Sunrise Sunset Calculator
Calculate sunrise, sunset, and daylight hours for any location and date on Earth. Enter values for instant results with step-by-step formulas.
Formula
Hour Angle = arccos((sin(-0.833°) - sin(lat) × sin(dec)) / (cos(lat) × cos(dec)))
The sunrise/sunset hour angle is computed from the observer's latitude and the Sun's declination. The -0.833° accounts for atmospheric refraction (0.567°) and the Sun's apparent radius (0.266°). Solar declination is derived from the ecliptic longitude, which depends on the date via the solar mean anomaly and equation of center.
Worked Examples
Example 1: Summer Day in New York
Problem: Find sunrise and sunset for New York City (40.71°N, 74.01°W) on June 21.
Solution: Using solar position calculations:\nSolar declination ≈ +23.44°\nHour angle ≈ 112.8°\nSunrise ≈ 05:25 UTC (local 01:25 EDT → adjusted)\nDaylight ≈ 15.05 hours
Result: Sunrise: ~05:25, Sunset: ~20:31 (UTC) — approximately 15 hours of daylight
Example 2: Winter in London
Problem: Find sunrise and sunset for London (51.51°N, 0.13°W) on December 21.
Solution: Solar declination ≈ -23.44°\nAt 51.5°N with negative declination, very short day\nDaylight ≈ 7.9 hours
Result: Sunrise: ~08:04, Sunset: ~15:53 (UTC) — approximately 7.9 hours of daylight
Frequently Asked Questions
How are sunrise and sunset times calculated?
Sunrise and sunset are calculated using the sun's position relative to the observer. The algorithm computes the Julian date, solar mean anomaly, equation of center, ecliptic longitude, solar declination, and hour angle. Sunrise occurs when the sun's center is 0.833° below the horizon (accounting for atmospheric refraction of 0.567° and the sun's apparent radius of 0.266°). These calculations use the NOAA solar position algorithm, accurate to within 1-2 minutes.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
How accurate are the results from Sunrise Sunset Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
What formula does Sunrise Sunset Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I use Sunrise Sunset Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.