics in 2025.

Solar Geometry in Astronomical Observation

Accurate sun position data is foundational for astronomers, serving multiple critical purposes beyond simple curiosity. It's essential for the precise calibration of telescopes and other observational instruments, ensuring that they are correctly aligned or shielded from direct sunlight when observing faint objects. For planning observations of solar system objects, such as planetary transits or occultations, knowing the sun's exact elevation and azimuth is paramount to ensure visibility and prevent solar interference. Furthermore, understanding the sun's position helps astronomers account for atmospheric effects like refraction and extinction, which vary with solar angle and can impact the clarity and intensity of observed light. The concept of the ecliptic plane, along which the sun appears to move throughout the year, is central to these calculations.

Calculating Solar Angles and Times

The Sun Position Calculator determines key solar metrics using fundamental astronomical equations. The core calculations involve the sun's declination (its angular distance north or south of the celestial equator) and the solar hour angle (how far the sun is from its highest point).

The primary formulas are:

Declination = 23.45 × sin(toRad((360 / 365) × (Day of Year - 81)))

Sin(Elevation) = sin(Latitude) × sin(Declination) + cos(Latitude) × cos(Declination) × cos(Hour Angle)

Where:

toRad(): Converts degrees to radians.
Day of Year: The sequential day number (1-365).
Hour Angle: Represents the time difference from solar noon, converted to degrees (15° per hour).

💡 Just as we calculate the sun's precise position, astronomers use similar principles to determine the orientation of distant objects. The Saturn Ring Tilt Calculator offers insight into another fascinating celestial angle.

Tracking the Sun's Path at 37° Latitude

Let's illustrate how the Sun Position Calculator works with a practical example. Consider someone located at 37° North latitude and 0° longitude, interested in the sun's position on day 172 of the year (approximately June 21st, the summer solstice in the Northern Hemisphere) at 2:00 PM local solar time.

Input Latitude: 37°
Input Longitude: 0° (used for reference, but solar time is given)
Input Day of Year: 172
Input Local Solar Time (Hour): 14 (for 2:00 PM)

First, the calculator determines the sun's declination for day 172, which is approximately 23.45°. Next, it calculates the solar hour angle, which for 2:00 PM (2 hours past solar noon) is 30°. These values, along with the latitude, are then used in the elevation formula:

Sin(Elevation) = sin(37°) × sin(23.45°) + cos(37°) × cos(23.45°) × cos(30°) Sin(Elevation) ≈ 0.6018 × 0.3979 + 0.7986 × 0.9173 × 0.8660 Sin(Elevation) ≈ 0.2396 + 0.6347 ≈ 0.8743 Elevation ≈ arcsin(0.8743) ≈ 60.9°

The sun's elevation is approximately 60.9°. The calculator would then proceed to find the azimuth, daylight hours, sunrise, and sunset times. This high elevation indicates a strong summer sun, ideal for solar energy collection or bright outdoor lighting.

💡 Understanding the sun's position relative to Earth is fundamental to astronomy, much like understanding the distances of other planets from the sun. Our Planet Distance from Sun Calculator can help you explore solar system geometry further.

Typical Solar Angles for Key Applications

Precise solar position data is not just an academic exercise; it underpins numerous practical applications across various industries. For instance, in solar energy system design, optimal photovoltaic panel tilt angles are typically set to the latitude of the installation, adjusted seasonally by ±15° to maximize energy capture throughout the year. During winter, a steeper angle (latitude + 15°) captures more low-angle sun, while a shallower angle (latitude - 15°) is better for the high summer sun. In passive solar building design, architects target low winter sun angles (typically 20-30° elevation at solar noon) to maximize heat gain through south-facing windows, while designing overhangs to block high summer sun (often 60-70° elevation) to prevent overheating. For outdoor photography, the "golden hour" is a prized time, occurring when the sun's elevation is between approximately 5° and 15° above the horizon after sunrise and before sunset, casting soft, warm light and long shadows. These benchmarks guide professionals in optimizing performance, efficiency, and aesthetic outcomes based on the sun's predictable path.

Frequently Asked Questions

What is the difference between sun elevation and azimuth?

Sun elevation, also known as solar altitude, is the angle of the sun above the horizon, ranging from 0° at the horizon to 90° directly overhead. Sun azimuth is the horizontal direction of the sun, measured clockwise from true North (0°). For example, 90° azimuth is East, 180° is South, and 270° is West. Together, these two angles precisely pinpoint the sun's position in the sky at any given moment.

How does the day of the year affect sun position?

The day of the year primarily affects the sun's declination, which is its angular distance north or south of the Earth's equator. This declination changes throughout the year due to Earth's axial tilt, ranging from approximately +23.45° at the summer solstice to -23.45° at the winter solstice. This change in declination is what drives seasonal variations in sun elevation and daylight duration at different latitudes, particularly impacting the sun's height at solar noon.

Why is local solar time important for sun position calculations?

Local solar time is crucial because it accounts for the sun's actual position in the sky relative to your specific longitude, rather than a standardized time zone. Standard clock time can vary significantly from local solar time due to time zones being broad bands and daylight saving adjustments. Using local solar time ensures the calculation accurately reflects when the sun is highest (solar noon) or at specific angles, which is vital for precise solar energy calculations, astronomical observations, and shadow analysis.

What is the typical range for sun elevation?

The sun's elevation can range from 0° at sunrise/sunset to a maximum of 90° (directly overhead). The maximum elevation depends on your latitude and the sun's declination. For example, at the equator, the sun can be directly overhead (90°) on the equinoxes. At the poles, the maximum elevation is 23.45° during their respective summer solstices, and it remains below the horizon for months during winter. At mid-latitudes, summer solar noon elevations are typically between 60° and 75°.