Sunrise and sunset are recomputed once with the sun's position at the first estimate (as NOAA does), then shifted by London, UTC+01:00.
About the sunrise and sunset calculator
The calculator follows NOAA's Solar Calculator, which uses Jean Meeus's formulas for the sun's declination and the equation of time on the chosen date. It then solves for the hour angle at which the centre of the sun is 90.833° from the zenith: the extra 0.833° allows 34′ for atmospheric refraction and 16′ for the sun's radius, so sunrise is the moment the top of the disc meets a flat horizon. Civil dawn and dusk use 96°, the sun's centre 6° below the horizon.
Photographers, walkers, sailors and anyone planning around daylight use it. In London on the June solstice 2026 the sun rises at 04:43 and sets at 21:22 BST, 16 h 38 min of daylight; on the December solstice the day lasts 7 h 50 min.
Times assume sea level and a clear, flat horizon. For the London, Singapore and Delhi examples below they match the US Naval Observatory's figures to the minute.
Worked examples
London on the June solstice
Latitude
51.5074 ° N
Longitude
-0.1278 ° E
Date
2026-06-21
Show times in
Time zone
Time zone
London
Sunrise – sunset
04:43 – 21:22
Sunrise
04:43
Sunset
21:22
Solar noon
13:02
Civil dawn (sun 6° below horizon)
03:55
Civil dusk
22:09
Day length
16 h 38 min 30 s
Checked against: NOAA Solar Calculator main.js run in Node: rise 04:43:05, set 21:21:35, day 998.49 min; civil twilight from the same code at 96°; USNO API: rise 04:43, set 21:22, transit 13:02, civil twilight 03:55–22:09
Singapore at the March equinox, fixed offset
Latitude
1.3521 ° N
Longitude
103.8198 ° E
Date
2026-03-20
Show times in
UTC offset
UTC offset
8 hours
Sunrise
07:09
Sunset
19:15
Solar noon
13:12
Civil dawn (sun 6° below horizon)
06:48
Civil dusk
19:36
Checked against: NOAA Solar Calculator main.js: rise 07:09:00, set 19:15:29; USNO API: rise 07:09, set 19:15, transit 13:12, civil twilight 06:48–19:36
Midnight sun in Tromsø
Latitude
69.6492 ° N
Longitude
18.9553 ° E
Date
2026-06-21
Show times in
Time zone
Time zone
Oslo
Daylight
Midnight sun
Day length
1 d
Sunrise – sunset
Sun up all day
Checked against: NOAA main.js finds no sunrise or sunset on this date; USNO API: “Object continuously above the horizon”
Polar night in Tromsø, with civil twilight
Latitude
69.6492 ° N
Longitude
18.9553 ° E
Date
2026-12-21
Show times in
Time zone
Time zone
Oslo
Daylight
Polar night
Day length
0 s
Civil dawn (sun 6° below horizon)
09:31
Civil dusk
13:53
Checked against: USNO API: “Object continuously below the horizon”, civil twilight 09:31–13:53 (UTC+1); NOAA main.js at 96° gives 09:31:13 and 13:53:13
Questions
Why is the day longer than 12 hours at the equinox?
Because sunrise and sunset are timed at the top edge of the sun, and refraction lifts the sun's image by about 34′ near the horizon. Together they add several minutes of daylight at both ends. On 20 March 2026 the day lasts 12 h 6 min in Singapore and 12 h 10 min in London. In London, day and night are closest to equal on 17 March, three days before the equinox.
What is the difference between civil, nautical and astronomical twilight?
They are defined by how far the sun's centre is below the horizon: civil twilight ends at 6°, nautical at 12° and astronomical at 18°. In London on 21 June 2026 civil dusk comes at 22:09, 47 minutes after sunset. Around midsummer the sun gets no lower than about 15° below London's horizon, so astronomical twilight lasts all night.
What is solar noon, and why isn't it at 12:00?
Solar noon is the moment the sun crosses the meridian and stands highest in the sky. Clock time differs from it for three reasons: your longitude within the time zone, daylight saving time, and the equation of time, which varies from about −14 minutes in February to about +16 minutes in early November. In London in June solar noon is at about 13:02 BST.
Where do the midnight sun and polar night happen?
North of the Arctic Circle, at about 66.6° N, and south of the Antarctic Circle. In Tromsø, at 69.6° N, the sun stays above the horizon for weeks around the June solstice and does not rise from late November to mid-January. Even on 21 December, civil twilight there lasts from 09:31 to 13:53, so the polar night is not completely dark.
How accurate is the sunrise and sunset calculator?
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “London on the June solstice” is checked against NOAA Solar Calculator main.js run in Node: rise 04:43:05, set 21:21:35, day 998.49 min; civil twilight from the same code at 96°; USNO API: rise 04:43, set 21:22, transit 13:02, civil twilight 03:55–22:09.
Where does the method come from?
NOAA Global Monitoring Laboratory — Solar Calculator (and its main.js / spreadsheet); NOAA — Solar Calculation Details; J. Meeus, Astronomical Algorithms, 2nd ed. (1998), ch. 25 and 28; US Naval Observatory — Sun and Moon rise/set data (cross-check).