Calculate Position of Sun in Sky

The position of the sun in the sky changes throughout the day and year. Solar position refers to the sun's altitude (angle above the horizon) and azimuth (compass direction from north). These factors affect solar energy collection, lighting, and shadows.

What is Solar Position?

Solar position describes where the sun appears in the sky at any given time. Two key measurements define this position:

Solar Altitude: The angle of the sun above the horizon, measured in degrees. At sunrise/sunset, this is 0°. At solar noon, it reaches its maximum value.
Solar Azimuth: The compass direction of the sun from north, measured in degrees clockwise from north. East is 90°, south is 180°, and west is 270°.

These values change continuously throughout the day and vary by location and time of year. Solar position calculations are essential for solar energy systems, architecture, and environmental science.

How to Calculate Solar Position

Calculating solar position requires these inputs:

Latitude and longitude of the location
Date and time (including timezone)
Local standard time meridian (LSTM) for the timezone

The calculation involves several steps including:

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

Our calculator handles these calculations automatically using standard astronomical algorithms.

Formula

The solar position is calculated using these key formulas:

Solar Declination (δ) = -23.45° × cos(360/365 × (n + 10))

Equation of Time (EOT) = 9.87 × sin(2B) - 7.53 × cos(B) - 1.5 × sin(B)

Solar Time (ST) = (Local Time + 4 × (Longitude - LSTM) + EOT) / 60

Hour Angle (H) = 15 × (ST - 12)

Solar Altitude (α) = asin(sin(φ) × sin(δ) + cos(φ) × cos(δ) × cos(H))

Solar Azimuth (A) = acos((sin(α) × sin(φ) - sin(δ)) / (cos(α) × cos(φ)))

Where:

n = day of year (1-365)
φ = latitude
B = 2π × (n - 81) / 364
LSTM = 15 × timezone offset

Example Calculation

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

Day of year (n) = 172
Solar declination (δ) = -23.45° × cos(360/365 × (172 + 10)) ≈ 23.44°
Equation of time (EOT) ≈ -0.16 minutes
Solar time (ST) = (12 + 4 × (74.01 - (-75)) + (-0.16)) / 60 ≈ 12.00 hours
Hour angle (H) = 15 × (12 - 12) = 0°
Solar altitude (α) ≈ 71.57°
Solar azimuth (A) ≈ 180° (south)

At this time, the sun is directly overhead (altitude 71.57°) and due south (azimuth 180°).

How to Interpret Results

Understanding solar position results helps with:

Solar energy systems: Optimal panel angles and tracking systems
Architecture: Natural lighting design and shading analysis
Environmental science: Studying climate patterns and ecosystems
Everyday life: Determining sunrise/sunset times and daylight duration

For example, a solar altitude of 45° means the sun is halfway between the horizon and zenith. An azimuth of 135° indicates the sun is southeast.

FAQ

What is the difference between solar altitude and azimuth?

Solar altitude measures the sun's height above the horizon (0° to 90°), while solar azimuth measures the compass direction from north (0° to 360°). Together they define the sun's position in the sky.

How does solar position change throughout the year?

The sun's path changes with seasons due to Earth's tilt. In summer, the sun reaches higher altitudes and stays above the horizon longer. In winter, it's lower and visible for less time.

What factors affect solar position calculations?

Key factors include location coordinates, date, time, and timezone. Atmospheric refraction and observer height can also have small effects.