Astronomy and time
Sunrise, sunset, solar noon and twilight calculator
Sunrise, sunset, solar noon, day length and civil, nautical and astronomical twilight for any coordinates and date, in local time, by the NOAA method.
Runs in your browser. What you enter stays on this page and is not uploaded.
Showing the worked example. Results update as you type.
Result
| Event | Morning | Evening | Dates, offsets and UTC |
|---|---|---|---|
| Astronomical twilight (108°) | 03:28 | 22:36 | UTC−06:00; 09:27:54 UTC · UTC−06:00; 04:35:44 UTC |
| Nautical twilight (102°) | 04:17 | 21:47 | UTC−06:00; 10:16:40 UTC · UTC−06:00; 03:46:58 UTC |
| Civil twilight (96°) | 04:58 | 21:05 | UTC−06:00; 10:58:26 UTC · UTC−06:00; 03:05:13 UTC |
| Sunrise / sunset (90.833°) | 05:31 | 20:32 | UTC−06:00; 11:31:19 UTC · UTC−06:00; 02:32:20 UTC |
- Times are for the centre of the Sun at sea level with standard refraction; at the horizon real refraction varies, so observed times can differ by a minute or more, and more near the poles.
Method and limits
The calculation follows NOAA’s solar calculator, which uses Jean Meeus’s solar coordinates. For the date, the Sun’s declination δ and the equation of time E are computed; solar noon is when the Sun crosses the meridian, 720 − 4λ − E minutes after 0h UTC (λ in degrees east). An event at zenith angle z happens at the hour angle H where
cos H = (cos z − sin φ sin δ) / (cos φ cos δ)
before (morning) or after (evening) solar noon, 4 minutes per degree of H. Each event is recomputed with δ and E at the event itself. The zenith angles are 90.833° for sunrise and sunset (the Sun’s upper edge on the horizon: 0.833° for refraction and the solar semidiameter), 96° for civil, 102° for nautical and 108° for astronomical twilight. If |cos H| exceeds 1 the Sun never reaches that angle that day: midnight sun or polar night.
Worked example: at 40°N, 105°W on 21 June 2010 in UTC−6, NOAA’s spreadsheet gives sunrise 05:31:16 and sunset 20:32:09; this page gives 05:31 and 20:32, solar noon 13:01:49 and civil twilight from 04:58 to 21:05.
Assumptions and limits
NOAA states the method is accurate to within a minute between 72°N and 72°S and within about 10 minutes nearer the poles, for years 1800 to 2100. Times are for sea level on a flat horizon with standard refraction; elevation, hills and unusual temperature profiles change what you see. Local times use the pinned IANA rules for 2020–2035; choose a fixed UTC offset for other years. The page opens on today’s date in your browser.
References
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