What drives sunrise and sunset times
Two things: your latitude and the Earth's tilt. The planet spins at a constant speed, but its axis leans 23.4°, so the sun's path across your sky swings higher in summer and lower in winter. Near the equator (Singapore in the city list) daylight barely changes all year — about 12 hours, give or take minutes. At 50° latitude (London, Berlin) summer days stretch past 16 hours and winter ones shrink under 8.
Solar noon is the anchor
Sunrise and sunset are symmetric around solar noon — the moment the sun crosses your meridian. That is why the calculator also shows solar noon: if sunrise seems unusually late, check whether solar noon shifted, often the fingerprint of daylight saving time or a time-zone boundary rather than the season.
The maths behind the answer
The tool uses the standard low-precision solar equations published by NOAA: the sun's declination for the date, the hour angle at which the upper limb touches the 90.833° zenith (which includes refraction and the sun's apparent radius), and your longitude converted to local clock time. Accuracy is within about a minute for these latitudes.
Day length is the number that answers the actual question
People search for sunrise and sunset because they want to know how much daylight exists on a date — to plan a drive, a shoot, a shift, a run. Day length follows from one equation, and the equation is a single arc-cosine of three numbers: your latitude, the sun's declination that day, and the altitude you call "sunset".
The standard sunrise/sunset altitude is −0.833°, not 0°. That figure folds in two corrections: atmospheric refraction near the horizon (about 0.5667°, which lifts the sun into view before it is geometrically up) and the sun's apparent radius (about 0.2667°). Using 0° puts every result about 2–3 minutes late at mid-latitudes.
cos H = ( sin(a) − sin(φ) · sin(δ) ) / ( cos(φ) · cos(δ) )
where H is the hour angle at which the sun sits at altitude a, φ is your latitude and δ is the solar declination. Day length is then 2H / 15 hours, because the sun moves 15° of hour angle per hour and the day is symmetric about solar noon.
| City | Latitude | Day length at June solstice | At December solstice | At equinox |
|---|---|---|---|---|
| Singapore | 1.35°N | 12:12 | 12:03 | 12:07 |
| Tokyo | 35.68°N | 14:35 | 9:44 | 12:08 |
| New York | 40.71°N | 15:06 | 9:15 | 12:09 |
| Paris | 48.86°N | 16:11 | 8:15 | 12:10 |
| London | 51.51°N | 16:38 | 7:49 | 12:11 |
| Moscow | 55.76°N | 17:34 | 7:00 | 12:12 |
| Reykjavik | 64.15°N | 21:09 | 4:07 | 12:15 |
Two things fall out of that table. First, the swing grows with latitude: Singapore moves 9 minutes across the year while Reykjavik moves 17 hours. Second, the equinox column is not exactly 12:00 — it runs 12:07 to 12:15, because refraction lifts the sun into view while it is still below the geometric horizon. At the equator on the equinox you get roughly 12 hours 7 minutes of "day".
Working the hour angle by hand
Take New York (40.71°N) on 21 June. Solar declination that day is +23.44°, the maximum. Substitute directly:
- Numerator: sin(−0.833°) − sin(40.71°) · sin(23.44°) = −0.01454 − 0.6523 × 0.3977 = −0.2739
- Denominator: cos(40.71°) · cos(23.44°) = 0.7579 × 0.9174 = 0.6953
- cos H = −0.2739 / 0.6953 = −0.3939 → H = 113.20°
- Day length = 2 × 113.20 / 15 = 15.09 h = 15 h 06 min
- Sunrise = solar noon − 7.55 h. In local solar time that is 04:27; convert to clock time with your longitude correction and the equation of time.
The gain from doing this by hand is that you can see which input moved the answer. Change the date and only δ changes. Change the city and only φ changes. Compare New York at 40.71° against Moscow at 55.76° on the same date and the whole 2.5-hour gap comes from that one term.
The two corrections people forget. The equation of time — the difference between mean and apparent solar time — peaks near ±16 minutes in early November and mid-February. Longitude shifts the clock by 4 minutes per degree away from your time zone's central meridian. Ignore both and a "sunset at 19:41" answer can be off by half an hour.
Golden hour is an elevation band, not a duration
Photographers are told golden hour "lasts about an hour". It does not. Golden hour is the interval in which the sun's elevation sits between −4° and +6°; how long the sun takes to cross that band is a function of latitude and season, not of the clock. In Singapore it is about 40 minutes all year. In Reykjavik in June the sun never leaves the band at all.
| City | Golden hour, June solstice | Equinox | December solstice |
|---|---|---|---|
| Singapore | 44 min | 40 min | 44 min |
| Tokyo | 56 min | 49 min | 57 min |
| New York | 62 min | 53 min | 63 min |
| Paris | 75 min | 61 min | 79 min |
| London | 83 min | 64 min | 87 min |
| Moscow | 99 min | 71 min | 108 min |
| Reykjavik | all night | 92 min | all night |
The reason is geometry rather than weather. Near the equator the sun sinks almost vertically, so it crosses ten degrees of elevation quickly. Approaching the poles it descends at a shallow angle, tracking sideways as much as down, and takes far longer to cover the same vertical distance. That is why a calculator that simply adds sixty minutes to sunset is wrong almost everywhere.
Blue hour is the band immediately below: sun elevation between −6° and −4°. It is short — roughly 8 to 20 minutes in most populated latitudes, stretching past 25 minutes in a high-latitude summer — and it is when the sky still holds deep colour while street lighting reads as bright and balanced. If you shoot cityscapes, this is the window you schedule, not golden hour.
The three depths of twilight, and what each one is for
Below sunset the sky passes through three named zones, each defined by a solar elevation. They matter for more than photography: aviation rules, astronomical observation and civil lighting codes all reference them.
| Zone | Sun elevation | What is still usable |
|---|---|---|
| Golden hour | −4° to +6° | Warm directional light, long shadows, full colour on the ground |
| Blue hour | −6° to −4° | Deep saturated sky, artificial light balances naturally |
| Civil twilight | −6° | Terrain still visible unaided; most road-lighting rules key off this |
| Nautical twilight | −12° | Horizon still discernible at sea; bright navigational stars appear |
| Astronomical twilight | −18° | Sun's scattered light stops affecting the sky; deep-sky imaging begins |
Anything past −18° is true night. Above the Arctic Circle in midsummer the sun may never reach −18°, so astronomical twilight never ends — a genuine problem for observatories at high latitude, and a reminder that these are local definitions, not absolute times.
Why the earliest sunset is not the shortest day
The earliest sunset of the year arrives about two weeks before the December solstice, while the latest sunrise lands about two weeks after it. The solstice is still the shortest day — total daylight is at its minimum — but the clock times of sunrise and sunset are pushed apart by the equation of time. In early December the sun is up to 16 minutes "ahead" of mean solar time; by early January it is behind by a similar margin.
The practical consequence: if you are planning around a specific sunset time rather than around day length, the worst day of the year for your window is not the solstice. Check the actual date.
Planning a shoot around sunrise and sunset
The times decide when; the bearing and the light decide where to stand. These are the items photographers and early risers keep for the twilight windows this page computes.
- Compass — A sunrise time is only half the answer. The Sun breaks the horizon somewhere off due east or west depending on the date, and a compass puts you on that bearing.
- Camera tripod — Before sunrise and after sunset the light is too low for a hand-held exposure. A tripod is what makes those twilight minutes usable.
- Graduated ND filter — At the horizon the sky can be several stops brighter than the land below it. A graduated filter holds detail in both.
- Red headlamp — Setting up before dawn or after dark needs light you can aim, and that will not ruin your night vision in the process.
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Sources and standards
Where these figures come from
Every formula on this page is implemented from the published reference material below. Where a value depends on a regional code, the calculator lets you override it rather than assuming one jurisdiction.
- NOAA Global Monitoring Laboratory — Solar Calculator — the solar position algorithm underlying sunrise, sunset and solar noon.
- NASA Science — Sun — solar geometry and the definition of civil, nautical and astronomical twilight.
- NIST Time and Frequency Division — time standards and the definition of the day.
Figures, formulas and reference tables last verified: 24 September 2026