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Sunrise and Sunset Calculator

Overview

Find sunrise and sunset times, solar noon, civil twilight, golden hour, blue hour and day length for any city and date, shown in the city's local time using the NOAA solar equations.

Pick a city and a date to see when the Sun rises and sets there, how long the day lasts, and when the soft light photographers look for begins and ends. The calculator follows the NOAA solar equations: it finds the Sun's declination and the equation of time for that day, works out solar noon from the city's longitude, then measures how long before and after noon the Sun crosses each altitude that matters: −0.833° for sunrise and sunset, −4° and +6° for golden hour, and −6° for civil dawn and dusk. Every time is shown in the city's own time zone, including daylight saving time, so you can plan a sunrise hike, a golden-hour shoot or a blue-hour long exposure without converting anything. Above the Arctic and Antarctic circles it tells you when the Sun never sets or never rises.

Formula and example

Horizontal sun-altitude bands from 6° above to 6° below the horizon: a warm golden-hour band from +6° down to −4° containing the horizon line at 0° and a dashed line at −0.833°, a cool blue-hour band from −4° to −6°, a dashed line at −6°, and the Sun's morning path climbing diagonally through them with the Sun drawn on the −0.833° line.

The sun altitudes the calculator times. Sunrise and sunset happen when the Sun's centre crosses −0.833°, just below the horizon, because refraction and the Sun's radius make its top edge visible first.

  1. Golden hour: Sun between −4° and +6°
  2. Horizon: 0°
  3. Sunrise and sunset: Sun's centre at −0.833°
  4. Blue hour: Sun between −6° and −4°
  5. Civil dawn and dusk: Sun at −6°
Line chart of hours of daylight through 2024, months 1 to 12 on the horizontal axis and 0 to 24 hours on the vertical axis. A dashed line for the equator stays flat just above 12 hours. A curve for London rises from 7 h 50 m in late December to 16 h 38 m at the June solstice, marked by a dashed vertical line. A steeper curve for Tromsø stays at 0 hours until mid-January, climbs to a flat top at 24 hours from mid-May to late July, and falls back to 0 hours from late November.

Hours of daylight through the year (months 1 to 12) at three latitudes. Near the equator every day lasts about 12 hours; the farther from it, the bigger the swing between winter and summer, until above the Arctic Circle the Sun stays down or up for weeks.

  1. Equator (0°): 12h 6m to 12h 8m of daylight all year
  2. London (51.5° N): 7h 50m on 21 December, 16h 38m on 21 June
  3. Tromsø (69.6° N): from no sunrise at all to no sunset in four months
  4. June solstice (21 June): the longest day north of the equator
  5. Polar day in Tromsø, 18 May to 24 July: the Sun never sets
  6. Polar night in Tromsø, 27 November to 14 January: the Sun never rises
Noon=720−4×Longitude−EoT\displaystyle \text{Noon} = 720 - 4 \times \text{Longitude} - \text{EoT}
cos⁡Hour angle=sin⁡Alt−sin⁡Latsin⁡Deccos⁡Latcos⁡DecSunrise, sunset=Noon∓4×Hour angle\displaystyle \begin{gathered} \cos \text{Hour angle} = \frac{\sin \text{Alt} - \sin \text{Lat} \sin \text{Dec}}{\cos \text{Lat} \cos \text{Dec}} \\[12pt] \text{Sunrise, sunset} = \text{Noon} \mp 4 \times \text{Hour angle} \end{gathered}

Where:

Noon
— Solar noon, when the Sun is highest, in minutes after midnight UTC; the calculator converts it to the city's local time.
Longitude
— The city's longitude in degrees, east positive. Each degree moves solar noon by 4 minutes.
EoT
— The equation of time: how far sundial time runs ahead of or behind clock time, between about −14 and +16 minutes over the year.
Hour angle
— How many degrees the Earth turns between solar noon and the event. It turns 15° an hour, so each degree is 4 minutes.
Alt
— The Sun's altitude for the event: −0.833° for sunrise and sunset, −6° for civil dawn and dusk, −4° and +6° for the edges of golden hour.
Lat
— The city's latitude in degrees, north positive.
Dec
— The Sun's declination: the latitude where it is straight overhead that day, from about −23.44° in December to +23.44° in June.
Sunrise, sunset
— Sunrise is 4 × Hour angle minutes before solar noon and sunset the same time after it. If the fraction is above 1 or below −1 there is no sunrise or no sunset that day: a polar night or a polar day.

Worked example

London (51.5074° N, 0.1278° W) on 21 June 2024, the calculator's default city. That day the Sun's declination is 23.437° and the equation of time is −1.93 minutes; London is on BST (UTC+1).

  1. Solar noon: 722.44 minutes after midnight UTC is 12:02 UTC, or 13:02 BST (782.44 minutes)

    720−4×(−0.1278)−(−1.93)≈722.44\displaystyle 720 - 4 \times (-0.1278) - (-1.93) \approx 722.44

  2. Hour angle for the sunrise altitude of −0.833° (the fraction is −0.5706)

    arccos⁡−0.01454−0.78269×0.397740.62241×0.91750≈124.79∘\displaystyle \arccos \frac{-0.01454 - 0.78269 \times 0.39774}{0.62241 \times 0.91750} \approx 124.79^{\circ}

  3. Sunrise and sunset in BST, 4 × 124.79 = 499.16 minutes either side of noon

    782.44∓499.16=283.28, 1281.60⇒04:43, 21:21\displaystyle 782.44 \mp 499.16 = 283.28,\ 1281.60 \Rightarrow 04{:}43,\ 21{:}21

Result

Sunrise is at 04:43 BST and sunset at 21:21 BST, so the day lasts 16h 38m. The calculator repeats these steps at each event's own time, which moves the results by a few seconds but not the minute shown.

FAQs

What time are sunrise and sunset in London on the longest and shortest days?

On 21 June 2024 the Sun rose in London at 04:43 BST and set at 21:21 BST, giving 16h 38m of daylight. On 21 December 2024 it rose at 08:04 GMT and set at 15:53 GMT, a day of about 7h 50m. Solar noon moved from 13:02 BST in June to 11:58 GMT in December.

Why is the day longer than 12 hours on the equinox?

Sunrise and sunset are timed when the top edge of the Sun touches the horizon, not its centre, and the atmosphere bends light so the Sun looks about half a degree higher than it is. Together these put the Sun's centre at −0.833° at sunrise and sunset, which adds a few minutes at both ends. In London on 20 March 2024 the Sun rose at 06:02 and set at 18:14, a day of 12h 12m. Even in Quito, on the equator, the day lasts 12h 7m to 12h 8m all year.

What are golden hour and blue hour?

Golden hour is when the Sun is low, between 4° below and 6° above the horizon, so the light is warm and shadows are long. Blue hour is the deeper twilight next to it, with the Sun 4° to 6° below the horizon. In London on 21 June 2024 the evening golden hour ran from 20:27 to 21:49 BST and the blue hour from 21:49 to 22:09. Near the equator the Sun drops steeply, so both are shorter: in Quito the evening golden hour lasts about 44 minutes.

What does the calculator show during the midnight sun or polar night?

If the Sun never drops below −0.833°, the sunrise and sunset rows read No sunrise today and No sunset today, the day length is 24h and a note marks a polar day. In Tromsø (69.6° N) on 15 June 2024 the morning golden hour ends at 02:58 and the evening one starts at 22:32 and lasts through the night, and there is no blue hour because the Sun never sinks below −4°. On 27 November 2024 Tromsø has a polar night: the day length is 0m, but civil twilight still lasts from 08:37 to 14:25.

Why is solar noon not at 12:00?

Solar noon is the moment the Sun is highest. It depends on where the city sits inside its time zone, on daylight saving time and on the equation of time, which moves it by up to about 16 minutes over the year. London, almost on the Greenwich meridian, has solar noon at 13:02 BST on 21 June 2024. Madrid lies far west of the Central European Time meridian, so its solar noon that day is 14:16 and the Sun does not set until 21:48.

How accurate are the times?

The NOAA equations agree with published almanac times to within about a minute between 72° N and 72° S. For New York on 21 December 2024 they give sunrise at 07:16 and sunset at 16:32 EST. What you actually see can differ by a few minutes because of hills or buildings on the horizon, your elevation, and unusual refraction near the poles. Times are rounded down to the minute.

How to use

Choose a city and a date to get that day's sunrise, sunset and twilight times in local time.

  1. Choose the cityStart typing the city's name and pick it from the list. The calculator uses the city's latitude, longitude and time zone, so London gives times in BST in summer and GMT in winter.
  2. Pick the dateToday is filled in by default. Choose any day, month and year up to ten years ahead; the results update as soon as you change it.
  3. Read sunrise, sunset and day lengthThe top card shows sunrise and sunset in the city's local time and the day length in hours and minutes, for example 16h 38m in London on 21 June 2024.
  4. Plan around twilightThe table lists solar noon, civil dawn and dusk, and the morning and evening golden and blue hours. Save a scenario, then pick another date or city to compare day lengths side by side.

Assumptions

  • Times follow the NOAA solar equations for a sea-level observer with a flat horizon and standard refraction, so the Sun's centre is at −0.833° at sunrise and sunset. Hills, buildings and elevation are not taken into account.
  • Each city is a single point at its centre. At London's latitude 1° of longitude is about 69 km and shifts every time by 4 minutes, so places far east or west of the centre differ slightly.
  • Golden hour is the Sun between −4° and +6° and blue hour between −6° and −4°; other apps use slightly different bands. If the Sun never climbs above +6°, golden hour runs until solar noon.
  • Times are shown in the city's time zone with its daylight saving rules and rounded down to the minute; an event that falls on another calendar day is labelled with its weekday.

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