Calculator Sun Position

The sun's position in the sky changes throughout the day and year. Calculating solar position helps in solar energy applications, astronomy, and navigation. This calculator determines the sun's azimuth and elevation angles based on your location and time.

What is Sun Position?

Sun position refers to the angular location of the sun relative to an observer on Earth. It's defined by two main angles:

Azimuth angle - The angle between the sun's position and true north, measured clockwise from north.
Elevation angle - The angle between the sun's rays and a line perpendicular to the Earth's surface.

These angles change continuously throughout the day and vary with the seasons due to Earth's axial tilt. Understanding sun position is crucial for solar panel installation, daylighting design, and astronomical observations.

How to Calculate Sun Position

To calculate the sun's position, you need to know:

Your location's latitude and longitude
The date and time of interest
Your local time zone

The calculation involves several steps including:

Determining the day of the year
Calculating solar declination
Computing the equation of time
Finding the hour angle
Calculating the solar zenith and azimuth angles

Note: This calculator uses the SPA (Solar Position Algorithm) for accurate results. The calculations account for atmospheric refraction and solar geometry.

Formulas

The sun position calculation involves several astronomical formulas. Here are the key components:

Solar Declination (δ)

δ = -23.45° × cos(360/365 × (n + 10))

Where n is the day of the year (1-365)

Equation of Time (E)

E = 9.87 × sin(2B) - 7.53 × cos(B) - 1.5 × sin(B)

Where B = (360/365) × (n - 81)

Hour Angle (H)

H = 15° × (t - 12) + E + (λ - 15°)

Where t is the local time in hours, λ is the longitude, and E is the equation of time

Solar Zenith Angle (θ)

θ = arccos(sin(φ) × sin(δ) + cos(φ) × cos(δ) × cos(H))

Where φ is the latitude and δ is the solar declination

Solar Azimuth Angle (A)

A = arctan2(sin(H), cos(H) × sin(φ) - tan(δ) × cos(φ))

This gives the angle from north to the sun's position

The elevation angle is simply 90° - θ. The azimuth angle is converted to a compass bearing by adjusting for the quadrant.

Example Calculation

Let's calculate the sun's position for New York City (40.71° N, 74.01° W) on June 21 at 12:00 PM EDT.

Parameter	Value
Date	June 21
Time	12:00 PM
Latitude	40.71° N
Longitude	74.01° W
Day of year (n)	172
Solar declination (δ)	23.45°
Equation of time (E)	-0.32 minutes
Hour angle (H)	0°
Solar zenith angle (θ)	40.7°
Solar elevation angle	49.3°
Solar azimuth angle	180° (South)

At this time, the sun is directly overhead in New York City, with an elevation of 49.3° and an azimuth of 180° (South).

Frequently Asked Questions

How accurate is this sun position calculator?: This calculator uses the Solar Position Algorithm (SPA) which provides accurate results within ±0.0003° for most locations and times.
Does this calculator account for atmospheric refraction?: Yes, the SPA algorithm includes corrections for atmospheric refraction to provide more accurate elevation angles.
Can I use this calculator for solar panel installation?: Yes, the azimuth and elevation angles calculated here are useful for determining optimal solar panel orientation.
What's the difference between solar time and clock time?: The equation of time accounts for this difference. Solar time is based on the sun's position, while clock time follows a uniform 24-hour cycle.
How does the sun's position change throughout the year?: The solar declination changes throughout the year, causing the sun's path to shift north and south. This creates the seasons.