Calculate The Sun's Position in The Sky

This calculator determines the sun's position in the sky based on your location, date, and time. It provides solar azimuth, altitude, and day length, which are essential for solar energy applications, astronomy, and outdoor activities.

How to Use This Calculator

To calculate the sun's position:

Enter your latitude and longitude coordinates
Select the date and time you're interested in
Click "Calculate" to see the results
Review the solar azimuth, altitude, and day length

The calculator uses standard astronomical algorithms to provide accurate results. The solar azimuth is the compass direction the sun is facing, measured in degrees clockwise from north. Solar altitude is the angle of the sun above the horizon, and day length shows how many hours of daylight occur on the selected date.

What Is Solar Position?

The solar position refers to the sun's location in the sky at any given time and location. This information is crucial for:

Solar energy systems design and optimization
Photovoltaic panel orientation
Astronomical observations and research
Outdoor activities planning
Weather forecasting and climate studies

Understanding solar position helps maximize energy production from solar panels and plan activities that depend on sunlight.

How to Calculate Solar Position

Calculating the sun's position involves several steps:

Determine the day of the year (1-365)
Calculate the solar declination angle
Compute the equation of time
Determine the solar hour angle
Calculate the solar zenith and azimuth angles

These calculations account for Earth's axial tilt, orbital eccentricity, and atmospheric refraction to provide accurate results.

The Formula

Solar Position Calculation

The solar position is calculated using the following formulas:

Solar declination (δ): δ = -23.45° × cos(360/365 × (n + 10))
Equation of time (EOT): EOT = 9.87 × sin(2B) - 7.53 × cos(B) - 1.5 × sin(B)
Solar hour angle (H): H = 15° × (t - 12) + lon - EOT
Solar altitude (α): α = arcsin(sin(lat) × sin(δ) + cos(lat) × cos(δ) × cos(H))
Solar azimuth (A): A = arctan2(sin(H), cos(H) × sin(lat) - tan(δ) × cos(lat))

Where:

n = day of year (1-365)
B = 2π × (n - 81) / 365
t = local time (24-hour format)
lon = longitude (positive east)
lat = latitude (positive north)

Worked Example

Let's calculate the sun's position for New York City (40.7128° N, 74.0060° W) on June 21 at 12:00 PM:

Day of year (n) = 172 (June 21)
Solar declination (δ) = -23.45° × cos(360/365 × (172 + 10)) ≈ 23.44°
Equation of time (EOT) ≈ -0.16 hours
Solar hour angle (H) = 15° × (12 - 12) + (-74.0060) - (-0.16) ≈ -73.85°
Solar altitude (α) ≈ 66.56°
Solar azimuth (A) ≈ 180° (south)

At this time, the sun is directly overhead in the southern hemisphere, which is why the azimuth is 180°.

Frequently Asked Questions

What is solar azimuth?

Solar azimuth is the compass direction from which the sun is shining, measured in degrees clockwise from north. A value of 0° means the sun is coming from the north, 90° from the east, 180° from the south, and 270° from the west.

What is solar altitude?

Solar altitude is the angle of the sun above the horizon, measured in degrees. A value of 0° means the sun is on the horizon, 90° means it's directly overhead, and negative values indicate the sun is below the horizon (nighttime).

How does latitude affect solar position?

Latitude directly affects the maximum solar altitude. Locations closer to the equator experience higher solar altitudes, while locations closer to the poles experience lower altitudes. The sun's path also varies more dramatically near the poles.

What is the equation of time?

The equation of time accounts for the discrepancy between solar time (based on the sun's position) and mean solar time (based on a uniform 24-hour day). It varies throughout the year, causing the sun to appear slightly ahead or behind its expected position.