Sunrise/Sunset Approximation
Estimate day length using latitude and day-of-year approximation.
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What This Calculator Does
Calculate approximate sunrise and sunset times by latitude and day of year using solar declination and hour angle equations. Results include total daylight duration and approximate solar noon.
It combines Latitude, Day of Year to estimate Daylight Duration, Approx Sunrise, Approx Sunset.
Formula & Method
Notation used in the formulas: = Daylight Duration; = Latitude; = Day of Year.
Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.
Use this for trip planning, photography golden-hour timing, agricultural scheduling, and any application where you need daylight duration or approximate solar event times by geographic location and date.
Worked Examples
Atlanta, GA (lat 33.7°) — Summer vs Winter contrast
June 21 (day 172 — summer solstice, lat = 33.7°): Solar declination ≈ +23.4° Hour angle H₀ = arccos(−tan(33.7°) × tan(23.4°)) ≈ 108.3° Daylight = 2 × 108.3° / 15°/hr ≈ 14.4 hours Sunrise ≈ 12:00 − 7.2 hr ≈ 4:48 AM solar time Sunset ≈ 12:00 + 7.2 hr ≈ 7:12 PM solar time December 21 (day 355 — winter solstice): Solar declination ≈ −23.4° Daylight ≈ 9.6 hours Sunrise ≈ 7:12 AM solar time Sunset ≈ 4:48 PM solar time The seasonal contrast is ~4.8 hours of daylight difference at this latitude.
Civil, Nautical, and Astronomical Twilight Explained
- Civil Twilight
- The sun is between 0° and 6° below the horizon. Outdoor activities are still possible without artificial light. The sky is bright enough to see clearly, and the horizon is easily distinguishable. Civil twilight ends at the point most people consider true darkness. Starts and ends about 20–30 minutes after sunset / before sunrise depending on latitude and season.
- Nautical Twilight
- The sun is between 6° and 12° below the horizon. The horizon is still visible at sea but the sky is dark enough to see major stars. Historically used by sailors for celestial navigation. Begins and ends roughly 40–60 minutes after sunset / before sunrise.
- Astronomical Twilight
- The sun is between 12° and 18° below the horizon. The sky is nearly completely dark and nearly all stars are visible. Any remaining atmospheric glow from the sun is negligible. Astronomers use this boundary to define true darkness for observing faint objects.
Frequently Asked Questions
- How is sunrise time calculated?
- Sunrise time is calculated from solar declination (the sun's angle relative to the equator, which changes throughout the year) and the observer's latitude. The hour angle at sunrise is arccos(−tan(latitude) × tan(declination)). This angle is converted to time: every 15° of hour angle equals one hour. The result gives hours before solar noon.
- What is civil twilight?
- Civil twilight is the period when the sun is between 0° and 6° below the horizon — after sunset but before full darkness. During civil twilight, there is enough ambient light for most outdoor activities without artificial lighting. The sky transitions from the bright post-sunset glow to near-darkness.
- Why does sunrise time change throughout the year?
- Sunrise time changes because the Earth's axial tilt (23.4°) causes the sun's apparent path across the sky to shift seasonally. At the summer solstice, the sun rises earliest and sets latest (for northern hemisphere). At the winter solstice, it rises latest and sets earliest. The rate of change is fastest at the equinoxes and slowest near the solstices.
- How do I find sunrise time for my location?
- Enter your latitude (in degrees, positive for north and negative for south) and the day of the year (1–365). The calculator returns approximate sunrise, sunset, and daylight duration using solar geometry equations. For local clock time, you would also need to apply your time zone offset and longitude correction.
Inputs Used
- Latitude: Used directly in the calculation.
- Day of Year: Used directly in the calculation.
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