Sunrise Sunset Calculator Degrees

This calculator determines the sunrise and sunset times in degrees from the horizon for any location and date. It accounts for the observer's latitude, longitude, date, and timezone, providing both the time of sunrise/sunset and the corresponding solar elevation angles.

How to Use This Calculator

To calculate sunrise and sunset times in degrees:

Enter your location's latitude and longitude in decimal degrees
Select the date for which you want to calculate the times
Choose your timezone from the dropdown menu
Click "Calculate" to generate the results
Review the sunrise and sunset times along with their corresponding solar elevation angles

The calculator will display the results in a clear format, including the exact times and the solar elevation angles at those moments. A chart will visualize the solar elevation throughout the day.

Formula Used

The calculations are based on the following astronomical formulas:

Julian Date = JDN - 2451545.0 Solar Mean Anomaly = 0.98560028 * Julian Date Solar True Longitude = Solar Mean Anomaly + 1.914 * sin(Solar Mean Anomaly) + 0.02 * sin(2 * Solar Mean Anomaly) + 282.94 Solar Right Ascension = atan2(cos(23.44 * π/180) * sin(Solar True Longitude), cos(Solar True Longitude)) Solar Declination = asin(sin(23.44 * π/180) * sin(Solar True Longitude)) Hour Angle = acos((sin(-0.833 * π/180) - sin(Latitude * π/180) * sin(Solar Declination)) / (cos(Latitude * π/180) * cos(Solar Declination))) Solar Elevation = asin(sin(Latitude * π/180) * sin(Solar Declination) + cos(Latitude * π/180) * cos(Solar Declination) * cos(Hour Angle))

These formulas account for the Earth's elliptical orbit, axial tilt, and the observer's geographic position to calculate accurate sunrise and sunset times and solar elevation angles.

Interpreting Results

The calculator provides several key pieces of information:

Sunrise Time: The exact time when the sun appears above the horizon
Sunset Time: The exact time when the sun disappears below the horizon
Sunrise Elevation: The angle of the sun above the horizon at sunrise (typically around 0.5°)
Sunset Elevation: The angle of the sun above the horizon at sunset (typically around 0.5°)

These values help photographers, astronomers, and outdoor planners understand the lighting conditions throughout the day. The solar elevation chart provides a visual representation of how the sun's position changes during the day.

Worked Examples

Example 1: New York City on June 21

For New York City (40.7128° N, 74.0060° W) on June 21, 2023:

Metric	Value
Sunrise Time	5:20 AM EDT
Sunset Time	8:25 PM EDT
Sunrise Elevation	0.53°
Sunset Elevation	0.53°

This example shows the long daylight hours typical of the summer solstice in the Northern Hemisphere.

Example 2: Sydney on December 21

For Sydney (33.8688° S, 151.2093° E) on December 21, 2023:

Metric	Value
Sunrise Time	5:30 AM AEDT
Sunset Time	8:30 PM AEDT
Sunrise Elevation	0.52°
Sunset Elevation	0.52°

This example demonstrates the long daylight hours typical of the summer solstice in the Southern Hemisphere.

Frequently Asked Questions

What is the difference between solar elevation and solar azimuth?: Solar elevation measures the angle of the sun above the horizon, while solar azimuth measures the angle of the sun relative to north. This calculator focuses on elevation angles.
Why do sunrise and sunset times vary throughout the year?: The variation is caused by the Earth's axial tilt (23.44°) and its elliptical orbit around the sun. The tilt causes the seasons, while the elliptical orbit results in the Earth moving faster when closer to the sun (perihelion) and slower when farther away (aphelion).
How accurate are the calculations?: The calculator uses precise astronomical formulas and accounts for the observer's exact location and date. The results are accurate to within a few minutes for most locations.
Can I use this calculator for any location on Earth?: Yes, the calculator accepts any valid latitude and longitude coordinates. Simply enter the coordinates for your desired location and the calculator will provide accurate results.
What is the significance of the 0.5° solar elevation at sunrise/sunset?: The 0.5° elevation is the standard definition of sunrise and sunset, when the sun's upper limb is 0.5° below the horizon. This accounts for atmospheric refraction and the sun's apparent diameter.