An astronomical estimate
This site uses SunCalc 2.0.2 at observer height zero. Sunrise and sunset model the upper solar edge with standard refraction. Terrain and actual atmospheric conditions are not included.
Dates belong to the selected place
The calculation selects the solar day containing local noon. Event times are then formatted in the selected IANA time zone. An adjacent-day marker is shown if an event falls outside the selected civil date.
When an event is missing
We never replace a missing event with midnight. Polar day, polar night, and unavailable twilight events are reported explicitly. Unusual locations and civil-day boundaries need careful validation.
Limits
Use these results for everyday planning. Do not use them as a guarantee of visibility, weather, or a legal definition of daylight. Results are rounded to the nearest minute.
How sunrise and sunset are calculated, step by step
- Your browser finds the instant that is 12:00 on the chosen civil date in the selected time zone, using its built-in IANA data, which also handles daylight saving time.
- SunCalc takes that instant, the latitude and the longitude and finds the solar transit (solar noon) of that solar day, then the Sun’s declination at that moment.
- For each event it computes the hour angle at which the Sun’s center reaches a target altitude: −0.833° for sunrise and sunset (the upper edge on the horizon with standard refraction), −6°, −12° and −18° for the twilight boundaries, +6° for golden hour and −4° and −8° for the blue-hour convention.
- The hour angle is converted into instants before and after transit and refined once against the Sun’s changing position. If the target altitude is never reached, the event is reported as Unavailable.
- Each instant is rounded to the nearest minute and formatted in the selected zone. If it falls on a different civil date, that date is shown in brackets.
The formula in brief
For latitude φ, solar declination δ and target altitude h₀, the hour angle H₀ satisfies cos H₀ = (sin h₀ − sin φ · sin δ) / (cos φ · cos δ). When that value is outside −1 to 1 the Sun never reaches h₀ on that day, which is the polar case. Otherwise sunrise is roughly transit − H₀ / 360° days and sunset transit + H₀ / 360° days. Solar position itself comes from standard low-precision series for the Sun’s mean anomaly, ecliptic longitude and the obliquity of the ecliptic.
Accuracy and comparison with other sources
Simplified algorithms of this kind generally agree with observatory tables to within a minute or two at mid-latitudes. Near the polar circles, where the Sun’s path grazes the horizon, a small change in assumptions moves the time by many minutes. Other services may use a different refraction value, an observer above sea level or a different rounding rule, so their times can differ by a minute without either being wrong. Independent city-by-city validation of this site has not been completed; treat the results as a planning reference.
Sources
- SunCalc repository: the open-source library (BSD-2-Clause, copyright Volodymyr Agafonkin) bundled with this site.
- U.S. Naval Observatory: rise, set and twilight definitions.
- NOAA solar calculator details.