Sun Position Calculator
Accurate solar azimuth and elevation tracking for any coordinate on Earth.
–°
Angle of the sun above the horizon.
–°
–°
— min
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Sun Path (24-Hour Cycle)
Hourly Sun Position Table
| Time | Elevation (°) | Azimuth (°) | Status |
|---|
What is a Sun Position Calculator?
A sun position calculator is a precise astronomical tool used to determine the exact coordinates of the sun in the sky from any specific point on Earth at a given time. By processing geographic coordinates—latitude and longitude—along with the specific date and time, the sun position calculator outputs two primary angles: azimuth and elevation.
Architects use a sun position calculator to design energy-efficient buildings that maximize natural light. Solar engineers rely on the sun position calculator to optimize the tilt and orientation of photovoltaic panels. Even photographers and outdoor enthusiasts use a sun position calculator to predict “Golden Hour” or identify when shadows will be longest. Understanding the sun position calculator mechanics is essential for anyone working with solar geometry, renewable energy, or spatial planning.
Sun Position Calculator Formula and Mathematical Explanation
The sun position calculator utilizes spherical trigonometry and the simplified version of the NOAA Solar Position Algorithm. The math involves calculating the Julian Day, the solar declination, and the equation of time.
The Step-by-Step Derivation
First, the sun position calculator determines the fractional year ($\gamma$) in radians:
γ = (2π / 365) * (day_of_year - 1 + (hour - 12) / 24)
From $\gamma$, we estimate the Equation of Time (eqt) and Solar Declination ($\delta$):
eqt = 229.18 * (0.000075 + 0.001868 cos(γ) - 0.032077 sin(γ) - 0.014615 cos(2γ) - 0.040849 sin(2γ))
The solar elevation angle ($e$) is then calculated using the observer’s latitude ($\phi$):
sin(e) = sin(φ) sin(δ) + cos(φ) cos(δ) cos(H)
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Latitude (φ) | Angular distance from Equator | Degrees | -90° to 90° |
| Declination (δ) | Sun’s angle relative to Earth’s equator | Degrees | -23.44° to 23.44° |
| Azimuth (α) | Compass direction of the sun | Degrees | 0° to 360° |
| Elevation (e) | Height of sun above horizon | Degrees | -90° to 90° |
Practical Examples of Sun Position Calculator Usage
Example 1: Solar Panel Installation in Los Angeles
A homeowner in Los Angeles (Lat: 34.05, Lon: -118.24) wants to know the sun’s height at noon on the Winter Solstice (Dec 21). By entering these details into the sun position calculator, they find the elevation is approximately 32.5°. This helps them realize they must tilt their panels steeper in winter to capture maximum irradiance.
Example 2: Architectural Shadow Analysis in London
A developer in London (Lat: 51.50) uses the sun position calculator for a June morning (10:00 AM). The calculator shows an azimuth of 128° and an elevation of 48°. This data allows the architect to model exactly how long the shadows will be, ensuring that neighboring gardens are not blocked from sunlight, which is a key planning requirement.
How to Use This Sun Position Calculator
- Enter Geographic Coordinates: Input your Latitude and Longitude. Use decimal format (e.g., 40.71 for North, -74.00 for West).
- Select Date: Pick the specific day for your observation. The sun position calculator accounts for seasonal variations in the Earth’s tilt.
- Set Local Time and Time Zone: Input the time of day and your offset from UTC. Note that Daylight Savings may change your offset.
- Review Results: The sun position calculator instantly updates the Azimuth (where the sun is on the compass) and Elevation (how high it is).
- Analyze the Path: Look at the chart and table below to see how the sun’s position changes throughout the 24-hour cycle.
Key Factors That Affect Sun Position Calculator Results
- Geographic Latitude: The distance from the equator is the most significant factor in determining the sun’s maximum daily elevation.
- Time of Year (Orbit): Earth’s axial tilt of 23.4° causes the sun to appear higher in summer and lower in winter, a variation captured by the sun position calculator.
- Longitude and Time Zone: Your specific longitudinal position relative to your time zone meridian determines when “Solar Noon” actually occurs.
- Atmospheric Refraction: When the sun is near the horizon, the atmosphere “bends” light, making the sun appear slightly higher than its geometric position.
- Equation of Time: Earth’s elliptical orbit and axial tilt mean solar days aren’t exactly 24 hours; the sun position calculator corrects for this “wobble.”
- Altitude of the Observer: While minor for most ground calculations, being high on a mountain can slightly change when the sun first clears the horizon.
Frequently Asked Questions (FAQ)
This sun position calculator uses standard astronomical algorithms accurate to within approximately 0.01 degrees, which is more than sufficient for solar energy and photography purposes.
Elevation is the vertical angle (0° at horizon, 90° at zenith), while Azimuth is the horizontal compass direction (0° North, 90° East, 180° South, 270° West).
A negative elevation means the sun is currently below the horizon (nighttime). The calculator continues to track the sun’s geometric position even after sunset.
You must manually adjust the UTC offset in the sun position calculator to account for DST (e.g., if you are normally -5 but in DST, use -4).
Solar noon depends on your exact longitude and the Equation of Time. The sun position calculator calculates the “noon offset” for your specific location.
No, the moon follows a completely different orbital path. This sun position calculator is strictly designed for solar geometry.
Yes, the sun position calculator includes a standard refraction correction for angles near the horizon to improve real-world accuracy.
This sun position calculator uses the standard 0-360 degree system where 0 is North, 90 is East, 180 is South, and 270 is West.
Related Tools and Internal Resources
- Solar Energy Calculator – Estimate the power output of your solar panels based on sun position.
- Sunrise Sunset Calculator – Find the exact moment the sun rises and sets in your city.
- Daylight Hours Tracker – Compare how the length of the day changes throughout the year.
- Moon Phase Calendar – Track lunar cycles alongside solar positions.
- Solar Angle Optimization Guide – Learn the best tilt for panels using a sun position calculator.
- Golden Hour Calculator – Perfect timing for photographers using solar azimuth data.