Sunrise Calculator
Free Sunrise Calculator. Free online tool with accurate results using verified formulas. Includes worked examples, FAQ, and instant calculations.
Formula
Cos(HourAngle) = -Tan(Lat) × Tan(Dec)
Uses spherical trigonometry based on your latitude and the sun's declination (seasonal angle) to find the hour angle when the sun crosses the horizon.
Worked Examples
Example 1: New York Summer Solstice
Problem: NYC (40.7°N) on June 21.
Solution: Day Length: ~15 hours\nSunrise: ~5:25 AM\nSunset: ~8:30 PM\nResult: Longest day of the year.
Result: ~15h 5m Daylight
Example 2: London Winter Solstice
Problem: London (51.5°N) on Dec 21.
Solution: Day Length: ~7 hours 50 mins\nSunrise: ~8:00 AM\nSunset: ~3:50 PM\nResult: Shortest day of the year.
Result: ~7h 50m Daylight
Frequently Asked Questions
Why do sunrise and sunset times change daily?
The Earth revolves around the Sun while tilted on its axis (23.5°). This tilt means the angle of the Sun changes slightly every day relative to your location, causing the days to get longer or shorter depending on the season.
Do longitude coordinates affect sunrise time?
Yes. For every degree of longitude you move west within a time zone, sunrise and sunset occur about 4 minutes later. This explains why the sun sets much later in western parts of a time zone compared to eastern parts.
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.
How do I verify Sunrise Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
How accurate are the results from Sunrise 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.
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.