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Day Length Calculator

Overview

See how many hours of daylight and darkness a city gets on any date, how much longer or shorter the day is than the day before, and that year's longest and shortest days.

How much daylight do you actually get? Pick a city and a date and the calculator gives the hours and minutes between sunrise and sunset, the hours of night left over, and how many minutes and seconds the day has gained or lost since the day before. It also works through every day of that year for the same city, so you can see how far you are from the longest and the shortest day: in London the days stretch from 7h 50m in late December to 16h 39m in June, while in Quito they never move more than two minutes from 12h 7m. Above the Arctic and Antarctic circles it counts the days of midnight sun and polar night instead.

Formula and example

cos⁡Hour angle=sin⁡(−0.833∘)−sin⁡Latsin⁡Deccos⁡Latcos⁡Dec\displaystyle \cos \text{Hour angle} = \frac{\sin(-0.833^{\circ}) - \sin \text{Lat} \sin \text{Dec}}{\cos \text{Lat} \cos \text{Dec}}
Day=8×Hour angleNight=1440−Day\displaystyle \begin{gathered} \text{Day} = 8 \times \text{Hour angle} \\[12pt] \text{Night} = 1440 - \text{Day} \end{gathered}
Change=Daydate−Dayday before\displaystyle \text{Change} = \text{Day}_{\text{date}} - \text{Day}_{\text{day before}}

Where:

Hour angle
— How many degrees the Earth turns between sunrise and solar noon, at −0.833°, when the top edge of the Sun meets the horizon. It turns 15° an hour, so each degree is 4 minutes.
Lat
— The city's latitude in degrees, north positive.
Dec
— The Sun's declination that day: the latitude where it is overhead, from about −23.44° in December to +23.44° in June.
Day
— Day length in minutes: 4 minutes per degree before noon and 4 after. If the fraction is below −1 the Sun never sets (24h); above 1 it never rises (0m).
Night
— Night length in minutes: the 1440 minutes of a day minus the day length.
Change
— The selected date's day length minus the previous calendar day's at the same city, in seconds; positive while the days are getting longer.

Worked example

London (51.5074° N) on 20 March 2024, the day of the March equinox. At solar noon the Sun's declination is 0.149°; on 19 March it was −0.246°.

  1. Hour angle at sunrise and sunset on 20 March (sin −0.833° = −0.01454)

    arccos⁡−0.01454−0.78269×0.002600.62241×1.00000≈91.526∘\displaystyle \arccos \frac{-0.01454 - 0.78269 \times 0.00260}{0.62241 \times 1.00000} \approx 91.526^{\circ}

  2. Day length: 732.21 minutes is 12h 12m

    8×91.526≈732.21 min\displaystyle 8 \times 91.526 \approx 732.21 \text{ min}

  3. Night length: 707.79 minutes is 11h 48m

    1440−732.21=707.79 min\displaystyle 1440 - 732.21 = 707.79 \text{ min}

  4. The same steps for 19 March give an hour angle of 91.029°

    8×91.029≈728.23 min\displaystyle 8 \times 91.029 \approx 728.23 \text{ min}

  5. Change since 19 March: 3.98 minutes is about 3m 59s

    732.21−728.23=3.98 min\displaystyle 732.21 - 728.23 = 3.98 \text{ min}

Result

On 20 March 2024 London has 12h 12m of daylight and 11h 48m of night, and the day is 3m 59s longer than on 19 March. The calculator refines sunrise and sunset at their own instants, so its seconds can differ slightly from this hand calculation.

FAQs

How many hours of daylight does London get on the longest and shortest days?

In 2024 London's longest day was 20 June, with 16h 39m between sunrise and sunset, one second more than 21 June (16h 38m). The shortest was 21 December with 7h 50m: sunrise at 08:04 and sunset at 15:53 GMT. Midsummer has almost 8h 50m more daylight than midwinter.

Is the day exactly 12 hours long at the equator?

No, slightly longer. Sunrise and sunset are timed when the top edge of the Sun meets the horizon, and the atmosphere bends its light so it looks about half a degree higher than it is, which adds a few minutes each day. In Quito the day lasts between 12h 6m and 12h 8m all year, and in Singapore (1.35° N) between 12h 3m and 12h 12m.

How fast do the days get longer or shorter?

Fastest around the equinoxes and slowest around the solstices. In London the day grows by 3m 59s a day in mid-March and shrinks by up to 3m 55s a day in mid-September, but changes by only a second or two around 21 June and 21 December. The farther from the equator, the faster the change: up to about 2m 44s a day in New York and 5m 28s in Oslo.

When are the longest and shortest days in the southern hemisphere?

The other way round. In Sydney the longest day of 2024 was 21 December with 14h 25m of daylight, and the shortest was 21 June with 9h 54m. The calculator works through the year for whichever city you pick, so the dates follow automatically.

What happens above the Arctic Circle?

The Sun can stay up or down all day. In Tromsø (69.6° N) the calculator finds 68 days of midnight sun in 2024, from 18 May to 24 July, and 49 days of polar night, from 1 to 14 January and from 27 November. On those days the day length reads 24h or 0m and the sunrise or sunset row says there is none. The changes around them are large: on 15 January the Sun is up for just 17 minutes, and the next day it is up 50m 20s longer.

Does night length include twilight?

Yes. Night length here is 24 hours minus the time between sunrise and sunset, so it includes dawn and dusk twilight, when the sky is already or still light. In London on 21 December 2024 the night length is 16h 10m, but civil twilight brightens about 40 minutes of it at each end.

How to use

Choose a city and a date to see its hours of daylight, the change since the day before and the year's longest and shortest days.

  1. Choose the cityType the name and pick it from the list. Day length depends mostly on latitude, so cities on the same parallel get almost the same answer.
  2. Pick the dateToday is filled in by default. Choose any date; the calculator also checks the day before it and every day of that year.
  3. Read the hours of daylightThe top card shows day length, night length (24 hours minus day length) and the change since the day before, for example +3m 59s in London on 20 March 2024.
  4. Compare with the year's extremesThe table lists sunrise and sunset and the longest and shortest day of that year with their dates. Save a scenario and switch city or date to compare day lengths.

Assumptions

  • Day length runs from sunrise to sunset, when the top edge of the Sun touches a flat sea-level horizon with standard refraction (the Sun's centre at −0.833°). Hills, buildings and elevation are not taken into account.
  • Night length is 24 hours minus day length; it does not adjust for the hour gained or lost on the days the clocks change.
  • The change compares the selected date with the previous calendar day at the same city, in whole seconds. The longest and shortest days come from checking every day of the selected year; on a tie the earlier date is shown.
  • Each city is a single point at its centre, and the NOAA solar equations used are accurate to about a minute between 72° N and 72° S.

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