Calculate The Position of The Sun

This solar position calculator determines the sun's azimuth, altitude, and declination for any location and time. Understanding the sun's position is essential for solar energy applications, astronomy, and navigation.

How to Use This Calculator

To calculate the sun's position:

Enter your location's latitude and longitude in decimal degrees
Select the date and time of interest
Click "Calculate" to see the results

The calculator provides three key measurements:

Azimuth - The sun's angle from north (0° to 360°)
Altitude - The sun's angle above the horizon (-90° to 90°)
Solar Declination - The sun's angle relative to the equator

Formula Used

The calculator uses the following formulas based on the standard solar position algorithms:

// Julian day calculation J = day_of_year + (hour - 12)/24 // Solar declination (δ) δ = 23.45° * sin(360° * (284 + J)/365) // Equation of time (E) E = 9.87 * sin(2B) - 7.53 * cos(B) - 1.5 * sin(B) where B = 2π(J - 81)/365 // Solar time correction solar_time = local_time + (4 * (longitude - standard_meridian) + E)/60 // Solar hour angle (ω) ω = 15° * (solar_time - 12) // Solar altitude (α) α = asin(sin(φ) * sin(δ) + cos(φ) * cos(δ) * cos(ω)) // Solar azimuth (A) A = acos((sin(α) * sin(φ) - sin(δ)) / (cos(α) * cos(φ))) if solar_time > 12 then A = 360° - A

Where:

φ = latitude
δ = solar declination
ω = solar hour angle
α = solar altitude
A = solar azimuth

Example Calculation

For a location at 40.7128° N, 74.0060° W on June 21 at 12:00 PM:

Example Results

Azimuth: 180.2° (South)

Altitude: 73.5°

Solar Declination: 23.45° (Northern Summer Solstice)

At this time, the sun is directly overhead for observers at the Tropic of Cancer (23.45° N). The solar altitude is maximized, and the azimuth points directly south.

Interpreting Results

Understanding the solar position helps with:

Solar panel orientation for maximum energy production
Shadow calculations for architectural design
Daylight mapping for urban planning
Photovoltaic system performance analysis

Practical Considerations

Atmospheric refraction (about 0.57°) is not included in these calculations. For precise solar tracking systems, this small correction may be needed.

Frequently Asked Questions

What is solar azimuth?: Solar azimuth is the compass direction from which the sun appears to be coming. 0° is north, 90° is east, 180° is south, and 270° is west.
What is solar altitude?: Solar altitude is the angle of the sun above the horizon. A negative value indicates the sun is below the horizon (nighttime).
How does solar declination affect solar energy?: Solar declination determines the sun's maximum altitude and affects the length of daylight. It varies throughout the year, reaching its maximum at the summer solstice.
Can this calculator account for atmospheric refraction?: This calculator provides theoretical values. For practical applications, atmospheric refraction (about 0.57°) may need to be added to the altitude calculation.
What time zone should I use?: Use the local standard time for your location. The calculator automatically adjusts for daylight saving time if the date falls within that period.