Sun Path Calculator
Calculate the sun’s path, azimuth, and altitude for any location and date. Our free sun path calculator provides detailed charts and data for architects, photographers, and solar installers.
Calculator
Positive for North, Negative for South (e.g., 40.7128)
Positive for East, Negative for West (e.g., -74.0060)
Select the date for the calculation.
Select your local timezone relative to UTC.
Sun Path Chart
Sun altitude (degrees) vs. time of day. The blue line shows the selected date’s path, and the orange line shows the summer solstice path for comparison.
Key Solar Events
| Event | Time (Local) | Azimuth (°) | Altitude (°) |
|---|
Azimuth is measured clockwise from North (N=0°, E=90°, S=180°, W=270°).
Deep Dive into Solar Calculation
What is a Sun Path Calculator?
A sun path calculator is a powerful tool that determines the position of the sun in the sky at any given time, for any location on Earth. It computes key metrics like the sun’s altitude (its height above the horizon) and azimuth (its direction along the horizon). This information is indispensable for a wide range of professionals and hobbyists. Architects use a sun path calculator to design energy-efficient buildings with optimal natural lighting. Photographers use it to plan shoots during “golden hour” when the light is soft and warm. Solar panel installers rely on a sun path calculator to position panels for maximum energy generation. Gardeners can even use it to understand which parts of their yard receive the most sunlight throughout the day and year.
A common misconception is that the sun is always highest in the sky at 12:00 PM local time. However, a sun path calculator will show that “solar noon” (when the sun reaches its peak altitude) often occurs several minutes before or after noon on your clock, due to the Earth’s elliptical orbit and the equation of time. Understanding these nuances is key to accurate planning.
The Sun Path Calculator Formula and Mathematical Explanation
The calculations behind a sun path calculator are based on spherical trigonometry. They account for the Earth’s tilt, its rotation, and its orbit around the sun. Here is a step-by-step breakdown of the core formulas used.
- Day of Year (n): First, we determine the day of the year, from 1 (Jan 1st) to 365 or 366.
- Solar Declination (δ): This is the angle of the sun at noon relative to the equator, caused by the Earth’s axial tilt. It varies from +23.45° on the summer solstice to -23.45° on the winter solstice. The formula is approximately:
δ = -23.45 * cos( (360/365) * (n + 10) ) - Equation of Time (EoT): This corrects for the discrepancy between “mean” (clock) time and “apparent” (solar) time. It’s a complex formula but essential for accuracy.
- Hour Angle (H): This converts the local time of day into an angle. The sun moves 15 degrees per hour. The hour angle is 0° at solar noon, negative in the morning, and positive in the afternoon.
H = 15° * (Local Solar Time - 12) - Altitude (α): The sun’s angle above the horizon. It’s calculated with the formula:
sin(α) = sin(δ)sin(φ) + cos(δ)cos(φ)cos(H)where φ is the latitude. - Azimuth (A): The sun’s compass direction. The formula is more complex to avoid ambiguity, but one form is:
cos(A) = (sin(δ)cos(φ) - cos(δ)sin(φ)cos(H)) / cos(α). Adjustments are then made based on whether it is morning or afternoon.
This powerful combination of formulas allows the sun path calculator to pinpoint the sun’s location with high precision.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| φ (phi) | Latitude of the observer | Degrees | -90 to +90 |
| λ (lambda) | Longitude of the observer | Degrees | -180 to +180 |
| δ (delta) | Solar Declination | Degrees | -23.45 to +23.45 |
| H | Hour Angle | Degrees | -180 to +180 |
| α (alpha) | Altitude Angle | Degrees | -90 to +90 |
| A | Azimuth Angle (from North) | Degrees | 0 to 360 |
Practical Examples (Real-World Use Cases)
Example 1: Architectural Planning in London
An architect in London (Latitude: 51.5° N) wants to design a south-facing living room to maximize winter sunlight for passive heating. They use the sun path calculator for January 21st. The calculator shows that at solar noon, the sun’s altitude will only be about 18°. This low angle means sunlight will penetrate deep into the room. The azimuth at sunrise is around 125° (southeast) and at sunset is 235° (southwest). This data informs the size and placement of windows, and the need for overhangs to block the much higher summer sun (which can reach over 60° altitude).
Example 2: Photography in Sydney
A photographer in Sydney, Australia (Latitude: -33.8° S) wants to capture a photo of the Opera House during the “golden hour” in May. Using the sun path calculator, they find that sunset occurs at approximately 5:05 PM. The crucial data is the sun’s path just before sunset. An hour before, at 4:05 PM, the sun’s altitude is a low 11°, and its azimuth is 285° (west-northwest), casting long, soft shadows and bathing the landscape in warm light. They can now plan the exact location and time to set up for the perfect shot. For more tips on this, see our golden hour calculator guide.
How to Use This Sun Path Calculator
Using our sun path calculator is straightforward. Follow these steps for an accurate solar analysis:
- Enter Your Location: Input the latitude and longitude of your desired location. For northern hemisphere locations, latitude is positive. For the southern hemisphere, it’s negative. Longitude is negative for locations west of the Prime Meridian (like the Americas).
- Select the Date: Use the date picker to choose the specific day you want to analyze.
- Set Your Timezone: Choose the correct UTC offset for your location to ensure the sunrise, sunset, and solar noon times are accurate for your local clock.
- Review the Results: The calculator will instantly update. The primary result shows the sun’s peak altitude at solar noon. The intermediate boxes provide crucial times: sunrise, solar noon, sunset, and total daylight duration.
- Analyze the Chart and Table: The sun path chart visually represents the sun’s journey across the sky. The table provides precise time, azimuth, and altitude data for key moments of the day. This is the core output of any advanced sun path calculator.
Key Factors That Affect Sun Path Results
Several factors influence the sun’s path, and understanding them helps interpret the results from a sun path calculator.
- Latitude: This is the most significant factor. At the equator (0° latitude), the sun is directly overhead at noon on the equinoxes. Near the poles, the sun’s path is much lower in the sky.
- Day of the Year: This determines the sun’s declination. In the Northern Hemisphere’s summer, the Earth is tilted towards the sun, resulting in a higher solar path and longer days. The opposite is true in winter.
- Time of Day: This determines the Hour Angle, dictating the sun’s east-to-west position across the sky.
- Timezone and Longitude: These are used to convert solar time to local clock time. Two locations in the same timezone but at different longitudes will experience solar noon at different clock times. A detailed sunrise sunset times calendar can illustrate this.
- Atmospheric Refraction: Our sun path calculator accounts for the fact that the atmosphere bends light. This makes the sun appear slightly higher than it geometrically is, especially near sunrise and sunset.
- Elevation: While a minor factor for most, being at a higher altitude (e.g., on a mountain) can slightly alter the exact times of sunrise and sunset.
Considering these factors is vital for projects requiring high precision, such as using a solar angle calculator for optimizing energy output.
Frequently Asked Questions (FAQ)
This is due to the combination of your location within a timezone and the “Equation of Time.” A timezone can span a wide longitude, but clock time is uniform. Solar time is specific to your exact longitude. The Equation of Time accounts for the Earth’s non-circular orbit. Our sun path calculator correctly calculates this difference.
Yes. By entering a negative latitude, all calculations are adjusted correctly. For the Southern Hemisphere, the sun is in the northern part of the sky, and its highest path occurs during the December solstice.
Altitude is the vertical angle of the sun above the horizon (0° at the horizon, 90° directly overhead). Azimuth is the horizontal compass direction (e.g., 0° for North, 90° for East, 180° for South, 270° for West). A full azimuth and altitude chart is plotted above.
This calculator uses well-established astronomical algorithms and accounts for key factors like atmospheric refraction. For most practical purposes (architecture, photography, gardening), the accuracy is more than sufficient. For a deeper dive, consider our guide on solar panel efficiency.
Golden hour is the period shortly after sunrise and before sunset, when the sun is very low in the sky (typically below 6° altitude). This produces soft, diffused, warm light that is highly prized by photographers and cinematographers.
Absolutely. The sun path calculator helps you identify the optimal orientation (azimuth) and tilt (based on altitude) for your panels. It also helps you identify any potential shading from nearby objects throughout the day and year.
The summer solstice (around June 21st in the Northern Hemisphere) is the day with the longest period of daylight and when the sun follows its highest path across the sky. The winter solstice (around Dec 21st) is the shortest day with the lowest sun path.
It’s a critical tool. Architects use it to perform sun studies, ensuring that living spaces get adequate natural light, avoiding glare, and designing overhangs or shading devices that block high summer sun while allowing low winter sun. This is a core principle of architectural sun study.
Related Tools and Internal Resources
Explore our other calculators and guides for a comprehensive understanding of solar and date-related topics.