Sun Position Calculator
Calculate solar elevation, azimuth, and solar noon for any geographic location.
Formula: Position calculated using the Spencer (1971) and Reda & Andreas (2004) solar geometry algorithms for atmospheric refraction and orbital eccentricity.
Sun Path Today (Elevation vs. Time)
Graph showing the sun's elevation relative to the horizon over 24 hours.
| Time | Elevation (°) | Azimuth (°) | Position |
|---|
Hourly solar data for the selected date and location.
What is a Sun Position Calculator?
A Sun Position Calculator is a specialized tool used by astronomers, solar energy engineers, architects, and photographers to determine the precise location of the sun in the sky at any given time and place on Earth. By entering geographic coordinates (latitude and longitude) and a specific date and time, the Sun Position Calculator outputs two primary coordinates: altitude (elevation) and azimuth.
Who should use it? Homeowners looking to install solar panels use the Sun Position Calculator to find the best tilt angle. Architects use it to design shading for buildings, and photographers use it to predict the "Golden Hour." A common misconception is that the sun is always directly overhead at noon; however, the Sun Position Calculator shows that this only happens at specific latitudes during solstices.
Sun Position Calculator Formula and Mathematical Explanation
The mathematics behind a Sun Position Calculator involves complex spherical trigonometry and orbital mechanics. The process typically follows these steps:
- Julian Day Calculation: Converting the standard calendar date into a continuous count of days.
- Solar Declination: Calculating the angle between the rays of the sun and the plane of the Earth's equator.
- Equation of Time: Adjusting for the Earth's elliptical orbit and axial tilt.
- Hour Angle: Determining the sun's position relative to the local meridian.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| δ (Delta) | Solar Declination | Degrees | -23.45° to +23.45° |
| Φ (Phi) | Observer Latitude | Degrees | -90° to +90° |
| ω (Omega) | Hour Angle | Degrees | -180° to +180° |
| α (Alpha) | Elevation/Altitude | Degrees | -90° to +90° |
Practical Examples (Real-World Use Cases)
Example 1: Solar Panel Optimization
A user in Los Angeles (Lat: 34.05) wants to check the sun's height in mid-winter. Using the Sun Position Calculator for December 21st at 12:00 PM, the result shows an elevation of approximately 32.5°. This helps the user decide to tilt their solar panels at a steeper angle to capture maximum irradiance during winter months.
Example 2: Architectural Shading Design
An architect in London is designing a window overhang. They use the Sun Position Calculator to find the maximum solar azimuth on June 21st. By knowing the sun reaches an azimuth of 180° at its peak elevation of 62°, they can calculate the exact depth of the overhang required to keep the interior cool.
How to Use This Sun Position Calculator
Using our Sun Position Calculator is straightforward:
- Enter Coordinates: Input your Latitude and Longitude. You can find these using map services or your phone's GPS.
- Set the Date: Pick the specific calendar day you want to analyze.
- Set the Time: Input the local time. Ensure your Time Zone offset matches your local setting.
- Analyze Results: View the Elevation (how high the sun is) and Azimuth (the compass direction).
- Review the Chart: The dynamic sun path chart shows how the sun will move throughout that specific 24-hour period.
Key Factors That Affect Sun Position Calculator Results
- Axial Tilt: The Earth's 23.5° tilt is the primary driver of seasonal solar variation calculated by the Sun Position Calculator.
- Orbital Eccentricity: Earth's orbit is not a perfect circle, meaning the sun's "speed" across the sky varies slightly throughout the year (Equation of Time).
- Atmospheric Refraction: Near the horizon, the atmosphere bends light, making the sun appear higher than it actually is. Advanced Sun Position Calculator algorithms account for this.
- Latitude: Your distance from the equator dictates the maximum possible elevation angle.
- Time Zone Offsets: Incorrect UTC offsets are the most common cause of errors in Sun Position Calculator outputs.
- Topography: While the Sun Position Calculator gives the geometric position, local mountains or buildings may block the sun even if it has a positive elevation.
Frequently Asked Questions (FAQ)
Elevation is the vertical angle (0° is horizon, 90° is zenith). Azimuth is the horizontal compass direction (0° is North, 180° is South).
Negative elevation means the sun is below the horizon (nighttime). A value of -0.83° usually indicates sunrise or sunset.
Yes, the Sun Position Calculator is an essential tool for determining the optimal tilt and orientation for solar energy collection.
For most applications, sea level is assumed. High altitude slightly changes the time of sunrise/sunset due to the horizon dip, but not the sun's central position.
Solar noon is the exact moment the sun crosses the local meridian and reaches its highest point in the sky for that day.
Our algorithm accounts for leap years and long-term orbital changes, remaining accurate for several decades.
The Sun Position Calculator tracks the shift in the Earth's tilt relative to the sun, which causes the sunrise azimuth to migrate between solstices.
The Equation of Time is the difference between apparent solar time and mean solar time, which can vary by up to 16 minutes.
Related Tools and Internal Resources
- Solar Panel Tilt Calculator – Optimize your energy harvest using results from the Sun Position Calculator.
- Daylight Hours Tool – Calculate total daylight duration for any date.
- Golden Hour Tracker – Perfect for photographers using Sun Position Calculator data.
- Moon Phase Calendar – Track lunar cycles alongside solar data.
- UV Index Forecast – Understand how solar elevation affects UV intensity.
- Equinox and Solstice Guide – Learn about the key dates in the solar calendar.