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Sunrise and sunset calculator

Sunrise and sunset times for any place and date, with solar noon, day length and civil twilight, worked out with NOAA's solar calculator method.

Updated Checked against 5 worked examples

° N
Decimal degrees; south is negative.
° E
Decimal degrees; west is negative.
= 2026-09-27
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Sunrise – sunset
06:55 – 18:48
Sunrise – sunset: 06:55 – 18:48
Sunrise
06:55
Sunset
18:48
Solar noon
12:52
Day length
11 h 52 min 57 s
Civil dawn (sun 6° below horizon)
06:21
Civil dusk
19:21
Daylight
Sun rises and sets
Sun's declination
−1.75°
Equation of time
9.00min
UTC offset used
London, UTC+01:00
Times assume a flat horizon at sea level with standard refraction; hills, buildings and weather can shift them by a few minutes.

On Sun 27 Sep 2026 at 51.5074° N, 0.1278° W the sun rises at 06:55 and sets at 18:48 (London, UTC+01:00), giving 11 h 52 min of daylight.

Sun's elevation on Sun 27 Sep 2026: daylight shaded, civil twilight in grey

-40°-20°0°20°05101520Local time (hours)ElevationHorizonCivil twilight limitSunriseSolar noonSunset
How it's calculated S
  1. Julian day and century

    JD=20723+2440587.5=2,461,310.5,T=JD−245154536525=0.26736482JD = 20723 + 2440587.5 = 2{,}461{,}310.5,\quad T = \frac{JD - 2451545}{36525} = 0.26736482
  2. Sun's position at solar noon

    δ=−1.7496∘,E=8.998 min\delta = -1.7496^\circ,\qquad E = 8.998\ \text{min}

    δ is the declination; E, the equation of time, is how far sundial time runs ahead of clock time.

  3. Hour angle of sunrise

    cos⁡H=cos⁡90.833∘cos⁡51.5074∘cos⁡−1.750∘−tan⁡51.5074∘tan⁡−1.750∘=0.01504⇒H=89.138∘\cos H = \frac{\cos 90.833^\circ}{\cos 51.5074^\circ \cos -1.750^\circ} - \tan 51.5074^\circ \tan -1.750^\circ = 0.01504 \Rightarrow H = 89.138^\circ

    90.833° allows for refraction (34′) and the sun's radius (16′).

  4. Clock times

    tnoon=720−4×−0.1278−E=711.51 min UTC,trise=354.55, tset=1,067.51t_{\text{noon}} = 720 - 4 \times -0.1278 - E = 711.51\ \text{min UTC},\quad t_{\text{rise}} = 354.55,\ t_{\text{set}} = 1{,}067.51

    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).

About this calculator

cos⁡H=cos⁡90.833∘cos⁡φcos⁡δ−tan⁡φtan⁡δ,trise/set=720−4(λ±H)−E min (UTC)\cos H = \frac{\cos 90.833^\circ}{\cos\varphi\cos\delta} - \tan\varphi\tan\delta,\qquad t_{\text{rise/set}} = 720 - 4(\lambda \pm H) - E\ \text{min (UTC)}

Sources

  1. NOAA Global Monitoring Laboratory — Solar Calculator (and its main.js / spreadsheet)
  2. NOAA — Solar Calculation Details
  3. J. Meeus, Astronomical Algorithms, 2nd ed. (1998), ch. 25 and 28
  4. US Naval Observatory — Sun and Moon rise/set data (cross-check)

Checked against references

5 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.

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