Sun Position Calculator

This {primary_keyword} provides the precise azimuth and altitude of the sun for any location and time. Enter your coordinates, date, and time to get started.

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What is a Sun Position Calculator?

A sun position calculator is a tool used to determine the exact location of the sun in the sky from a specific point on Earth at a specific time. The sun’s position is defined by two primary coordinates: azimuth (its direction along the horizon) and altitude (its height above the horizon). This information is critical for a wide range of professionals and hobbyists, including photographers planning shoots, architects designing buildings for optimal sunlight, astronomers, and engineers installing solar panels. Our {primary_keyword} uses precise astronomical algorithms to deliver accurate results for any scenario.

Sun Position Formula and Explanation

Calculating the sun’s position is a multi-step process involving several astronomical concepts. The core idea is to convert the date, time, and location into a set of celestial coordinates and then translate those into the observer’s local sky. The key formulas for elevation (altitude) and azimuth are:

Altitude (α): α = arcsin(sin(δ) * sin(Φ) + cos(δ) * cos(Φ) * cos(HRA))

Azimuth (A): A = arccos((sin(δ) * cos(Φ) - cos(δ) * sin(Φ) * cos(HRA)) / cos(α))

These formulas rely on several intermediate values, which this {primary_keyword} calculates automatically.

Key Calculation Variables

Variable	Meaning	Unit	Typical Range
Φ (Phi)	Latitude of the observer.	Degrees	-90 to +90
δ (Delta)	Solar Declination: the angle of the sun relative to the celestial equator.	Degrees	-23.45 to +23.45
HRA	Hour Angle: the angular distance of the sun from the local solar noon.	Degrees	-180 to +180
α (Alpha)	Altitude: The sun’s angle above the horizon.	Degrees	-90 to +90
A	Azimuth: The sun’s direction along the horizon, measured clockwise from North.	Degrees	0 to 360

Practical Examples

Example 1: Photographer in Paris

A photographer in Paris (Latitude: 48.8566°, Longitude: 2.3522°) wants to capture the “golden hour” light on October 26, 2024. They use the sun position calculator to find the sun’s position just before sunset, around 18:00.

• Inputs: Lat: 48.8566, Lon: 2.3522, Date: 2024-10-26, Time: 18:00
• Results: The calculator would show a low Altitude (e.g., ~5°) and an Azimuth pointing towards the west-southwest (e.g., ~245°). This helps them set up their shot perfectly. For further reading, an {related_keywords} on {internal_links} might be useful.

Example 2: Solar Panel Installation in Sydney

An engineer in Sydney, Australia (Latitude: -33.8688°, Longitude: 151.2093°) needs to determine the optimal tilt angle for solar panels. They are most interested in the sun’s path during the summer solstice, December 21st, to maximize energy capture. Using the {primary_keyword}, they find the sun’s altitude at solar noon.

• Inputs: Lat: -33.8688, Lon: 151.2093, Date: 2024-12-21, Time: 12:45 (approx. solar noon)
• Results: The calculator shows a very high Altitude (e.g., ~79.5°), confirming the sun passes almost directly overhead. This data informs the ideal panel orientation for peak summer efficiency. Learning more about {related_keywords} could be beneficial, and one can start with this guide on {internal_links}.

How to Use This Sun Position Calculator

1. Enter Latitude: Input the latitude of your location in decimal degrees. Use positive values for the Northern Hemisphere and negative values for the Southern Hemisphere.
2. Enter Longitude: Input the longitude of your location in decimal degrees. Use positive values for locations East of the Prime Meridian and negative values for West.
3. Select Date and Time: Choose the exact date and local time for the calculation.
4. Review the Results: The calculator instantly updates. The primary result shows the sun’s Altitude and Azimuth. You can also see intermediate values like Solar Declination and the Hour Angle.
5. Analyze the Chart: The sun path chart visualizes the sun’s altitude throughout the selected day, helping you understand its trajectory from sunrise to sunset. You might find a related {related_keywords} article on {internal_links} insightful.

Key Factors That Affect Sun Position

• Latitude: Your north-south position on Earth is the most significant factor. It determines the maximum and minimum altitude the sun reaches throughout the year.
• Day of the Year: The Earth’s axial tilt (~23.45°) causes the seasons. This tilt changes the sun’s declination daily, affecting its path across the sky.
• Time of Day: From sunrise to sunset, the sun’s apparent movement across the sky changes its altitude and azimuth continuously, dictated by the Earth’s rotation.
• Longitude: Your east-west position affects the timing of solar events (like solar noon) relative to your local clock time.
• Time Zone & Daylight Saving: These are human constructs that shift clock time relative to solar time, which is why the {primary_keyword} requires your local time as input for accurate conversion.
• Atmospheric Refraction: Our atmosphere bends light, making the sun appear slightly higher than it geometrically is, especially near the horizon. Our calculations account for this. A {related_keywords} page on {internal_links} has more details.

Frequently Asked Questions (FAQ)

What is Azimuth?

Azimuth is the direction of the sun, measured as an angle clockwise from true North. An azimuth of 0° is North, 90° is East, 180° is South, and 270° is West.

What is Altitude?

Altitude (or elevation) is the height of the sun in the sky, measured as an angle from the horizon. An altitude of 0° means the sun is on the horizon, while 90° means it is directly overhead (at the zenith).

Why is my result showing a negative altitude?

A negative altitude means the sun is below the horizon at the selected time (i.e., it is nighttime).

What is Solar Noon?

Solar noon is the time of day when the sun reaches its highest point in the sky for a given location. It rarely aligns perfectly with 12:00 PM on a clock due to time zones and the Equation of Time.

How accurate is this sun position calculator?

This calculator uses well-established algorithms from astronomical science, providing high accuracy for most practical purposes. The calculations are based on formulas presented in resources like Jean Meeus’ “Astronomical Algorithms”.

Can I use this for historical or future dates?

Yes, you can select any date in the past or future. The calculator uses algorithms that are valid for centuries.

Does this calculator account for Daylight Saving Time?

The calculator uses the local time you provide. It’s your responsibility to ensure the time entered is correct for your location, including any Daylight Saving Time adjustments.

What is Declination?

Solar declination is the latitude on Earth where the sun is directly overhead at noon. It varies from +23.45° on the June solstice to -23.45° on the December solstice.