Sun Altitude Calculator
This powerful sun altitude calculator allows you to determine the precise position of the sun in the sky (its altitude and azimuth) for any location, date, and time. This information is invaluable for architects, photographers, solar energy professionals, and astronomers.
Sun Altitude
--°
Where L=Latitude, δ=Declination, H=Hour Angle
Chart showing Sun Altitude and Azimuth for the selected day.
| Time | Altitude | Azimuth |
|---|---|---|
| Enter details above to populate data. | ||
What is a Sun Altitude Calculator?
A sun altitude calculator is a digital tool that computes the sun's position in the sky for a specific geographical location and time. The two primary coordinates it provides are altitude and azimuth. Altitude (or elevation) is the angle of the sun above the horizon, ranging from 0° at sunrise/sunset to a maximum of 90° when it's directly overhead. Azimuth is the sun's compass direction, typically measured in degrees clockwise from true north (0°). This powerful tool replaces complex manual calculations and astronomical charts, providing instant and accurate results. A precise sun altitude calculator is essential for a wide range of professions.
Architects use a sun altitude calculator to design energy-efficient buildings, planning window placements to maximize sunlight in winter and minimize heat gain in summer. Photographers and cinematographers use it to plan shoots around the 'golden hour' or to predict the direction and quality of light and shadows. Installers of photovoltaic systems rely on an accurate solar panel angle calculator to determine the optimal tilt and orientation for solar panels, maximizing energy generation throughout the year. For anyone needing to understand the sun's path, a sun altitude calculator is an indispensable resource.
Sun Altitude Formula and Mathematical Explanation
Calculating the sun's position requires several steps that account for the Earth's rotation, its tilted axis, and its orbit around the sun. The primary goal is to determine the solar altitude and azimuth angles.
The core formula for calculating the sun's altitude (β) is:
sin(β) = sin(L) × sin(δ) + cos(L) × cos(δ) × cos(H)
To use this, we first need to calculate the intermediate variables: the solar declination (δ) and the hour angle (H).
- Day of the Year (n): Convert the calendar date into the day number of the year (e.g., Jan 1st is 1, Feb 1st is 32).
- Solar Declination (δ): This is the angle between the sun's rays and the plane of the Earth's equator, caused by the Earth's axial tilt (23.45°). A common approximation is:
δ = -23.45 × cos[ (360/365) × (n + 10) ] - Equation of Time (EoT): This corrects for the difference between a sundial's time and our clock time, caused by the Earth's elliptical orbit. It's a complex formula but results in a minute-based correction.
- Local Solar Time (LST): This is calculated by adjusting the local clock time for longitude (4 minutes per degree from the timezone's standard meridian) and the Equation of Time.
- Hour Angle (H): This converts the Local Solar Time into an angle, representing the sun's movement across the sky. The formula is:
H = 15° × (LST - 12)
The hour angle is 0° at solar noon, negative in the morning, and positive in the afternoon. - Azimuth Angle (α): After finding the altitude, you can calculate the azimuth (compass direction) using a related formula. The azimuth angle calculation helps pinpoint the sun's direction relative to true north.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| β (beta) | Sun Altitude Angle | Degrees | 0 to 90 |
| α (alpha) | Sun Azimuth Angle | Degrees | 0 to 360 |
| L | Local Latitude | Degrees | -90 to +90 |
| δ (delta) | Solar Declination | Degrees | -23.45 to +23.45 |
| H | Hour Angle | Degrees | -180 to +180 |
Practical Examples (Real-World Use Cases)
Example 1: Architect in New York City
An architect is designing an apartment building in NYC (Latitude: 40.71° N, Longitude: -74.00° W) and wants to check the sun's position on the winter solstice (Dec 21st) at 3:00 PM to assess natural light in a south-facing unit.
- Inputs: Lat=40.71, Lon=-74.00, Date=Dec 21, Time=15:00, Timezone=UTC-5
- Calculator Output:
- Sun Altitude: ~12.5°
- Azimuth: ~228° (South-West)
- Interpretation: The architect learns that the sun will be very low in the sky but will still be shining into the south-facing windows from a south-westerly direction. This confirms that the apartment will receive direct, although not intense, sunlight in the mid-afternoon, even on the shortest day of the year. This is a key selling point found with a reliable sun altitude calculator.
Example 2: Solar Panel Installer in Phoenix
A solar installer in Phoenix (Latitude: 33.45° N, Longitude: -112.07° W) uses a sun position calculator to explain the daily sun path to a client. They check the sun's peak altitude on the summer solstice (June 21st) to determine the maximum solar intensity.
- Inputs: Lat=33.45, Lon=-112.07, Date=June 21, Time=12:30 PM (approx. solar noon), Timezone=UTC-7
- Calculator Output:
- Sun Altitude: ~79.9°
- Azimuth: ~180° (Due South)
- Interpretation: The installer shows the client that at its peak in summer, the sun is nearly directly overhead. This helps justify the chosen panel tilt angle, which is a compromise to capture optimal energy throughout the entire year, not just on this single day. The sun altitude calculator provides the data to back up their professional recommendation.
How to Use This Sun Altitude Calculator
Our sun altitude calculator is designed for ease of use and accuracy. Follow these steps to get precise results:
- Enter Your Latitude: Input the latitude of your location in decimal degrees. The Northern Hemisphere is positive (0 to 90), and the Southern Hemisphere is negative (0 to -90).
- Enter Your Longitude: Input the longitude in decimal degrees. East of the Prime Meridian is positive (0 to 180), and West is negative (0 to -180). You can find your coordinates using our latitude-longitude finder.
- Select the Date: Use the date picker to choose the day for the calculation.
- Select the Time: Use the time input to set the local time for the calculation.
- Choose Your Timezone: Select the correct timezone offset from UTC for your location. Remember to account for Daylight Saving Time if it's in effect.
- Read the Results: The calculator will instantly update. The primary result is the Sun Altitude, displayed prominently. You'll also see key intermediate values like Azimuth, Declination, and Hour Angle. The chart and table will update automatically to show the sun's path throughout the entire day.
Key Factors That Affect Sun Altitude Results
The position of the sun in the sky is not random; it's a predictable event governed by a few key factors. Understanding these is crucial when using a sun altitude calculator.
- Geographical Latitude: This is the most significant factor. Your north-south position on Earth determines the fundamental angle at which you view the sun. Locations closer to the equator will experience higher sun altitudes year-round compared to polar regions.
- Time of Year (Date): Due to the Earth's 23.45° axial tilt, the sun's apparent path across the sky changes throughout the year. This causes the seasons and results in a higher maximum sun altitude in the summer and a lower maximum in the winter.
- Time of Day: The Earth's daily rotation on its axis causes the sun to appear to rise, travel across the sky, and set. The sun's altitude is 0° at sunrise, increases to its maximum at solar noon, and decreases back to 0° at sunset.
- Longitude & Timezone: While latitude determines the height of the sun, longitude in combination with your local timezone determines *when* the peak altitude (solar noon) occurs. Solar noon rarely aligns perfectly with 12:00 PM on a clock due to these factors. A good sun altitude calculator uses this to find the correct solar time.
- Atmospheric Refraction: As sunlight enters the Earth's atmosphere, it bends slightly. This effect is most pronounced at sunrise and sunset, making the sun appear higher on the horizon than it geometrically is. Our sun altitude calculator accounts for standard refraction.
- Elevation/Altitude of Observer: Being at a higher altitude (e.g., on a mountain) can slightly change the time of sunrise and sunset and offers a clearer view of the horizon, but it has a minimal effect on the measured altitude angle itself unless very high up.
Frequently Asked Questions (FAQ)
1. What is the difference between sun altitude and sun elevation?
Sun altitude and solar elevation angle refer to the same thing: the angle of the sun above the horizon. The terms are used interchangeably.
2. What is solar noon?
Solar noon is the moment when the sun reaches its highest point in the sky for a given day. It rarely occurs at exactly 12:00 PM clock time. You can use a solar noon calculator to find the exact time for your location.
3. Why is the azimuth important?
Azimuth tells you the sun's compass direction. For example, an architect needs to know not just how high the sun is (altitude) but also if it's in the east, south, or west (azimuth) to predict where shadows will fall.
4. Does this sun altitude calculator work for the Southern Hemisphere?
Yes. By entering a negative value for latitude, all calculations will be correct for the Southern Hemisphere. For example, in the Southern Hemisphere, the sun is in the northern part of the sky at midday.
5. How does this relate to an architectural sun study?
An architectural sun study uses data from a sun altitude calculator for multiple times and dates to create models of how a building will interact with the sun, ensuring proper daylighting and avoiding overheating.
6. Can I use this calculator for gardening?
Absolutely. Gardeners use a sun altitude calculator to map out areas of full sun, partial shade, and full shade in their garden throughout the day and across different seasons, helping them place plants correctly.
7. Why is my "Copy Results" button not working?
The copy feature requires your browser to support the modern Clipboard API and may require you to grant permission. Ensure you are using an up-to-date browser like Chrome, Firefox, or Safari.
8. How accurate is this calculator?
This sun altitude calculator uses well-established astronomical algorithms. The results are highly accurate for most practical purposes, like architecture and solar installations. For high-precision scientific work, specialized software from astronomical institutions might be needed.