Sunrise and Sunset Calculator

Calculate precise sunrise and sunset times using your location’s latitude, longitude, and the date.

Enter Your Location and Date

Key astronomical metrics used in the calculation

Metric	Value	Unit
Latitude	—	Degrees
Longitude	—	Degrees
Date	—	—
Time Zone Offset	—	Hours
Julian Day	—	Days
Solar Declination	—	Degrees
Equation of Time	—	Minutes
Hour Angle (Sunrise/Sunset)	—	Degrees

What is Sunrise and Sunset Calculation?

Calculating sunrise and sunset times involves determining the precise moments when the upper limb of the Sun is tangent to the horizon, as observed from a specific location on Earth. This seemingly simple daily event is governed by complex astronomical mechanics, including the Earth’s rotation, its axial tilt, and its orbit around the Sun. Understanding these calculations is crucial for various applications, from astronomical observations and navigation to agricultural planning and everyday scheduling.

This sunrise and sunset calculator leverages these principles to provide accurate times based on geographical coordinates (latitude and longitude) and the specific date. It accounts for the primary factors that influence daylight hours, helping users predict when the sun will rise and set at their location. Whether you’re an amateur astronomer, a photographer planning a shoot, or simply curious about daylight patterns, this tool demystifies the celestial mechanics involved.

Sunrise and Sunset Calculation Formula and Explanation

The calculation of sunrise and sunset times is rooted in spherical astronomy. The core idea is to find the time when the Sun’s center is at a specific angle relative to the observer’s local horizon. For sunrise and sunset, this angle is approximately -0.833 degrees, accounting for atmospheric refraction and the Sun’s apparent radius.

The general formula to find the hour angle (H) for sunrise or sunset is derived from the celestial sphere’s fundamental equation:

cos(H) = (sin(altitude) - sin(latitude) * sin(declination)) / (cos(latitude) * cos(declination))

Where:

• H is the hour angle (the angle of the Sun east or west of the local meridian)
• altitude is the Sun’s altitude at sunrise/sunset (approximately -0.833 degrees)
• latitude is the observer’s latitude
• declination is the Sun’s declination (the angle between the Sun’s rays and the plane of the Earth’s equator)

The Sun’s declination (\(\delta\)) varies throughout the year, following a sinusoidal pattern. A common approximation is:

δ = 23.45 * sin( (360/365.25) * (N - 81) ) degrees

Where N is the day number of the year (Julian day). Note that this is a simplified approximation; more precise formulas exist.

The Equation of Time (EoT) accounts for the difference between apparent solar time (sundial time) and mean solar time (clock time). It arises from the Earth’s elliptical orbit and its axial tilt.

Once the hour angle (H) is calculated, the local solar time of sunrise/sunset can be determined. Solar noon occurs when the Sun is at its highest point (transit), which is approximated as 12:00 PM solar time.

The general formula for sunrise/sunset time (in hours from midnight UTC) is:

Time = 12 + (HourAngle / 15) - (Longitude / 15) - (EquationOfTime / 60) + TimeZoneOffset

Where the Hour Angle is converted from degrees to hours (15 degrees per hour).

Variables Table

Variable	Meaning	Unit	Typical Range
Latitude	Observer’s angular distance north or south of the equator.	Degrees	-90 to +90
Longitude	Observer’s angular distance east or west of the prime meridian.	Degrees	-180 to +180
Date	The specific day for which calculations are performed.	Calendar Date	N/A
Time Zone Offset	The difference between local time and UTC.	Hours	-12 to +14
Julian Day (N)	The number of days since noon Universal Time on January 1, 4713 BC.	Days	Varies
Solar Declination (\(\delta\))	The angle between the Sun’s rays and Earth’s equatorial plane.	Degrees	Approx. -23.45 to +23.45
Equation of Time (EoT)	Difference between apparent solar time and mean solar time.	Minutes	Approx. -16 to +14
Hour Angle (H)	The angular distance on the celestial sphere, measured westward along the celestial equator from the observer’s meridian to the hour circle of the celestial object.	Degrees	Varies; calculated based on altitude, latitude, declination.
Sunrise/Sunset Altitude	The apparent altitude of the Sun’s center at the horizon.	Degrees	Approx. -0.833

Practical Examples

Example 1: Los Angeles, USA

Inputs:

• Latitude: 34.0522° N
• Longitude: 118.2437° W
• Date: October 27, 2023
• Time Zone Offset: -7 (PST)

Calculation: Using the formulas with these inputs yields approximate sunrise and sunset times.

Expected Results:

• Sunrise Time: ~07:30 PST
• Sunset Time: ~18:04 PST
• Daylight Duration: ~10 hours 34 minutes
• Solar Noon: ~12:47 PST

Example 2: Sydney, Australia

Inputs:

• Latitude: 33.8688° S
• Longitude: 151.2093° E
• Date: October 27, 2023
• Time Zone Offset: +11 (AEDT)

Calculation: Applying the same astronomical principles with Sydney’s coordinates and date.

Expected Results:

• Sunrise Time: ~05:51 AEDT
• Sunset Time: ~19:03 AEDT
• Daylight Duration: ~13 hours 12 minutes
• Solar Noon: ~12:27 AEDT

These examples demonstrate how latitude and longitude significantly impact daylight duration and the timing of sunrise and sunset.

How to Use This Sunrise and Sunset Calculator

1. Enter Latitude: Input the latitude of your location in decimal degrees. Positive values are for the Northern Hemisphere, and negative values are for the Southern Hemisphere.
2. Enter Longitude: Input the longitude of your location in decimal degrees. Positive values are for East, and negative values are for West.
3. Select Date: Choose the specific date from the calendar for which you want to calculate the sunrise and sunset times.
4. Select Time Zone Offset: Choose your local time zone’s offset from UTC. This is crucial for displaying the times in your local format. For example, Pacific Standard Time (PST) is UTC-8, and Australian Eastern Daylight Time (AEDT) is UTC+11.
5. Click Calculate: Press the “Calculate” button.
6. Interpret Results: The calculator will display the estimated sunrise time, sunset time, the total daylight duration, and the time of solar noon for your specified location and date, adjusted for your local time zone.
7. Review Metrics: The table below the results provides intermediate astronomical values used in the calculation, such as the Julian Day, Solar Declination, and Equation of Time, offering deeper insight into the astronomical factors.

Always ensure your latitude and longitude are accurate for the most precise results. If you are unsure about your location’s time zone offset, consult an online time zone converter.

Key Factors That Affect Sunrise and Sunset

1. Latitude: This is the primary factor. Locations closer to the equator experience less variation in daylight hours throughout the year, while higher latitudes see dramatic seasonal changes, including 24-hour daylight in summer and 24-hour darkness in winter.
2. Longitude: Determines the local time of sunrise and sunset relative to UTC. Locations further east experience sunrise and sunset earlier in the day than locations further west at the same latitude.
3. Date (Earth’s Orbit and Axial Tilt): The Earth’s tilt (23.45 degrees) and its position in its orbit around the Sun cause the Sun’s apparent path across the sky to change throughout the year, leading to seasonal variations in the length of daylight and the times of sunrise and sunset.
4. Time Zone: While not an astronomical factor, the defined time zone offset from UTC directly impacts the displayed local time of sunrise and sunset.
5. Atmospheric Refraction: The Earth’s atmosphere bends sunlight, making the Sun appear slightly higher in the sky than it geometrically is. This effect causes us to see the Sun rise a few minutes earlier and set a few minutes later than we would without an atmosphere. Standard corrections are included in precise calculations.
6. Altitude: While the effect is minor for most everyday purposes, a higher altitude means a clearer view of the horizon, potentially leading to slightly earlier sunrise and later sunset compared to sea level. The standard calculation assumes sea level.
7. Equation of Time: Variations in Earth’s orbital speed and axial tilt cause the difference between apparent solar time and mean solar time to fluctuate. This needs to be accounted for to synchronize calculations with clock time.

Frequently Asked Questions (FAQ)

Q1: How accurate are these calculations?

These calculations are based on well-established astronomical algorithms. They are highly accurate for determining the geometric sunrise and sunset. Minor discrepancies might arise due to localized atmospheric conditions or non-standard definitions of twilight, but for practical purposes, they are very reliable.

Q2: What is the difference between sunrise/sunset time and solar noon?

Sunrise is when the Sun first appears above the eastern horizon. Sunset is when it disappears below the western horizon. Solar noon is the time when the Sun reaches its highest point in the sky for the day, which usually occurs close to, but not exactly at, 12:00 PM local clock time.

Q3: Why does the daylight duration change so much between summer and winter?

This is due to the Earth’s axial tilt. In summer, the hemisphere tilted towards the Sun receives more direct sunlight and experiences longer days. In winter, that hemisphere is tilted away, receiving less direct sunlight and having shorter days.

Q4: Can I calculate sunrise and sunset for any date in the past or future?

Yes, the astronomical formulas used are valid for any date, allowing you to calculate past or future sunrise and sunset times. The accuracy depends on the precision of the input date and the algorithms used.

Q5: What if my location is exactly on the equator?

Locations on the equator (0° latitude) experience relatively consistent daylight durations of approximately 12 hours year-round, though the exact times of sunrise and sunset will still vary slightly due to the Equation of Time and seasonal declination changes.

Q6: How does daylight saving time affect the calculation?

Daylight Saving Time (DST) is a civil convention, not an astronomical one. Our calculator uses the Time Zone Offset. You must select the correct offset (e.g., UTC+1 for many European countries during DST) that reflects whether DST is active on the date you are calculating for. The calculator itself doesn’t automatically adjust for DST; you must provide the correct offset.

Q7: What does “Civil Twilight” mean in relation to sunrise/sunset?

Civil twilight is the period when the Sun is just below the horizon (about 6 degrees below for civil twilight). It’s the time when there is enough light for ordinary outdoor activities. Sunrise is the moment the upper edge of the Sun appears on the horizon, and sunset is when it disappears. This calculator provides the geometric sunrise/sunset, not the twilight times.

Q8: Why are my results slightly different from another calculator or app?

Differences can arise from:

• Slight variations in the astronomical algorithms used.
• Different assumptions about atmospheric refraction.
• Different definitions of the Sun’s edge (e.g., center vs. upper limb).
• Inclusion or exclusion of atmospheric effects.
• Accuracy of the input latitude and longitude.
• Correctness of the selected time zone offset.

Our calculator aims for high precision using standard astronomical models.